CN106448429B - Multilayer frame teaching experiment model and experiment method - Google Patents
Multilayer frame teaching experiment model and experiment method Download PDFInfo
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Abstract
The invention provides a multi-layer frame teaching experiment model and an experiment method. The multilayer frame teaching experiment model comprises a multilayer frame structure, a static loading device, a vibration exciter loading device, a vibration table loading device and measuring equipment; a worm and gear elevator in the static loading device realizes loading and unloading of the frame structure by rotating a hand wheel on the worm and gear elevator, and the loaded load is displayed on a computer through a force sensor. The invention can be used for displacement method experiments, free vibration experiments of a two-degree-of-freedom system, forced vibration experiments of the two-degree-of-freedom system and experiments for solving three-layer rigid frame fundamental frequency by an approximation method. The invention has the advantages that the experimental model is flexible and variable, students can independently perform tests under different parameters, and the error of the obtained experimental result is very small compared with the theoretical value obtained by structural mechanics calculation, so that the invention is suitable for colleges and universities to carry out related teaching experiments and further design and expansion.
Description
Technical Field
The invention belongs to the field of civil engineering professional structural mechanics experiment teaching, and relates to a multilayer frame teaching experiment model which can be used for displacement method experiments, free vibration experiments of a two-degree-of-freedom system, forced vibration experiments of the two-degree-of-freedom system, and experiments of solving three-layer frame fundamental frequency by an approximation method.
Background
The structural mechanics is a necessary subject for civil engineering major in higher schools, wherein the multilayer frame is an important model in structural mechanics teaching, and two types of problems (hyperstatic structural problem solving by a displacement method, structural dynamic characteristic solving by a rigidity method and dynamic response problem solving by the model) related to the model are classical teaching example problems of the structural mechanics.
The displacement method is a basic method for solving the internal force and displacement of the statically indeterminate structure under the static load by structural mechanics. The statically indeterminate structure is different from the statically indeterminate structure in calculation, the internal force of the statically indeterminate structure cannot be obtained from the static equilibrium condition alone, and the deformation coordination condition must be considered at the same time. For the convenience of the calculation problem, a part of all unknowns of the hyperstatic structure is often selected as the basic unknowns. The displacement method is a method for solving the statically indeterminate structure according to static equilibrium conditions by taking certain displacements as basic unknowns.
The stiffness method is a basic method for solving the dynamic characteristics of a structure through structural mechanics. The rigidity method establishes a differential equation from a force system balance angle, wherein the action of inertia force is considered, and the structural dynamic characteristic and the dynamic response are obtained by solving the equation.
At present, the teaching method of the structural mechanics of colleges and universities is mainly theoretical teaching, and because of lack of experimental verification of relevant theories, partial students inevitably have insufficient understanding of the relevant theories, and even doubts are generated on the relevant theories. The introduction of experimental contents into daily teaching of structural mechanics in colleges and universities is a necessary trend of structural mechanics teaching development in future.
In the multi-layer frame teaching experiment model, the static force loading device of the loading device part is similar to the content in the Chinese patent (2015107123346 a teaching experiment device for visualizing the force method; 2015107079593 a teaching experiment device for visualizing the displacement method) already disclosed by the subject group, the disclosed content only plays a loading role in the whole device and is not an innovative structure of the invention, and other structures of the vibration exciter loading device and the vibration table loading device are completely different from the content disclosed by the previous patent.
Disclosure of Invention
Aiming at the current situation that related experimental contents are lacked in the current structural mechanics teaching, the experimental method can realize the experimental of the structural mechanics teaching contents, realize the verification of the displacement method theory and the rigidity method theory, and find out the reason of experimental errors through the difference between the experiment and the theory, so that students can more deeply understand the theoretical knowledge of structural mechanics in the in-person practice and analysis.
The technical scheme of the invention is as follows:
a multi-layer frame teaching experiment model comprises a multi-layer frame structure, a static force loading device, a vibration exciter loading device, a vibration table loading device and measuring equipment.
The multi-layer frame structure comprises a plurality of cross beams 3, a bottom layer beam 4, two upright posts 5, a cross beam clamp 6 and a bottom layer beam clamp 7; the number of the cross beams is adjusted to be 1-3 according to the experimental requirement, the height and the mass of each cross beam can be adjusted, and the cross beams are connected with the mass block 8 to adjust the mass of the cross beams; the two ends of each beam are clamped and connected with the upright post 5 through a beam clamp 6, so that beam-column rigid connection is realized; the two ends of the bottom beam 4 are clamped and connected with the bottom ends of the upright posts 5 through bottom beam clamps 7, so that beam-column rigid connection is realized; the middle part of the bottom beam 4 is connected with the trolley platform. Because the rigidity of the beam is far greater than that of the upright column, the rigidity of the beam relative to that of the upright column can be seen to be infinite, and when the multi-layer frame structure is only subjected to transverse load, the beam column node has no angular displacement and only has linear displacement.
The static loading device comprises a worm gear lifter 9, a force sensor 10, a spherical hinge 11, a loading rod 12, a thread conversion rod 13 and an upright loading clamp 14; one end of the worm gear lifter 9 is fixedly connected with a trolley platform 15, the trolley platform 15 is arranged on a guide rail of the reaction frame 1, and the position of the trolley platform 15 can be adjusted randomly along the guide rail of the reaction frame 1; the other end of the worm gear lifter 9 is connected with one end of a force sensor 10; the other end of the force sensor 10, the spherical hinge 11, the loading rod 12 and one end of the thread switching rod 13 are sequentially connected through threads; the other end of the thread switching rod 13 is connected with the beam clamp 6 through threads, and the side surface of the beam clamp 6 is provided with a matched threaded hole; or the other end of the screw thread switching rod 13 is connected with the upright post loading clamp 14 through screw threads, and the upright post loading clamp 14 is arranged at any position of the upright post 5 in a clamping manner. The spherical hinge 11 avoids the influence of a loading device on bending moment of the frame structure through free rotation of the spherical hinge, and when an experimenter loads or unloads the frame structure, the experimenter can load and unload the frame structure by rotating a hand wheel on the worm gear and worm elevator, and the load is displayed on a computer through the force sensor 10.
