CN106777654B - Method for determining equivalent damping of dry friction damping vibration isolator - Google Patents
Method for determining equivalent damping of dry friction damping vibration isolator Download PDFInfo
- Publication number
- CN106777654B CN106777654B CN201611136502.2A CN201611136502A CN106777654B CN 106777654 B CN106777654 B CN 106777654B CN 201611136502 A CN201611136502 A CN 201611136502A CN 106777654 B CN106777654 B CN 106777654B
- Authority
- CN
- China
- Prior art keywords
- damping
- vibration isolator
- finite element
- dry friction
- response curve
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Active
Links
Images
Classifications
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/20—Design optimisation, verification or simulation
- G06F30/23—Design optimisation, verification or simulation using finite element methods [FEM] or finite difference methods [FDM]
Landscapes
- Engineering & Computer Science (AREA)
- Physics & Mathematics (AREA)
- Theoretical Computer Science (AREA)
- Computer Hardware Design (AREA)
- Evolutionary Computation (AREA)
- Geometry (AREA)
- General Engineering & Computer Science (AREA)
- General Physics & Mathematics (AREA)
- Management, Administration, Business Operations System, And Electronic Commerce (AREA)
- Testing Of Devices, Machine Parts, Or Other Structures Thereof (AREA)
Abstract
The equivalent damping determination method of the dry friction damping vibration isolator comprises the following steps of 1, establishing a theoretical model of the dry friction damping vibration isolator; step 2, carrying out a frequency sweep test on the vibration isolator loaded with the load, and step 3, carrying out finite element simulation; and 4, carrying out finite element calculation, 5, optimizing the damping, and 6, and determining the actual equivalent damping C of the vibration isolator. The method for determining the equivalent damping of the dry friction damping vibration isolator utilizes a method combining test and theoretical simulation, obtains the vibration isolation curve of the vibration isolator through a sweep frequency vibration test, takes the test vibration isolation curve as an optimization target, determines the equivalent damping of the dry friction damping vibration isolator by using a finite element simulation method by taking the damping of each frequency band as a variable, and finds a new effective method for determining the equivalent damping of the dry friction damping vibration isolator.
Description
Technical Field
The invention belongs to the field of machinery, and particularly relates to an equivalent damping determination method.
Background
In the field of nonlinear vibration research, vibration isolation systems containing dry friction damping have received much attention. In a mechanical structure, dry friction can quickly and effectively inhibit dynamic response of external interference excitation on a system, so that the dry friction is widely applied to vibration isolation of structures such as blades of aircraft engines, crystal oscillators and the like.
In recent years, a large amount of research has been conducted by domestic and foreign scholars on vibration systems constituted by nonlinear vibration isolators having dry friction. For example, an equivalent linearization calculation method of the simple harmonic excitation response of the viscous damping hysteresis vibrator is researched by Baihongbai and the like; the literature studies the periodic motion behavior of the friction vibrator excited by simple harmonics, and solves and numerically simulates the sliding process. In the aspect of energy, the friction force is equivalent to the overall viscous damping, and the resonance peak-free characteristic of dry friction damping is researched. However, none of the above prior art documents provides a clear equivalent method for the correspondence between the frictional force, the damping and the frequency.
Disclosure of Invention
The invention applies a method combining experimental test and theoretical simulation, divides the damping value into a plurality of different frequency bands according to the frequency, obtains the damping values of the different frequency bands by an optimization method, and finds a new effective method for determining the equivalent damping of the dry friction damping vibration isolator.
The invention provides a method for determining equivalent damping of a dry friction damping vibration isolator, which is characterized by comprising the following steps of:
and 6, correspondingly obtaining the optimized damping parameter value corresponding to the finite element calculation response curve from the optimized finite element calculation response curve obtained in the step 5, thereby determining the actual equivalent damping C of the vibration isolator under the load of M.
In the method for determining the equivalent damping of the dry friction damping vibration isolator, the method can further comprise the following steps: and 7, obtaining theoretical equivalent damping C multiplied by t under any load M multiplied by t through proportion calculation according to the actual equivalent damping C of the vibration isolator under the load M in the step 6, wherein t is a proportional value and is a constant.
In addition, in the method for determining the equivalent damping of the dry friction damping vibration isolator, the method can also have the following characteristics: wherein, the damping C in step 1 is generated by dry friction, and the magnitude of the damping C is related to and changes along with the external excitation frequency.