The vibration exciter loading device comprises a vibration exciter 16, an adapter plate 17, a connecting rod 18, a power amplifier and a vibration controller; one end of the vibration exciter 16 is fixedly connected with the adapter plate 17 through a bolt, and the adapter plate 17 is connected with the trolley platform 15; the other end of the vibration exciter 16 is connected with a connecting rod 18 through threads, and the connecting rod 18 is connected with the beam clamp 6 through threads; the vibration exciter 16 is connected with the power amplifier and the vibration controller through data lines, the vibration exciter 16 is controlled by the data lines and the vibration controller to excite dynamic load, the vibration exciting frequency is input through a computer, and the amplitude of the vibration exciting force is adjusted through a gain knob on the vibration controller.
The vibration table loading device comprises a high-power vibration exciter 19, a vibration exciter fixing device 20, a vibration table bottom plate 21 and a connecting plate 22; the vibration exciter fixing device 20 and the bottom end of the vibration table bottom plate 21 are connected with the laboratory ground through bolts; the high-power vibration exciter 19 is fixedly connected with one side of the vibration exciter fixing device 20 through a bolt; the connecting plate 22 is connected with the upper part of the vibrating table bottom plate 21 through balls, the connecting plate 22 and the vibrating table bottom plate 21 can slide relatively, and bolt holes are formed in the connecting plate 22; the bottom beam 4 is connected with the connecting plate 22 through bolts; the high-power vibration exciter 19 is connected with the power amplifier and the vibration controller through data lines, the high-power vibration exciter 19 and the vibration controller are used for controlling the high-power vibration exciter 19 to excite dynamic load, the vibration exciting frequency is input through a computer, and the amplitude of the vibration exciting force is adjusted through a gain knob on the vibration controller.
The measuring device comprises a force sensor 10, an acceleration sensor 24 and a dial indicator. The force sensor measures a static load value applied by the worm gear lifter to the multilayer frame structure; the dial indicator is characterized in that a meter body is fixed on a meter frame through a magnetic meter seat, and a measuring rod can be directly contacted with any position of the multilayer frame structure and is used for measuring displacement of each point of the multilayer frame structure under the action of static load; the acceleration sensor can be fixed on a beam clamp 6 of the multi-layer frame structure and is used for measuring the absolute acceleration value of a beam of the multi-layer frame structure under the action of dynamic load. The dial indicator can directly read on a liquid crystal screen of the dial indicator, other measuring equipment is connected with a computer through a data line, and various data are visualized through a data acquisition and analysis system in the computer.
The multilayer frame teaching experiment model can be used for displacement method experiments, free vibration experiments of a two-degree-of-freedom system, forced vibration experiments of the two-degree-of-freedom system and three-layer frame fundamental frequency experiments of an approximation method, and comprises the following specific experiment steps:
when the multilayer frame teaching experiment model is used for displacement method experiments, the specific steps are as follows:
firstly, assembling a two-layer frame structure, and determining the position of each experimental point, wherein A, B are marked at two ends of a bottom layer beam 4, C, D are marked on a first layer beam 3, E and F are marked on a second layer beam 3, A, C and E are positioned on a left upright post, and B, D, F is positioned on a right upright post; the middle of F and D is labeled G. And testing the distance between the cross beams 3, namely the lengths of AC, CE, BD and DF, preloading the multi-layer frame teaching experiment model and balancing the force sensors.
Secondly, applying a load F through a static loading device at a point GpMeasuring the horizontal displacement delta of the first layer beam 3CD actual measurementAnd horizontal displacement delta of the second floor beam 3EF actual measurement。
And thirdly, repeating the second step of experiment at least three times.
Fourthly, the first layer of beam 3C point and the second layer of beam 3E point are respectively and simultaneously loaded by two static loading devicesWhile applying horizontal restraint, assembling the experimental device as shown in FIG. 7, and applying a load F at a point GpMeasuring the counter force V of two static loading devices at the C point and the E pointCPAnd VEP。
And fifthly, repeating the experiment of the fourth step at least three times.
Sixthly, removing the static loading device and the balance force sensor of the G point; applying a graded horizontal displacement Δ at point CCMeasuring the counter force V of two static loading devices at the C point and the E pointCCAnd VEC(ii) a And unloading after loading to the highest-level displacement.
And seventhly, repeating the experiment of the sixth step at least three times, and solving the rigidity coefficient k through a formulaCC、kEC。
Step eight, balancing the force sensor, and applying a graded horizontal displacement delta at the point EEMeasuring the counter force V of two static loading devices at the C point and the E pointCEAnd VEE(ii) a And unloading after loading to the highest-level displacement.
And ninthly, repeating the eighth step for at least three times, and calculating the rigidity coefficient k through a formulaCEAnd kEE。
Tenth step, the result obtained in the above steps is calculated according to the basic equation set of the displacement method to obtain the derivation value deltaCD derivation、ΔEF derivation。
Eleventh step, comparative analysis ΔCD measurement、ΔEF actual measurementAnd ΔCD derivation、ΔEF derivationAnd analyzing the error to draw a conclusion.
When the multi-layer frame teaching experimental model is used for a free vibration experiment of a two-degree-of-freedom system, the steps are as follows:
firstly, assembling a two-layer frame structure, and determining the position of each experimental point, wherein the two ends of a bottom layer beam 4 are marked with A, B, the two ends of a first layer beam 3 are marked with C, D, the two ends of a second layer beam 3 are marked with E and F, A, C and E are positioned on a left side upright post, and B, D, F is positioned on a right side upright post; the middle of F and D is labeled G. Testing the distance between the beams 3, i.e. the length of AC, CE, BD, DF;
secondly, determining the dynamic characteristics of the structure by adopting a rigidity coefficient measuring method
2.1) groupInstalling an experimental device and a balance force sensor; applying a graded horizontal displacement Δ at point CCMeasuring the counter force V of two static loading devices at the C point and the E pointCCAnd VEC(ii) a And unloading after loading to the highest-level displacement.
2.2) repeating the sixth step for at least three times, and solving the rigidity coefficient k through a formulaCC、kEC。
2.3) balance force sensor, applying a graded horizontal displacement Δ at point EEMeasuring the counter force V of two static loading devices at the C point and the E pointCEAnd VEE(ii) a And unloading after loading to the highest-level displacement.
2.4) repeating the eighth step for at least three times, and calculating the rigidity coefficient k through a formulaCEAnd kEE。
And 2.5) calculating the dynamic characteristics of the frame structure by using the rigidity coefficient and the mass of the cross beam, wherein the dynamic characteristics comprise the natural vibration frequency and the vibration mode of the structure.
Thirdly, determining the dynamic characteristics of the structure by adopting a sudden unloading method
3.1) Assembly experiment device, connecting the worm gear and worm lifter 9 with the frame structure by using the thin wire 23, and applying the initial displacement y at the point F0，
3.2) cutting off the thin line after the system is static, and obtaining D, F two-point acceleration change curve through the reaction spectrum measured by the acceleration sensor 24 to obtain the structure natural frequency and the vibration mode corresponding to each order of natural frequency.
And fourthly, comparing and analyzing the experimental results of the rigidity coefficient measuring method and the sudden unloading method, analyzing errors and obtaining a conclusion.
When the multi-layer frame teaching experimental model is used for a forced vibration experiment of a two-degree-of-freedom system, the steps are as follows:
firstly, assembling a two-layer frame structure, and determining the position of each experimental point, wherein the two ends of a bottom layer beam 4 are marked with A, B, the two ends of a first layer beam 3 are marked with C, D, the two ends of a second layer beam 3 are marked with E and F, A, C and E are positioned on a left side upright post, and B, D, F is positioned on a right side upright post; the middle of F and D is labeled G. Testing the spacing between the beams 3, i.e. the length of AC, CE, BD, DF;
secondly, determining the dynamic characteristics of the structure by adopting a vibration table excitation method:
2.1) assembling an experimental device, measuring the lengths of AC, CE, BD and DF and the sectional sizes of the cross beam and the upright post, mounting the multilayer frame structure on a vibrating table loading device, inputting a white noise signal, and obtaining the natural vibration frequency of the structure through a reaction spectrum measured by an acceleration sensor 24.
2.2) inputting a sine wave signal corresponding to the first-order frequency to the vibration table, and obtaining D, F two-point acceleration amplitude values through a reaction spectrum obtained by the acceleration sensor 24.
2.3) inputting a sine wave signal corresponding to the second-order frequency to the vibration table, and obtaining D, F two-point acceleration amplitude values through a reaction spectrum obtained by the acceleration sensor 24.
And 2.4) processing the original experimental data of the vibration table excitation method to obtain the structure natural vibration frequency and the vibration mode corresponding to each order of natural vibration frequency.
Thirdly, determining the dynamic characteristics of the structure by adopting a vibration exciter excitation method:
3.1) assembling an experimental device, and measuring the lengths of AC, CE, BD and DF and the sectional sizes of the cross beam and the upright column;
3.2) using the vibration exciter to apply dynamic load at the point D by using the vibration exciter, obtaining D, F acceleration change curves at two points through the reaction spectrum measured by the acceleration sensor 24 to obtain the natural vibration frequency and the vibration mode
And fourthly, comparing and analyzing the experimental results of the vibration table excitation method and the vibration exciter excitation method, analyzing errors and obtaining a conclusion.
When the multi-layer frame teaching experiment model is used for an experiment for solving the fundamental frequency of the three-layer frame by an approximation method, the steps are as follows:
firstly, assembling an experimental device, installing a multilayer frame structure on a vibration table, inputting a white noise signal, and obtaining the natural vibration frequency of the structure through a reaction spectrum measured by an acceleration sensor 24.
Second, the experimental setup was assembled and a load equivalent to the weight of each beam was applied at point C, E, G and the displacement of D, F, H points was measured.
And thirdly, processing the original experimental data in the second step, obtaining the structure natural vibration frequency by using an approximation formula, and comparing and analyzing the structure natural vibration frequency with the experimental result in the first step.
The invention has the beneficial effects that: by adopting different loading devices and measuring equipment, the multi-layer frame model can carry out a plurality of experiments, including a displacement method experiment of a two-layer frame, a free vibration experiment of a multi-degree-of-freedom system, a forced vibration experiment of the multi-degree-of-freedom system and an experiment for solving the fundamental frequency of a three-layer steel frame by an approximation method. Meanwhile, the height of the cross beam of the multi-layer frame structure is adjustable, the mass of the cross beam can be adjusted through the mass block, the experimental model is flexible and variable, students can independently perform experiments under different parameters, and the obtained results can be compared with the experimental results under different parameters and also can be compared with theoretical calculation results. Through experimental verification, compared with a theoretical value obtained through structural mechanics calculation, an experimental result obtained through the experimental model has a small error, and the experimental model is suitable for colleges and universities to carry out related teaching experiments and further design and expansion.
Drawings
FIG. 1 is a schematic view of a two-layer frame construction;
FIG. 2 is a schematic view of a three-layer frame structure;
FIG. 3 is a schematic view of a static loading apparatus;
FIG. 4 is a schematic view of a vibration exciter loading apparatus;
FIG. 5 is a schematic view of a vibration table loading device;
FIG. 6 is a schematic diagram of an experimental original structure of a displacement method;
FIG. 7 is a schematic diagram of a basic structure experiment of a displacement method experiment;
FIG. 8 is a schematic diagram of a multi-layer frame stiffness coefficient measurement;
FIG. 9 is a schematic view of a burst unloading experiment;
FIG. 10 is a schematic diagram of a vibration table excitation experiment;
FIG. 11 is a schematic diagram of a vibration exciter excitation experiment;
FIG. 12 is an experimental schematic diagram of a three-deck steel frame vibration table;
FIG. 13 is an experimental schematic diagram of the fundamental frequency of three-layer steel frame by approximation.