In addition, in the method for determining the equivalent damping of the dry friction damping vibration isolator, the method can also have the following characteristics: the finite element model in the step 3 is to use a CBush unit in commercial software HyperWorks software to simulate the rigidity K and the damping C in the spring damping unit.
In addition, in the method for determining the equivalent damping of the dry friction damping vibration isolator, the method can also have the following characteristics: wherein the vibration isolator excitation curve in step 4 is input in the excitation loading unit in the finite element model.
In addition, in the method for determining the equivalent damping of the dry friction damping vibration isolator, the method can also have the following characteristics: and 4, the position for acquiring the finite element calculation response value in the step 4 is arranged at the common node of the spring damping unit and the bearing unit.
In addition, in the method for determining the equivalent damping of the dry friction damping vibration isolator, the method can also have the following characteristics: wherein, the damping optimization in step 5 comprises the following steps:
s5-1, determining a design variable, wherein the design variable is a value of nonlinear damping C on each key frequency point;
s5-2, establishing an objective function, wherein the expression of the objective function is as follows:
s5-3, minimizing an objective function, wherein the expression of the minimized objective function is as follows:
min(OBJ)，
wherein y isiCalculating the displacement response, delta, of each corresponding point on the response curve for the finite elementiAnd (3) obtaining the displacement response corresponding to each point after the sparse processing of the vibration isolator response curve, wherein i is 1, 2, 3 and … … n.
Action and Effect of the invention
The equivalent damping determination method of the dry friction damping vibration isolator comprises the following steps of 1, establishing a theoretical model of the dry friction damping vibration isolator; step 2, carrying out a frequency sweep test on the vibration isolator loaded with the load, and step 3, carrying out finite element simulation; and 4, carrying out finite element calculation, 5, optimizing the damping, and 6, and determining the actual equivalent damping C of the vibration isolator. The method for determining the equivalent damping of the dry friction damping vibration isolator utilizes a method combining test and theoretical simulation, obtains the vibration isolation curve of the vibration isolator through a sweep frequency vibration test, takes the test vibration isolation curve as an optimization target, determines the equivalent damping of the dry friction damping vibration isolator by using a finite element simulation method by taking the damping of each frequency band as a variable, and finds a new effective method for determining the equivalent damping of the dry friction damping vibration isolator.
Drawings
FIG. 1 is a theoretical model of a dry friction damped vibration isolator in an embodiment of the present invention;
figure 2 is a graph of vibration isolator excitation and response curves measured during testing of an embodiment of the present invention;
FIG. 3 is a finite element model of the isolator as established in finite element software according to an embodiment of the present invention;
FIG. 4 is a graph of a finite element calculation response curve before optimization and a test response curve in an embodiment of the present invention;
figure 5 is an iterative plot of isolator damping optimization in an embodiment of the present invention;
FIG. 6 is a graph of a finite element calculated response curve and a test response curve after optimization in an embodiment of the present invention;
FIG. 7 is a graph comparing a response curve obtained by a finite element calculation of a 10kg test specimen with a response curve measured by a test in an example of the present invention;
FIG. 8 is a graph comparing a response curve obtained by a finite element calculation of a 70kg test specimen in an example of the present invention with a response curve measured by a test; and
FIG. 9 is a graph comparing the response curve obtained by finite element calculation of 100kg test specimens in the example of the present invention with the response curve measured by the test.
Detailed Description
In order to make the technical means, the creation characteristics, the achievement purposes and the effects of the invention easy to understand, the following embodiments are combined with the accompanying drawings to specifically describe the method for determining the equivalent damping of the dry friction damping vibration isolator provided by the invention.
Examples
A theoretical model of a dry friction damped isolator is shown in fig. 1, which can be practically simplified as a spring damping unit. Because the rigidity K of the mechanical model of the vibration isolator is the rigidity of the spring, the value of the rigidity K can be accurately measured through tests, the damping C in the model is generated by dry friction, the value of the damping C is related to the external excitation frequency, and the damping C is a quantity which changes along with the frequency.
In the embodiment, the vibration isolation curve of the vibration isolator is obtained through a frequency sweep vibration test, the test vibration isolation curve is used as an optimization target, the damping of each frequency band is used as a variable, and the damping of the dry friction damping vibration isolator is determined by a finite element simulation method.