In the figure: 1, a reaction frame; 2 reaction frame base; 3, a cross beam; 4, a bottom beam; 5, upright posts; 6, a beam clamp; 7, a bottom beam clamp; 8 mass blocks; 9 worm gear lifter; 10 force sensors; 11, spherical hinge; 12 a loading rod; 13 a threaded transfer lever; 14, loading a clamp on the upright post; 15 a dolly platform; 16, a vibration exciter; 17 an adapter plate; 18 connecting rods; 19 high-power vibration exciter; 20, a vibration exciter fixing device; 21 vibrating table bottom plate; 22 a connecting plate; 23 thin wires; 24 acceleration sensor.
Detailed Description
A multi-layer frame teaching experiment model comprises a multi-layer frame structure, a static force loading device, a vibration exciter loading device, a vibration table loading device and measuring equipment.
The two ends of each beam in the multi-layer frame structure are clamped and connected with the upright post 5 through a beam clamp 6, so that beam-column rigid connection is realized; the two ends of the bottom beam 4 are clamped and connected with the bottom ends of the upright posts 5 through bottom beam clamps 7, so that beam-column rigid connection is realized; the middle part of the bottom beam 4 is connected with the trolley platform through 2 bolts. Because the rigidity of the beam is far greater than that of the upright column, the rigidity of the beam relative to that of the upright column can be seen to be infinite, and when the multi-layer frame structure is only subjected to transverse load, the beam column node has no angular displacement and only has linear displacement.
The static loading device is shown in fig. 3 and comprises a worm gear lifter 9, a force sensor 10, a spherical hinge 11, a loading rod 12, a thread switching rod 13 and a stand column loading clamp 14; one end of the worm gear lifter 9 is fixedly connected with the trolley platform 15 through a bolt, the trolley platform 15 is arranged on the guide rail of the reaction frame 1 through four sliding blocks at the bottom, and the position of the trolley platform 15 can be adjusted freely along the guide rail of the reaction frame 1; the other end of the worm gear lifter 9 is connected with one end of a force sensor 10 through threads; the other end of the force sensor 10, the spherical hinge 11, the loading rod 12 and one end of the thread switching rod 13 are sequentially connected through threads; the other end of the thread switching rod 13 is connected with the beam clamp 6 through threads, and the side surface of the beam clamp 6 is provided with a matched threaded hole; or the other end of the screw thread switching rod 13 is connected with the upright post loading clamp 14 through screw threads, and the upright post loading clamp 14 is installed at any position of the upright post 5 in a clamping mode. The spherical hinge 11 avoids the influence of a loading device on bending moment of the frame structure through free rotation of the spherical hinge, and when an experimenter loads or unloads the frame structure, the experimenter can load and unload the frame structure by rotating a hand wheel on the worm gear and worm elevator, and the load is displayed on a computer through the force sensor 10.
The vibration exciter loading device is shown in fig. 4 and comprises a vibration exciter 16, an adapter plate 17, a connecting rod 18, a power amplifier and a vibration controller; one end of the vibration exciter 16 is fixedly connected with the adapter plate 17 through a bolt, and the adapter plate 17 is connected with the trolley platform 15 through a bolt; the other end of the vibration exciter 16 is connected with a connecting rod 18 through threads, and the connecting rod 18 is connected with the beam clamp 6 through threads; the vibration exciter 16 is connected with the power amplifier and the vibration controller through data lines, the vibration exciter 16 is controlled by the data lines and the vibration controller to excite dynamic load, the vibration exciting frequency is input through a computer, and the amplitude of the vibration exciting force is adjusted through a gain knob on the vibration controller.
The vibration table loading device is shown in fig. 5 and comprises a high-power vibration exciter 19, a vibration exciter fixing device 20, a vibration table bottom plate 21 and a connecting plate 22; the vibration exciter fixing device 20 and the bottom end of the vibration table bottom plate 21 are connected with the laboratory ground through bolts; the high-power vibration exciter 19 is fixedly connected with one side of the vibration exciter fixing device 20 through a bolt; the connecting plate 22 is connected with the upper part of the vibrating table bottom plate 21 through balls, the connecting plate 22 and the vibrating table bottom plate 21 can slide relatively, and bolt holes are formed in the connecting plate 22; the bottom beam 4 is connected with the connecting plate 22 through bolts; the high-power vibration exciter 19 is connected with the power amplifier and the vibration controller through data lines, the high-power vibration exciter 19 and the vibration controller are used for controlling the high-power vibration exciter 19 to excite dynamic load, the vibration exciting frequency is input through a computer, and the amplitude of the vibration exciting force is adjusted through a gain knob on the vibration controller.
The measuring device comprises a force sensor 10, an acceleration sensor 24 and a dial indicator. The force sensor measures a static load value applied by the worm gear lifter to the multilayer frame structure; the dial indicator is characterized in that a meter body is fixed on a meter frame through a magnetic meter seat, and a measuring rod can be directly contacted with any position of the multilayer frame structure and is used for measuring displacement of each point of the multilayer frame structure under the action of static load; the acceleration sensor can be fixed on a beam clamp 6 of the multi-layer frame structure and is used for measuring the absolute acceleration value of a beam of the multi-layer frame structure under the action of dynamic load. The dial indicator can directly read on a liquid crystal screen of the dial indicator, other measuring equipment is connected with a computer through a data line, and various data are visualized through a data acquisition and analysis system in the computer.
The multilayer frame teaching experiment model can be used for displacement method experiments, free vibration experiments of a two-degree-of-freedom system, forced vibration experiments of the two-degree-of-freedom system and three-layer frame fundamental frequency experiments of an approximation method, and comprises the following specific experiment steps:
when the multilayer frame teaching experiment model is used for displacement method experiments, the specific steps are as follows:
firstly, assembling a two-layer frame structure as shown in fig. 6, and determining the position of each experimental point, as shown in fig. 1, marking A, B at two ends of a bottom layer beam 4, marking C, D a first layer beam 3, marking E, F, A, C and E on a left upright post, and marking B, D, F on a right upright post; the middle of F and D is labeled G. And testing the distance between the cross beams 3, namely the lengths of AC, CE, BD and DF, preloading the multi-layer frame teaching experiment model and balancing the force sensors.
Secondly, applying a load F through a static loading device at a point GpMeasuring the horizontal displacement delta of the first layer beam 3CD measurementAnd horizontal displacement delta of the second floor beam 3EF actual measurement。
And thirdly, repeating the second step of experiment at least three times.
Fourthly, respectively applying horizontal restraint to the first layer of cross beam 3C point and the second layer of cross beam 3E point through two static loading devices, assembling an experimental device as shown in figure 7, and applying a load F to the G pointpMeasuring the counter force V of two static loading devices at the C point and the E pointCPAnd VEP。
And fifthly, repeating the experiment in the step (4) at least three times.
Sixthly, assembling the experimental device as shown in fig. 8, removing the static loading device at the G point and the balance force sensor; applying a graded horizontal displacement Δ at point CCMeasuring the counter force V of two static loading devices at the C point and the E pointCCAnd VEC(ii) a LoadingAnd unloading after the displacement to the highest level.
Seventhly, repeating the experiment of the sixth step at least three times through a formula
Determining the stiffness coefficient kCC、kEC。
Step eight, balancing the force sensor, and applying a graded horizontal displacement delta at the point EEMeasuring the counter force V of two static loading devices at the C point and the E pointCEAnd VEE(ii) a And unloading after loading to the highest-level displacement.
Ninth, repeating the experiment of step (8) at least three times according to the formula
Determining the stiffness coefficient kCEAnd kEE。
Tenth step, the result obtained in the above steps is calculated according to the basic equation set of the displacement method to obtain the derivation value deltaCD derivation、ΔEF derivation。
Eleventh step, comparative analysis ΔCD measurement、ΔEF actual measurementAnd ΔCD derivation、ΔEF derivationAnd analyzing the error to draw a conclusion.
When the multi-layer frame teaching experiment model is used for the free vibration experiment of a two-degree-of-freedom system, the steps are as follows:
firstly, assembling a two-layer frame structure as shown in fig. 6, and determining the position of each experimental point, as shown in fig. 1, marking A, B at two ends of a bottom layer beam 4, marking C, D a first layer beam 3, marking E, F, A, C and E on a left upright post, and marking B, D, F on a right upright post; the middle of F and D is labeled G. Testing the spacing between the beams 3, i.e. the length of AC, CE, BD, DF;
secondly, determining the dynamic characteristics of the structure by adopting a rigidity coefficient measuring method
2.1) assembling the experimental device and the balance force sensor as shown in FIG. 8; applying a graded horizontal displacement Δ at point CCMeasuring the counter force V of two static loading devices at the C point and the E pointCCAnd VEC(ii) a Loaded to the highest levelAfter the displacement, unloading.
2.2) repeating the sixth step at least three times by the formula
Determining the stiffness coefficient kCC、kEC。
2.3) balance force sensor, applying a graded horizontal displacement Δ at point EEMeasuring the counter force V of two static loading devices at the C point and the E pointCEAnd VEE(ii) a And unloading after loading to the highest-level displacement.
2.4) repeating the experiment of step (8) at least three times by the formula
Determining the stiffness coefficient kCEAnd kEE。
And 2.5) calculating the dynamic characteristics of the frame structure by using the rigidity coefficient and the mass of the cross beam, including the natural vibration frequency and the vibration mode of the structure.
Thirdly, determining the dynamic characteristics of the structure by adopting a sudden unloading method
3.1) assemble the experimental setup as in FIG. 9 (see FIG. 1 for the positions of the points), connect the worm gear elevator (9) to the frame structure using the thin wire 23, and apply an initial displacement y at point F0，
3.2) cutting off the thin line after the system is static, and obtaining D, F two-point acceleration change curve through the reaction spectrum measured by the acceleration sensor 24 to obtain the structure natural frequency and the vibration mode corresponding to each order of natural frequency.
And fourthly, comparing and analyzing the experimental results of the rigidity coefficient measuring method and the sudden unloading method, analyzing errors and obtaining a conclusion.
When the multi-layer frame teaching experiment model is used for a forced vibration experiment of a two-degree-of-freedom system, the steps are as follows:
firstly, assembling a two-layer frame structure as shown in fig. 6, and determining the position of each experimental point, as shown in fig. 1, marking A, B at two ends of a bottom layer beam 4, marking C, D a first layer beam 3, marking E, F, A, C and E on a left upright post, and marking B, D, F on a right upright post; the middle of F and D is labeled G. Testing the spacing between the beams 3, i.e. the length of AC, CE, BD, DF;
secondly, determining the dynamic characteristics of the structure by adopting a vibration table excitation method:
2.1) assemble the experimental device as shown in FIG. 10 (see FIG. 1 for each point position), measure the AC, CE, BD, DF length and cross-sectional dimensions of the beam and the column (see FIG. 1 for each point position), mount the multi-layer frame structure on the vibration table loading device, input the white noise signal, and obtain the structure natural frequency through the response spectrum measured by the acceleration sensor 24.
2.2) inputting a sine wave signal corresponding to the first-order frequency to the vibration table, and obtaining D, F two-point acceleration amplitude values through a reaction spectrum obtained by the acceleration sensor 24.
2.3) inputting a sine wave signal corresponding to the second-order frequency to the vibration table, and obtaining D, F two-point acceleration amplitude values through a reaction spectrum obtained by the acceleration sensor (24).
And 2.4) processing the original experimental data of the vibration table excitation method to obtain the structure natural vibration frequency and the vibration mode corresponding to each order of natural vibration frequency.