And 2, performing a frequency sweep test on the vibration isolator loaded with the load M, respectively measuring an excitation value and a response value of the vibration isolator, and obtaining a corresponding vibration isolator excitation curve and a vibration isolator response curve.
A load with the mass of 50kg is arranged at the upper part of the vibration isolator, the rigidity of the vibration isolator is 46N/mm, and certain dry friction force exists. The dry friction damping values were determined with this embodiment by excitation with a known signal and the method was verified with different models of dry friction damping isolators.
A frequency sweep test was performed on a dry friction damped isolator with a nominal load of 50 kg. The vibration isolator is fixed on a vibration table, a mass block of 50kg is arranged at the upper part of the vibration isolator to serve as a load, an accelerometer is respectively arranged on the vibration table and the mass block, and an excitation value and a response value are measured.
The test condition is carried out according to sine sweep frequency vibration, equal displacement excitation is carried out in a frequency band of 5-16 Hz, and the single amplitude is 1 mm; and (3) exciting at equal acceleration in a frequency band of 16-176 Hz, wherein the amplitude of the acceleration is 1 g.
The vibration isolator excitation curves and vibration isolator response curves measured during the test are shown in figure 2.
In fig. 2, a curve 3 in the middle is a vibration isolator excitation signal curve, a curve 1 is a vibration isolator excitation signal high-limit failure curve, a curve 2 is a vibration isolator excitation signal high-limit early warning curve, a curve 4 is a vibration isolator excitation signal low-limit early warning curve, a curve 5 is a vibration isolator response curve, and a curve 6 is a vibration isolator excitation signal low-limit failure curve.
The excitation type is 1g equal acceleration excitation at 5-16 Hz, and 16-176 Hz is 1mm equal displacement excitation.
And 3, carrying out finite element simulation, and establishing a finite element model of the vibration isolator, which comprises an excitation loading unit, a spring damping unit and a bearing unit, in finite element software.
A finite element model 10 of the vibration isolator in which stiffness and damping are simulated using a CBush unit is built in a finite element software hyper works, the finite element model 10 of the vibration isolator is shown in fig. 3, and the finite element model 10 of the vibration isolator includes a load 11, a spring damping unit 12, and an excitation loading unit 13.
In the example, the load 11 is a 50kg mass. The excitation loading unit 13 at the bottom three corners loads the vibration isolator excitation curve in fig. 2, the vibration isolator excitation signal is transmitted to the upper 50kg mass block through the middle spring damping unit 12, and the output signal is detected at the position J of the common node of the spring damping unit 12 and the load 11. Therefore, by changing the stiffness and damping value of the spring damping unit 12, a response curve similar to the test response result can be obtained.
TABLE 1 damping sectional change initial value table
And 4, inputting the excitation curve of the vibration isolator in the finite element model 10 in the step 3 for finite element calculation to obtain a finite element calculation response value and a corresponding finite element calculation response curve.
Finite element calculation is carried out in finite element software HyperWorks, a spring damping unit is used for simulating the vibration isolator, but the parameters of stiffness damping need to be set. In this example, the stiffness was 46N/mm and the damping was initially assigned as shown in Table 1.
And inputting the vibration isolator excitation curve of fig. 2 into the finite element model to perform finite element calculation to obtain a response curve of the finite element calculation.
For comparison, the response curve of the finite element calculation and the response curve of the vibration isolator in fig. 2 are put together (taking 5-110 Hz), as shown in fig. 4. As can be seen from fig. 4, the response curve 41 obtained by finite element calculation and the experimentally measured response curve 42 of the vibration isolator have large errors, and parameters (dry friction damping) of the finite element model must be optimized.
And 5, damping optimization, namely continuously optimizing damping parameters in the finite element model, and fitting the finite element calculation response curve and the vibration isolator response curve to obtain the optimal finite element calculation response curve after the finite element calculation response curve is matched with the vibration isolator response curve.
And aiming at response data measured by the test, and optimizing the damping value of each key frequency point in the finite element model to ensure that the overall difference between the response result obtained by finite element calculation and the response result measured by the test is minimum. The method comprises the following steps:
① design variables
The design variable of the curve fitting is the value of nonlinear damping C on each key frequency point. The initial values and the variation ranges of the variables are shown in table 2.