Thirdly, determining the dynamic characteristics of the structure by adopting a vibration exciter excitation method:
3.1) assembling the experimental apparatus as shown in FIG. 11 (see FIG. 1 for each point), measuring AC, CE, BD, DF, the length and the cross-sectional dimensions of the cross-beam and the column (see FIG. 1 for each point)
3.2) using the vibration exciter to apply dynamic load at the point D by using the vibration exciter, obtaining D, F acceleration change curves at two points through the reaction spectrum measured by the acceleration sensor 24 to obtain the natural vibration frequency and the vibration mode
And fourthly, comparing and analyzing the experimental results of the vibration table excitation method and the vibration exciter excitation method, analyzing errors and obtaining a conclusion.
When the multi-layer frame teaching experiment model is used for an experiment for solving the fundamental frequency of the three-layer frame by an approximation method, the steps are as follows:
first, the experimental apparatus is assembled as shown in fig. 12 (see fig. 2 for each point position), the multi-layer frame structure is mounted on a vibration table, a white noise signal is input, and the structure natural frequency is obtained from the response spectrum measured by the acceleration sensor 24.
In the second step, the experimental set-up (see FIG. 2 for each point) was assembled as shown in FIG. 13, and a load equivalent to the weight of each beam was applied at point C, E, G, and displacement of D, F, H points was measured.
And thirdly, processing the original experimental data in the second step, obtaining the structure natural vibration frequency by using an approximation formula, and comparing and analyzing the structure natural vibration frequency with the experimental result in the first step.
Claims (5)
1. A displacement method experiment adopting a multilayer frame teaching experiment model is characterized in that the multilayer frame teaching experiment model comprises a multilayer frame structure, a static force loading device, a vibration exciter loading device, a vibration table loading device and measuring equipment;
the multi-layer frame structure comprises a plurality of cross beams (3), a bottom beam (4), two upright posts (5), a cross beam clamp (6) and a bottom beam clamp (7); the two ends of each beam are clamped and connected with the upright post (5) through a beam clamp (6) to realize rigid connection of the beams and the posts; two ends of the bottom beam (4) are connected with the bottom ends of the upright posts (5) in a clamping manner through a bottom beam clamp (7) to realize rigid connection of the beams and the posts; the middle part of the bottom layer beam (4) is connected with the trolley platform;
the vibration exciter loading device comprises a vibration exciter (16), an adapter plate (17), a connecting rod (18), a power amplifier and a vibration controller; one end of the vibration exciter (16) is fixedly connected with the adapter plate (17), and the adapter plate (17) is connected with the trolley platform (15); the other end of the vibration exciter (16) is connected with a connecting rod (18), and the connecting rod (18) is connected with the beam clamp (6); the vibration exciter (16) is connected with the power amplifier and the vibration controller through data lines;
the vibration table loading device comprises a high-power vibration exciter (19), a vibration exciter fixing device (20), a vibration table bottom plate (21) and a connecting plate (22); the bottom ends of the vibration exciter fixing device (20) and the vibrating table bottom plate (21) are both arranged on the ground of a laboratory; the high-power vibration exciter (19) is fixedly connected with one side of the vibration exciter fixing device (20); the connecting plate (22) is connected with the upper part of the vibrating table bottom plate (21) through balls, and the connecting plate (22) and the vibrating table bottom plate (21) can slide relatively; the bottom beam (4) is connected with the connecting plate (22); the high-power vibration exciter (19) is connected with the power amplifier and the vibration control instrument through a data line; a worm gear lifter (9) in the static loading device displays the loaded load on a computer through a force sensor (10);
the measuring equipment comprises a force sensor (10), an acceleration sensor (24) and a dial indicator; the dial indicator is fixed on the indicator frame (25) through a magnetic indicator seat; the acceleration sensor is fixed on a multi-layer frame structure beam clamp (6); the measuring equipment is connected with the computer through a data line, and various data are visualized through a data acquisition and analysis system in the computer;
the displacement method experiment comprises the following steps:
firstly, assembling a two-layer frame structure, determining the position of each experimental point, marking A, B at two ends of a bottom layer beam (4), marking C, D on a first layer beam (3), marking E and F on a second layer beam (3), wherein A, C and E are positioned on a left upright post, and B, D, F is positioned on a right upright post; labeling G in the middle of F and D; testing the distance between the cross beams (3), namely the lengths of AC, CE, BD and DF, preloading the multi-layer frame teaching experiment model and balancing the force sensors;
secondly, applying a load F through a static loading device at a point GpMeasuring the horizontal displacement delta of the first layer beam (3)CD actual measurementAnd the horizontal displacement Delta of the second-layer beam (3)EF actual measurement；
Thirdly, repeating the experiment of the second step at least three times;
fourthly, horizontal restraint is simultaneously applied to the C point of the first layer of cross beam (3) and the E point of the second layer of cross beam (3) through two static loading devices respectively, and a load F is applied to the G pointpMeasuring the counter force V of two static loading devices at the C point and the E pointCPAnd VEP；
Fifthly, repeating the experiment of the fourth step at least three times;
sixthly, removing the static loading device and the balance force sensor of the G point; applying a graded horizontal displacement Δ at point CCAnd measuring the counter force V of two static force loading devices at the point C and the point ECCAnd VEC(ii) a Unloading after loading to the highest-level displacement;
in the seventh step, the first step is,repeating the eighth step for at least three times to obtain the rigidity coefficient kCC、kEC；
Step eight, balancing the force sensor, and applying a graded horizontal displacement delta at the point EEMeasuring the counter force V of two static loading devices at the C point and the E pointCEAnd VEE(ii) a Unloading after loading to the highest-level displacement;
the ninth step, repeat the eighth step experiment at least three times, find the coefficient of rigidity kCEAnd kEE；
Tenth step, the result obtained in the above steps is calculated according to the basic equation set of the displacement method to obtain the derivation value deltaCD derivation、ΔEF derivation；
Eleventh step, comparative analysis of ΔCD measurement、ΔEF actual measurementAnd ΔCD derivation、ΔEF derivationAnd analyzing the error to draw a conclusion.
2. The displacement method experiment of claim 1, wherein the number of the cross beams is adjusted according to experiment requirements and is 1 to 3, and the height and the mass of each cross beam can be adjusted; the cross beam is connected with the mass block (8), and the mass of the cross beam is adjusted through the mass block (8).
3. A free vibration experiment of a double-freedom-degree system adopting a multilayer frame teaching experiment model is characterized in that the multilayer frame teaching experiment model comprises a multilayer frame structure, a static loading device, a vibration exciter loading device, a vibration table loading device and measuring equipment;
the multi-layer frame structure comprises a plurality of cross beams (3), a bottom beam (4), two upright posts (5), a cross beam clamp (6) and a bottom beam clamp (7); the two ends of each beam are clamped and connected with the upright post (5) through a beam clamp (6) to realize rigid connection of the beams and the posts; two ends of the bottom beam (4) are connected with the bottom ends of the upright posts (5) in a clamping manner through a bottom beam clamp (7) to realize rigid connection of the beams and the posts; the middle part of the bottom beam (4) is connected with the trolley platform;
the vibration exciter loading device comprises a vibration exciter (16), an adapter plate (17), a connecting rod (18), a power amplifier and a vibration controller; one end of the vibration exciter (16) is fixedly connected with the adapter plate (17), and the adapter plate (17) is connected with the trolley platform (15); the other end of the vibration exciter (16) is connected with a connecting rod (18), and the connecting rod (18) is connected with the beam clamp (6); the vibration exciter (16) is connected with the power amplifier and the vibration controller through data lines;
the vibration table loading device comprises a high-power vibration exciter (19), a vibration exciter fixing device (20), a vibration table bottom plate (21) and a connecting plate (22); the bottom ends of the vibration exciter fixing device (20) and the vibrating table bottom plate (21) are both arranged on the ground of a laboratory; the high-power vibration exciter (19) is fixedly connected with one side of the vibration exciter fixing device (20); the connecting plate (22) is connected with the upper part of the vibrating table bottom plate (21) through balls, and the connecting plate (22) and the vibrating table bottom plate (21) can slide relatively; the bottom beam (4) is connected with the connecting plate (22); the high-power vibration exciter (19) is connected with the power amplifier and the vibration control instrument through a data line; a worm gear lifter (9) in the static loading device displays the loaded load on a computer through a force sensor (10);
the measuring equipment comprises a force sensor (10), an acceleration sensor (24) and a dial indicator; the dial indicator is fixed on the indicator frame (25) through the magnetic indicator seat; the acceleration sensor is fixed on a multi-layer frame structure beam clamp (6); the measuring equipment is connected with the computer through a data line, and various data are visualized through a data acquisition and analysis system in the computer;
the free vibration experiment of the two-degree-of-freedom system comprises the following steps:
firstly, assembling a two-layer frame structure, determining the position of each experimental point, marking A, B at two ends of a bottom layer beam (4), marking C, D on a first layer beam (3), marking E and F on a second layer beam (3), wherein A, C and E are positioned on a left upright post, and B, D, F is positioned on a right upright post; labeling G in the middle of F and D; testing the distance between the cross beams (3), namely the length of AC, CE, BD, DF;
secondly, determining the dynamic characteristics of the structure by adopting a rigidity coefficient measuring method
2.1) assembling an experimental device and a balance force sensor; applying a graded horizontal displacement Δ at point CCMeasuring the counter force V of two static loading devices at the C point and the E pointCCAnd VEC(ii) a After loading to the highest level displacement, unloading;
2.2) repeating the sixth step at least three times to obtain the rigidity coefficient kCC、kEC；
2.3) balance force sensor, applying a graded horizontal displacement Δ at point EEMeasuring the counter force V of two static loading devices at the C point and the E pointCEAnd VEE(ii) a After loading to the highest level displacement, unloading;
2.4) repeating the eighth step at least three times to obtain the rigidity coefficient kCEAnd kEE；
2.5) calculating the dynamic characteristics of the frame structure by using the rigidity coefficient and the mass of the cross beam, wherein the dynamic characteristics comprise the natural vibration frequency and the vibration mode of the structure;
thirdly, determining the dynamic characteristics of the structure by adopting a sudden unloading method
3.1) Assembly experiment device, connecting the worm gear and worm lifter (9) with the frame structure by using a thin wire (23), and applying an initial displacement y at a point F0，
3.2) cutting off the thin line (23) after the system is static, and obtaining D, F two-point acceleration change curve through a reaction spectrum measured by the acceleration sensor (24) to obtain the structure natural vibration frequency and the vibration mode corresponding to each order of natural vibration frequency;
and fourthly, comparing and analyzing the experimental results of the rigidity coefficient measuring method and the sudden unloading method, analyzing errors and obtaining a conclusion.