Table 2 design variable value taking table
②, an objective function is established that,
wherein y isiCalculating the displacement response, delta, of each corresponding point on the response curve for the finite elementiIn the embodiment, n is 191, i is 1, 2, 3, … … n (frequency response analysis results output one point every 0.5Hz, and n values are total on the output curve) for the displacement response corresponding to each point after the vibration isolator response curve is subjected to sparse processing.
③ minimization of the objective function min (OBJ)
According to the objective function, the previous target value OBJ is 1.236. After the finite element HyperWorks optimization calculation, the target value OBJ is 0.199. The optimized iteration curve is shown in fig. 5.
And 6, correspondingly obtaining the optimized damping parameter value corresponding to the finite element calculation response curve from the optimized finite element calculation response curve obtained in the step 5, thereby determining the actual equivalent damping C of the vibration isolator under the load of M.
The response curve of the optimized finite element calculation and the response curve of the actually measured vibration isolator are shown in fig. 6, and the finite element result is basically consistent with the experimental measurement result.
The damping table after optimization is shown in table 3.
TABLE 3 optimized damping chart
And 7, obtaining theoretical equivalent damping C multiplied by t under any load M multiplied by t through proportion calculation according to the actual equivalent damping C of the vibration isolator under the load M in the step 5, wherein t is a proportional value and is a constant.
In order to verify the generalizability of the method, the damping values of dry friction damping vibration isolators of different models are simply calculated. The invention is verified by taking as an example a dry friction damped isolator with nominal loads of 10kg, 70kg and 100kg respectively.
The optimization method described in this embodiment can obtain equivalent damping values of each frequency band with a nominal load of 50kg, and the damping values are respectively expressed to obtain damping values of 10kg, 70kg and 100kg according to the mass ratio.
As shown in table 4, the magnitude of the damping value of the dry friction damped isolator is generally proportional to the magnitude of its nominal load.
Table 410 kg, 70kg and 100kg sample segment damping values
The damping values obtained in table 4 were substituted into the finite element model, and the same method was used to perform the finite element calculation, so as to obtain the response curves of the dry friction damping finite element calculation with nominal loads of 10kg, 70kg and 100kg, respectively. The response curve obtained by finite element calculation and the response curve of the vibration isolator measured by experiment are shown in figures 7, 8 and 9.
From the results, the response curve of the finite element calculation is basically consistent with the actually measured response curve, which shows that the optimization method can simply, conveniently and accurately determine the equivalent damping of the dry friction damping vibration isolator with different loads.
Effects and effects of the embodiments
The method for determining the equivalent damping of the dry friction damping vibration isolator according to the embodiment comprises the following steps of 1, establishing a theoretical model of the dry friction damping vibration isolator; step 2, carrying out a frequency sweep test on the vibration isolator loaded with the load, and step 3, carrying out finite element simulation; and 4, carrying out finite element calculation, 5, optimizing the damping, and 6, and determining the actual equivalent damping C of the vibration isolator. The method for determining the equivalent damping of the dry friction damping vibration isolator in the embodiment utilizes a method combining test and theoretical simulation, obtains the vibration isolation curve of the vibration isolator through a sweep frequency vibration test, takes the test vibration isolation curve as an optimization target, determines the equivalent damping of the dry friction damping vibration isolator by using a finite element simulation method by taking the damping of each frequency band as a variable, and finds a new effective method for determining the equivalent damping of the dry friction damping vibration isolator.
In addition, according to the actual equivalent damping C of the vibration isolator under the load of M in the step 6, the theoretical equivalent damping C multiplied by t under any load of M multiplied by t is obtained through proportion calculation, and therefore technicians can obtain the theoretical equivalent damping of the vibration isolator under any load conveniently.
The above embodiments are preferred examples of the present invention, and are not intended to limit the scope of the present invention.