4. A forced vibration experiment of a two-degree-of-freedom system adopting a multilayer frame teaching experiment model is characterized in that the multilayer frame teaching experiment model comprises a multilayer frame structure, a static loading device, a vibration exciter loading device, a vibration table loading device and measuring equipment;
the multi-layer frame structure comprises a plurality of cross beams (3), a bottom beam (4), two upright posts (5), a cross beam clamp (6) and a bottom beam clamp (7); the two ends of each beam are clamped and connected with the upright post (5) through a beam clamp (6) to realize rigid connection of the beams and the posts; two ends of the bottom beam (4) are connected with the bottom ends of the upright posts (5) in a clamping manner through a bottom beam clamp (7) to realize rigid connection of the beams and the posts; the middle part of the bottom beam (4) is connected with the trolley platform;
the vibration exciter loading device comprises a vibration exciter (16), an adapter plate (17), a connecting rod (18), a power amplifier and a vibration controller; one end of the vibration exciter (16) is fixedly connected with the adapter plate (17), and the adapter plate (17) is connected with the trolley platform (15); the other end of the vibration exciter (16) is connected with a connecting rod (18), and the connecting rod (18) is connected with the beam clamp (6); the vibration exciter (16) is connected with the power amplifier and the vibration controller through data lines;
the vibration table loading device comprises a high-power vibration exciter (19), a vibration exciter fixing device (20), a vibration table bottom plate (21) and a connecting plate (22); the bottom ends of the vibration exciter fixing device (20) and the vibrating table bottom plate (21) are both arranged on the ground of a laboratory; the high-power vibration exciter (19) is fixedly connected with one side of the vibration exciter fixing device (20); the connecting plate (22) is connected with the upper part of the vibrating table bottom plate (21) through balls, and the connecting plate (22) and the vibrating table bottom plate (21) can slide relatively; the bottom beam (4) is connected with the connecting plate (22); the high-power vibration exciter (19) is connected with the power amplifier and the vibration control instrument through a data line; a worm gear lifter (9) in the static loading device displays the loaded load on a computer through a force sensor (10);
the measuring equipment comprises a force sensor (10), an acceleration sensor (24) and a dial indicator; the dial indicator is fixed on the indicator frame (25) through the magnetic indicator seat; the acceleration sensor is fixed on a multi-layer frame structure beam clamp (6); the measuring equipment is connected with the computer through a data line, and various data are visualized through a data acquisition and analysis system in the computer;
the forced vibration experiment of the two-degree-of-freedom system comprises the following steps of:
firstly, assembling a two-layer frame structure, determining the position of each experimental point, marking A, B at two ends of a bottom layer beam (4), marking C, D on a first layer beam (3), marking E and F on a second layer beam (3), wherein A, C and E are positioned on a left upright post, and B, D, F is positioned on a right upright post; labeling G in the middle of F and D; testing the spacing between the cross beams (3), namely the length of AC, CE, BD, DF;
secondly, determining the dynamic characteristics of the structure by adopting a vibration table excitation method:
2.1) measuring the lengths of AC, CE, BD and DF and the sectional sizes of the cross beam and the upright post, mounting the multilayer frame structure on a vibrating table loading device, inputting a white noise signal, and obtaining the natural vibration frequency of the structure through a reaction spectrum measured by an acceleration sensor (24);
2.2) inputting a sine wave signal corresponding to the first-order frequency to the vibration table, and obtaining D, F two-point acceleration amplitude values through a reaction spectrum obtained by the acceleration sensor (24);
2.3) inputting a sine wave signal corresponding to a second-order frequency to the vibration table, and obtaining D, F two-point acceleration amplitude values through a reaction spectrum obtained by the acceleration sensor (24);
2.4) processing original experimental data of the vibration table excitation method to obtain the structure natural vibration frequency and the vibration mode corresponding to each order of natural vibration frequency;
thirdly, determining the dynamic characteristics of the structure by adopting a vibration exciter excitation method:
3.1) assembling an experimental device, and measuring the lengths of AC, CE, BD, DF, CD, EF and CG and the cross-sectional dimensions of the cross beam and the upright column;
3.2) using the vibration exciter to apply dynamic load at the point D by using the vibration exciter, obtaining D, F two-point acceleration change curve by using the reaction spectrum measured by the acceleration sensor (24) to obtain the natural vibration frequency and the vibration mode
And fourthly, comparing and analyzing the experimental results of the vibration table excitation method and the vibration exciter excitation method, analyzing errors and obtaining a conclusion.
5. An experiment for solving the fundamental frequency of a three-layer rigid frame by adopting an approximation method of a multilayer frame teaching experiment model is characterized in that the multilayer frame teaching experiment model comprises a multilayer frame structure, a static loading device, a vibration exciter loading device, a vibration table loading device and measuring equipment;
the multi-layer frame structure comprises a plurality of cross beams (3), a bottom beam (4), two upright posts (5), a cross beam clamp (6) and a bottom beam clamp (7); the two ends of each beam are clamped and connected with the upright post (5) through a beam clamp (6) to realize rigid connection of the beams and the posts; two ends of the bottom beam (4) are connected with the bottom ends of the upright posts (5) in a clamping manner through a bottom beam clamp (7) to realize rigid connection of the beams and the posts; the middle part of the bottom beam (4) is connected with the trolley platform;
the vibration exciter loading device comprises a vibration exciter (16), an adapter plate (17), a connecting rod (18), a power amplifier and a vibration controller; one end of the vibration exciter (16) is fixedly connected with the adapter plate (17), and the adapter plate (17) is connected with the trolley platform (15); the other end of the vibration exciter (16) is connected with a connecting rod (18), and the connecting rod (18) is connected with the beam clamp (6); the vibration exciter (16) is connected with the power amplifier and the vibration controller through data lines;
the vibration table loading device comprises a high-power vibration exciter (19), a vibration exciter fixing device (20), a vibration table bottom plate (21) and a connecting plate (22); the bottom ends of the vibration exciter fixing device (20) and the vibration table bottom plate (21) are both arranged on the ground of a laboratory; the high-power vibration exciter (19) is fixedly connected with one side of the vibration exciter fixing device (20); the connecting plate (22) is connected with the upper part of the vibrating table bottom plate (21) through balls, and the connecting plate (22) and the vibrating table bottom plate (21) can slide relatively; the bottom beam (4) is connected with the connecting plate (22); the high-power vibration exciter (19) is connected with the power amplifier and the vibration control instrument through a data line; a worm gear lifter (9) in the static loading device displays the loaded load on a computer through a force sensor (10);
the measuring equipment comprises a force sensor (10), an acceleration sensor (24) and a dial indicator; the dial indicator is fixed on the indicator frame (25) through the magnetic indicator seat; the acceleration sensor is fixed on a multi-layer frame structure beam clamp (6); the measuring equipment is connected with the computer through a data line, and various data are visualized through a data acquisition and analysis system in the computer;
the experiment for solving the fundamental frequency of the three-layer rigid frame by the approximation method comprises the following steps:
firstly, assembling an experimental device, mounting a multilayer frame structure on a vibration table, inputting a white noise signal, and obtaining the structure natural vibration frequency through a reaction spectrum measured by an acceleration sensor (24);
secondly, applying a load equal to the weight of each cross beam at point C, E, G, and measuring the displacement of each point D, F, H;
and thirdly, processing the original experimental data in the second step, obtaining the structure natural vibration frequency by using an approximation formula, and comparing and analyzing the structure natural vibration frequency with the experimental result in the first step.
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