Claims (5)
1. The method for determining the equivalent damping of the dry friction damping vibration isolator is characterized by comprising the following steps of:
step 1, establishing a theoretical model of a dry friction damping vibration isolator, wherein the model of the vibration isolator is a spring damping unit comprising a spring with the rigidity of K and an equivalent damping C connected with the spring in parallel;
step 2, performing a frequency sweep test on the vibration isolator loaded with the load M, respectively measuring an excitation value and a response value of the vibration isolator, and obtaining a corresponding vibration isolator excitation curve and a vibration isolator response curve;
step 3, carrying out finite element simulation, and establishing a finite element model of the vibration isolator, wherein the finite element model comprises an excitation loading unit, a spring damping unit and a load unit;
step 4, inputting the excitation curve of the vibration isolator in the finite element model in the step 3 for finite element calculation to obtain a finite element calculation response value and a corresponding finite element calculation response curve;
step 5, damping optimization, namely continuously optimizing damping parameters in the finite element model, and fitting the finite element calculation response curve and the vibration isolator response curve to obtain the optimal finite element calculation response curve after the finite element calculation response curve is matched with the vibration isolator response curve;
wherein the damping optimization comprises the steps of:
s5-1, determining a design variable, wherein the design variable is a value of nonlinear equivalent damping C on each key frequency point;
s5-2, establishing an objective function, wherein the expression of the objective function is as follows:
s5-3, minimizing an objective function, wherein the expression of the minimized objective function is as follows:
min(OBJ)，
wherein y isiCalculating the displacement response, delta, of each corresponding point on the response curve for the finite elementiThe displacement response corresponding to each point after the sparse processing of the response curve of the vibration isolator is represented by i which is 1, 2, 3 and … … n;
and 6, correspondingly obtaining the optimized damping parameter value corresponding to the finite element calculation response curve from the optimized finite element calculation response curve obtained in the step 5, thereby determining the actual equivalent damping C of the vibration isolator under the load of M.
2. The method for determining equivalent damping of a dry friction damped isolator according to claim 1 further comprising:
and 7, obtaining theoretical equivalent damping C multiplied by t under any load M multiplied by t through proportion calculation according to the actual equivalent damping C of the vibration isolator under the load M in the step 6, wherein t is a proportional value and is a constant.
3. The method for determining the equivalent damping of the dry friction damping vibration isolator according to claim 1, wherein:
wherein, the equivalent damping C in step 1 is generated by dry friction, and the magnitude of the equivalent damping C is related to and changes along with the external excitation frequency.
4. The method for determining the equivalent damping of the dry friction damping vibration isolator according to claim 1, wherein:
wherein the vibration isolator excitation curve in step 4 is input in the excitation loading unit in the finite element model.
5. The method for determining the equivalent damping of the dry friction damping vibration isolator according to claim 1, wherein:
and 4, setting the position for acquiring the finite element calculation response value in the step 4 at the common node of the spring damping unit and the load unit.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201611136502.2A CN106777654B (en) | 2016-12-12 | 2016-12-12 | Method for determining equivalent damping of dry friction damping vibration isolator |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201611136502.2A CN106777654B (en) | 2016-12-12 | 2016-12-12 | Method for determining equivalent damping of dry friction damping vibration isolator |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN106777654A CN106777654A (en) | 2017-05-31 |
| CN106777654B true CN106777654B (en) | 2020-04-03 |
Family
ID=58875620
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201611136502.2A Active CN106777654B (en) | 2016-12-12 | 2016-12-12 | Method for determining equivalent damping of dry friction damping vibration isolator |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN106777654B (en) |
Families Citing this family (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN111677806B (en) * | 2020-04-27 | 2021-03-02 | 清华大学 | Method and system for determining damping force of magnetorheological shock absorber |
Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN103047363A (en) * | 2012-12-27 | 2013-04-17 | 南京航空航天大学 | Active vibration isolation device with adjustable rigidity and damping |
| CN103473417A (en) * | 2013-09-16 | 2013-12-25 | 北京航空航天大学 | Particle damping vibration attenuation design method for umbrella-type vibration of wheel structure |
| CN104166778A (en) * | 2014-09-05 | 2014-11-26 | 上海理工大学 | Method for optimizing rigidity and damping of contact part of automobile seat guide rail |
| CN105729231A (en) * | 2016-03-04 | 2016-07-06 | 北京工业大学 | Elastic support frictional damping vibration attenuation method and structure for linear rolling guide rail clamping device |
| RU2015118832A (en) * | 2015-05-20 | 2016-12-10 | Татьяна Дмитриевна Ходакова | Vibration isolator spring |
Family Cites Families (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| DE10052786B4 (en) * | 2000-10-25 | 2009-01-02 | Zf Sachs Ag | Torsion damping mechanism with additional mass |
-
2016
- 2016-12-12 CN CN201611136502.2A patent/CN106777654B/en active Active
Patent Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN103047363A (en) * | 2012-12-27 | 2013-04-17 | 南京航空航天大学 | Active vibration isolation device with adjustable rigidity and damping |
| CN103473417A (en) * | 2013-09-16 | 2013-12-25 | 北京航空航天大学 | Particle damping vibration attenuation design method for umbrella-type vibration of wheel structure |
| CN104166778A (en) * | 2014-09-05 | 2014-11-26 | 上海理工大学 | Method for optimizing rigidity and damping of contact part of automobile seat guide rail |
| RU2015118832A (en) * | 2015-05-20 | 2016-12-10 | Татьяна Дмитриевна Ходакова | Vibration isolator spring |
| CN105729231A (en) * | 2016-03-04 | 2016-07-06 | 北京工业大学 | Elastic support frictional damping vibration attenuation method and structure for linear rolling guide rail clamping device |
Non-Patent Citations (3)
| Title |
|---|
| 《Principle and application of free resonance vibration isolation based on dry friction damper》;Hui Jieyu 等;《Applied Mechanics and Materials》;20111231;第59-63页 * |
| 《变滑动摩擦系数振子简谐激励Krylov-Bogoliubov计算方法》;白鸿柏 等;《机械强度》;20021231(第1期);第56-58页 * |
| 《某雷达常用减震器的减震缓冲特性比较》;余慧杰 等;《现代雷达》;20101231;第32卷(第12期);第99-102页 * |
Also Published As
| Publication number | Publication date |
|---|---|
| CN106777654A (en) | 2017-05-31 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| Schwingshackl et al. | Measured and estimated friction interface parameters in a nonlinear dynamic analysis | |
| Aykan et al. | Vibration fatigue analysis and multi-axial effect in testing of aerospace structures | |
| Ismail et al. | An investigation into the vibration analysis of a plate with a surface crack of variable angular orientation | |
| Gagnon et al. | A review of friction damping modeling and testing | |
| Mao et al. | The construction and comparison of damage detection index based on the nonlinear output frequency response function and experimental analysis | |
| Jrad et al. | Experimental characterization, modeling and parametric identification of the non linear dynamic behavior of viscoelastic components | |
| Di Maio et al. | Development of a test planning methodology for performing experimental model validation of bolted flanges | |
| Sayag et al. | Linear versus nonlinear response of a cantilevered beam under harmonic base excitation: theory and experiment | |
| Gastaldi et al. | Modeling complex contact conditions and their effect on blade dynamics | |
| Sun et al. | Modeling and parameter identification of amplitude-and frequency-dependent rubber isolator | |
| Gräbner et al. | Nonlinearities in friction brake NVH-experimental and numerical studies | |
| Peng et al. | Numerical analysis of cracked beams using nonlinear output frequency response functions | |
| Zippo et al. | Temperature gradient effect on dynamic properties of a polymeric circular cylindrical shell | |
| Radoičić et al. | Experimental identification of overall structural damping of system | |
| CN106777654B (en) | Method for determining equivalent damping of dry friction damping vibration isolator | |
| Li et al. | Dynamic stiffness and damping characteristics of a shaft damping ring: A combined hyperelastic and viscoelastic constitutive model | |
| Sokół et al. | Instability and vibration of multi-member columns subjected to Euler’s load | |
| Sadati et al. | Identification of a nonlinear joint in an elastic structure using optimum equivalent linear frequency response function | |
| Gastaldi et al. | Estimation accuracy vs. engineering significance of contact parameters for solid dampers | |
| Schwartz et al. | Understanding the effect of systematic errors on the accuracy of experimental measurements of fluid-film bearing dynamic coefficients | |
| Raviv Sayag et al. | Nonlinear structural, inertial and damping effects in an oscillating cantilever beam | |
| JP6988599B2 (en) | Analyst | |
| Guo et al. | Theory and experimental research for the double ended tuning fork in MEMS | |
| Li et al. | Study on the nonlinear dynamic characteristics of spherical rubber isolators by experiments and simulations based on harmonic balance method | |
| Mezghani et al. | Identification of nonlinear anti-vibration isolator properties |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |