CN101893497A - Out-of-plane frequency method for testing cable force of planar cable rod system - Google Patents

Abstract

The invention relates to an out-of-plane frequency method for testing the cable force of a planar cable rod system, which discloses an out-of-plane frequency method based on the cable force of a pulling cable of an out-of-plane self-oscillation frequency testing planar cable rod system and belongs to the fields of cable force monitoring, state (parameter) identification, health monitoring and the like of the construction phase and the use phase of a cable structure. The method is based on the cable force of the pulling cable of the out-of-plane self-oscillation frequency testing planar cable rod system, and continuous short cables in the planar cable rod system are converted into an out-of-plane long cable, the cable force is determined by measuring the out-of-plane self-oscillation frequency and establishing a cable force-out-of-plane self-oscillation frequency relation formula, and the method concretely comprises the following steps of: 1. carrying out the modal analysis of the finite element model of the planar cable rod system, and determining the out-of-plane calculated length; 2. measuring the out-of-plane self-oscillation frequency of the planar cable rod system; 3. identifying the out-of-plane bending rigidity according to the measured multistage out-of-plane self-oscillation frequency; 4. establishing the cable force-out-of-plane self-oscillation frequency relation formula; and 5. calculating the cable force.

Description

Frequency method outside the plane of test plane rope leverage Suo Li

Technical field

The invention discloses based on frequency method outside the plane of drag-line (as steel tendon rope, steel strand wires rope, steel wire cable and the reinforcing pull rod etc.) Suo Li of natural frequency of vibration test plane rope leverage outside the plane (as opening a string beam, truss string structure, opening the rope leverage in the structures such as string grid, cable truss, suspention), belong to the fields such as cable force monitoring, state (parameter) identification, health monitoring of construction stage of Cable Structure and operational phase.

Background technology

Drag-line in the Cable Structure is the important component part of structure, and its Suo Li changes not only influences the position of total shape, also influences the structural internal force situation, and its inefficacy causes the serious degradation of the rigidity of structure, usually causes the inefficacy of total.Therefore, the Suo Li of Cable Structure test is to guarantee that the construction stage pre-stressed state reaches one of important content of design object and operational phase safety of structure.

The main method of Suo Li test at present has frequency method, magnetic flux method, lifting jack method and fluctuation method etc., and wherein frequency method is used in bridge structure early and be comparatively extensive.

Frequency method is based on the natural frequency of vibration of drag-line and the numerical relation between the Suo Li, determines the method for Suo Li by the natural frequency of vibration of actual measurement tensioning backstay.The principal element that influences the natural frequency of vibration-Suo Li relation has: the edge-restraint condition of the effective length of drag-line, line weight, rope head weight, sag, bendind rigidity and guy anchor fixed end.According to the difference of Consideration, determine that at present the method for Suo Li-frequency relation mainly contains four classes:

The first kind mainly is to ignore the tensioning string theory of sag and bendind rigidity influence, promptly utilizes the fixing tensioning string in two ends to simulate suspension cable.Can release the Practical Formula 1 of calculating Suo Li by frequency equation, this formula strictness limits the use of in the elongated rope of low sag and low bendind rigidity.

$T={4\mathrm{ml}}^2{\left(\frac{f_n}{n}\right)}^2---\left(1\right)$

In the formula: the pulling force of T-rope; f _n-drag-line n rank the natural frequency of vibration; The line density of m-rope; The computational length of l-rope.

Second class mainly is to consider sag and the modern rope theory of ignoring the bendind rigidity influence.This method needs some additional informations, as original length of rope etc.; Need simultaneously to separate a nonlinear characteristic equation by trial and error.The Suo Li value error that this method is calculated exists the trend that increases with sag and bendind rigidity.

The 3rd class mainly is to consider bendind rigidity and the beam vibration theory of ignoring the sag influence.When disregard sag, when only considering that bendind rigidity influences, drag-line can be considered the beam that is subjected to axial tension.The relation of the beam natural frequency of vibration and axial tension is seen formula 2.

$T={4\mathrm{ml}}^2{\left(\frac{f_n}{n}\right)}^2-{\left(\frac{\mathrm{n\π}}{l}\right)}^2\mathrm{EI}---\left(2\right)$

In the formula: the bendind rigidity of EI-drag-line.

The 4th class mainly is some Suo Li computing method of considering sag and bendind rigidity influence simultaneously, basic thought is to derive the relation between the drag-line fundamental frequency and Suo Li when considering that respectively Suo Chuidu and bendind rigidity influence with energy method, sets up the fundamental frequency of drag-line and the relation formula of Suo Li by curve fitting again.

Above-mentioned four classes all are applicable to the Suo Li test of the soft ropes such as steel tendon, steel strand wires, wire rope of cable body softness based on the Suo Li computing method of the drag-line natural frequency of vibration, and require the length of drag-line long, rigidity bitter end is big and edge-restraint condition is clear and definite.Therefore frequency method is widely used in cable-stayed bridge and draws in the net tiltedly that the Suo Li of suspension cable tests in the lattice building structure.But for hard rope (as reinforcing pull rod) or tackline (length-to-diameter is less than 100), frequency method is difficult to be used.

Building opening string beam, truss string structure and opening the string network in the Cable Structure, by the firm structure that winds up (beam, truss, grid) and last quarter rope and between web member constitute; The cable truss structure, by steadying line, track cable and between web member (abdomen rope) constitute; Overhung construction, by top load-bearing suspension cable, the firm structure in bottom and between hoist cable constitute.Their common feature is: 1. the cable body of main rope is connected with web member (abdomen rope/hoist cable) by cord clip continuously; Although 2. the length of main rope self is longer continuously, some tackline sections have been divided into by web member (abdomen rope/hoist cable); 3. main rope and web member (abdomen rope/hoist cable) form a plane rope leverage in same plane; 4. rigidity rigidity in the plane outside the plane of this plane rope leverage.As seen, because long main rope has been divided into some rope sections by web member (abdomen rope/hoist cable), and the length of rope section is short, bendind rigidity be can not ignore, the edge-restraint condition complexity, therefore adopts conventional frequency method to be difficult to accurately measure the Suo Li of this class plane rope leverage.

Summary of the invention

Technical matters: the purpose of this invention is to provide based on frequency method outside the plane of natural frequency of vibration test plane rope leverage Suo Li outside the plane.In view of outside the plane of plane rope leverage and the plane in self-vibration characteristic difference big, rigidity rigidity in the plane outside the plane, low order self-vibration mode is based on vibration outside the plane, therefore the present invention is converted into out-of-plane long rope with the continuous tackline in the plane rope leverage, determines Suo Li by the natural frequency of vibration outside the actual measurement plane with the relation formula of setting up the natural frequency of vibration outside Suo Li-plane.With the long Suo Butong of routine be, plane foreign minister's rope is many broken lines shape, the natural frequency of vibration not only is subjected to the influence of drag-line self-condition and bitter end edge-restraint condition outside its plane, also be subjected to it the influence of the web member (abdomen rope/hoist cable) that laterally connects, so key technical problem is a relation how accurately to determine the natural frequency of vibration and Suo Li outside the plane.

Technical scheme: frequency method is based on drawing cable force in the natural frequency of vibration test plane rope leverage outside the plane outside the plane of test plane rope leverage Suo Li of the present invention, continuous tackline in the plane rope leverage is converted into out-of-plane long rope, determine specifically to comprise following steps by Suo Li with the relation formula of setting up the natural frequency of vibration outside Suo Li-plane by the natural frequency of vibration outside the actual measurement plane:

1) carries out the model analysis of plane rope leverage finite element model, determine computational length outside the plane;

2) natural frequency of vibration outside the plane of actual measurement plane rope leverage;

3) according to the natural frequency of vibration outside the multistage plane of actual measurement, bendind rigidity outside the identification plane;

4) set up the relation formula of the natural frequency of vibration outside Suo Li-plane;

5) calculate Suo Li.

The 1st) model analysis of stepping parallel planes rope leverage finite element model determines that the method for operating of computational length lw outside the plane is: select the cable elements and the bar unit that satisfy requirement of engineering precision for use, set up the finite element model of plane rope leverage; Take into full account non-linear and stress and just changed effect, determine corresponding different Suo Li T by model analysis ⁽ⁱ⁾The plane outside the self-vibration fundamental frequency Fitting formula:

Determine computational length l outside the plane _wIn the formula, m is the line density of drag-line, C _mBe cord clip node mass coefficient, l _wBe computational length outside the plane of drag-line in the plane rope leverage, Be and Suo Li T ⁽ⁱ⁾Self-vibration fundamental frequency outside the corresponding plane.

The 2nd) method of operating of the natural frequency of vibration is outside the plane of step actual measurement plane rope leverage: adopt vibro-pickup to survey the natural frequency of vibration outside the plane of plane rope leverage; The layout of vibro-pickup should be avoided equinox, quartile, eight branches and the rope head of drag-line; The vibration measuring direction should be perpendicular to plane, rope leverage place.

The 3rd) step according to the method for operating of bendind rigidity outside the outer natural frequency of vibration identification plane, the multistage plane of actual measurement is: according to the principle of " the calculating Suo Li T that surveys each order frequency correspondence should equate ", with natural frequency of vibration substitution formula outside the drag-line plane of surveying:

Can identify bendind rigidity outside the plane of drag-line;

In the formula, K _wBe bendind rigidity outside the plane of drag-line in the plane rope leverage, m is the line density of drag-line, C _mBe cord clip node mass coefficient, l _wBe computational length outside the plane of drag-line in the plane rope leverage, f _Wn1And f _Wn2Be respectively corresponding n ₁Rank and n ₂Rank (n ₁≠ n ₂) the actual measurement plane outside the natural frequency of vibration.

The 4th) going on foot the method for operating of setting up natural frequency of vibration relation formula outside Suo Li-plane is: the exact formulas that adopts natural frequency of vibration relation outside Suo Li-plane: For the plane rope leverage of large span, can ignore the influence of bendind rigidity outside the plane, directly with anchor-hold length as computational length outside the plane, the formula of reduction that adopts the outer natural frequency of vibration in Suo Li-plane to concern:

In the formula, T is Suo Li, K _wBe bendind rigidity outside the plane of drag-line in the plane rope leverage, m is the line density of drag-line, C _mBe cord clip node mass coefficient, l _wBe computational length outside the plane of drag-line in the plane rope leverage.

Beneficial effect: based on frequency method outside the plane of natural frequency of vibration test plane rope leverage Suo Li outside the plane, continuous tackline with the plane rope leverage is converted into out-of-plane long rope very cleverly, avoided frequency method to be difficult to be applied to the problem of tackline, solved the problem of Suo Li test in the Cable Structure that has the plane rope leverage (as opening a string beam, truss string structure, open string grid, cable truss, overhung construction etc.) and health detection, safety evaluation well.This method of testing is calculated simple, and is workable, the degree of confidence height.For the plane rope leverage of large span, can ignore the influence of bendind rigidity outside the plane, directly with anchor-hold length as computational length outside the plane, calculate Suo Li according to formula 7, can obtain higher Suo Li measuring accuracy; For medium and small plane rope leverage of striding, for improving measuring accuracy, computational length outside by finite element modal analysis correction plane, by surveying outside the multistage plane outside the natural frequency of vibration identification plane after the bendind rigidity, set up natural frequency of vibration relation formula outside accurate Suo Li-plane, thereby obtain high-precision Suo Li test result.The continuous rope that this method of testing is not only applicable in the plane rope leverage is the situation of soft ropes such as steel tendon, steel strand wires and wire rope, and is suitable too for the hard rope of reinforcing pull rod of continuous link.

Description of drawings

Fig. 1 is the process flow diagram based on frequency method outside the plane of drag-line (comprising steel tendon rope, steel strand wires rope, steel wire cable, reinforcing pull rod etc.) Suo Li in the natural frequency of vibration test plane rope leverage outside the plane.

Embodiment

Knot the present invention is converted into out-of-plane long rope with the continuous tackline in the plane rope leverage below, determine Suo Li by the natural frequency of vibration outside the actual measurement plane with the relation formula of setting up the natural frequency of vibration outside Suo Li-plane, its general steps is: 1. carry out the model analysis of plane rope leverage finite element model, determine computational length outside the plane; 2. survey the natural frequency of vibration outside the plane of plane rope leverage; 3. according to the natural frequency of vibration outside the multistage plane of actual measurement, discern bendind rigidity outside the plane; 4. set up the relation formula of the natural frequency of vibration outside Suo Li-plane; 5. calculate Suo Li.

The concrete steps of method of testing of determining plane rope leverage Suo Li based on the frequency method of the natural frequency of vibration outside the plane are as follows:

1) carries out the model analysis of plane rope leverage finite element model, determine computational length l outside the plane _w: select the cable elements and the bar unit that satisfy requirement of engineering precision for use, set up the finite element model of plane rope leverage; Take into full account non-linear and stress and just changed effect, determine self-vibration fundamental frequency outside the plane of corresponding different Suo Li by model analysis; Carry out match according to formula 3, determine computational length outside the plane, wherein for considering that the quality be fixed on the cord clip node on the drag-line cable body set a cord clip node mass coefficient C _m

$T^{\left(i\right)}={4C}_m{{\mathrm{ml}}_w}^2{f}_{w1}^{\left(i\right)2}---\left(3\right)$

In the formula: C _m-cord clip node mass coefficient; l _wComputational length outside the plane of-drag-line;

-with Suo Li T ⁽ⁱ⁾Self-vibration fundamental frequency outside the corresponding plane.

2) natural frequency of vibration outside the plane of actual measurement plane rope leverage: on engineering, adopt vibro-pickup to survey the natural frequency of vibration outside the plane of plane rope leverage; The layout of vibro-pickup should be avoided equinox, quartile, eight branches and the rope head of drag-line, and the vibration measuring direction should be perpendicular to plane, rope leverage place;

3) according to the natural frequency of vibration outside the multistage plane of actual measurement, bendind rigidity outside the identification plane: as seen by formula 2, the Suo Liying that obtains of the same order natural frequency of vibration is not identical, and the identification principle of bendind rigidity is " the calculating Suo Li T that surveys each order frequency correspondence should equate " outside the physical plane in view of the above; Obtain n by actual measurement ₁Rank and n ₂Rank (n ₁≠ n ₂) the plane outside natural frequency of vibration f _Wn1And f _Wn2, then have formula 4 to set up, and derive formula 5 by it; With natural frequency of vibration substitution formula 5 outside the drag-line plane of field measurement, can identify bendind rigidity outside the plane of drag-line;

$T={4C}_m{{\mathrm{ml}}_w}^2{\left(\frac{f_{\mathrm{wn}1}}{n_1}\right)}^2-{\left(\frac{n_1\mathrm{\π}}{l_w}\right)}^2$ $K_w={4C}_m{{\mathrm{ml}}_w}^2{\left(\frac{f_{\mathrm{wn}2}}{n_2}\right)}^2-{\left(\frac{n_2\mathrm{\π}}{l_w}\right)}^2{K}_w---\left(4\right)$

$K_w=\frac{{4C}_m{{\mathrm{ml}}_w}^4}{{\mathrm{\π}}^2}\×\frac{{\left(n_2{f}_{\mathrm{wn}1}\right)}^2-{\left(n_1{f}_{\mathrm{wn}2}\right)}^2}{n_1^2{n}_2^2(n_1^2-n_2^2)}---\left(5\right)$

In the formula: K _wBendind rigidity outside the-plane; f _Wn1, f _Wn2The corresponding n of-difference ₁Rank and n ₂Rank (n ₁≠ n ₂) the actual measurement plane outside the natural frequency of vibration.

4) set up the exact formulas that the natural frequency of vibration concerns outside Suo Li-plane:

$T={4C}_m{{\mathrm{ml}}_w}^2{\left(\frac{f_{\mathrm{wn}}}{n}\right)}^2-{\left(\frac{\mathrm{n\π}}{l_w}\right)}^2{K}_w---\left(6\right)$

In the formula: f _WnThe natural frequency of vibration outside the plane ,-Di n rank.

For the plane rope leverage of large span, engineering practice proves, can ignore the influence of bendind rigidity outside the plane, directly with anchor-hold length as computational length outside the plane, the formula of reduction of natural frequency of vibration relation is outside Suo Li-plane:

$T={4C}_m{{\mathrm{ml}}_a}^2{\left(\frac{f_{\mathrm{wn}}}{n}\right)}^2---\left(7\right)$

In the formula: l _aLength behind the-drag-line stretch-draw anchor.

5) calculate Suo Li: by the natural frequency of vibration outside the actual measurement plane, according to the relation formula calculating Suo Li of the natural frequency of vibration outside Suo Li-plane.

The present invention is described in more detail below in conjunction with accompanying drawing:

1. finite element modal analysis is determined computational length outside the plane; 2. survey the natural frequency of vibration outside the plane; 3. discern bendind rigidity outside the plane; 4. set up the relation formula of the natural frequency of vibration outside Suo Li-plane; 5. calculate Suo Li.

1) finite element modal analysis is determined computational length outside the plane

Select the cable elements and the bar unit that satisfy requirement of engineering precision for use, set up the finite element model of plane rope leverage; Take into full account non-linear and stress and just changed effect, determine self-vibration fundamental frequency outside the plane of corresponding different Suo Li by model analysis; Fitting formula:

Determine computational length outside the plane;

2) natural frequency of vibration outside the actual measurement plane

On engineering, adopt vibro-pickup to survey the natural frequency of vibration outside the plane of plane rope leverage; The layout of vibro-pickup should be avoided equinox, quartile, eight branches and the rope head of drag-line, and the vibration measuring direction should be perpendicular to plane, rope leverage place;

3) bendind rigidity outside the identification plane

According to the principle of " the calculating Suo Li T that surveys each order frequency correspondence should equate ", with the actual measurement the drag-line plane outside natural frequency of vibration substitution formula:

Can identify bendind rigidity outside the plane of drag-line;

4) set up the exact formulas that the natural frequency of vibration concerns outside Suo Li-plane: For the plane rope leverage of large span, can ignore the influence of bendind rigidity outside the plane, directly with anchor-hold length as computational length outside the plane, the formula of reduction of natural frequency of vibration relation is outside Suo Li-plane:

5) calculate Suo Li: by the natural frequency of vibration outside the actual measurement plane, according to the relation formula calculating Suo Li of the natural frequency of vibration outside Suo Li-plane.

Claims (5)

1. frequency method outside the plane of testing plane rope leverage Suo Li, it is characterized in that this method is based on drawing cable force in the natural frequency of vibration test plane rope leverage outside the plane, continuous tackline in the plane rope leverage is converted into out-of-plane long rope, determine specifically to comprise following steps by Suo Li with the relation formula of setting up the natural frequency of vibration outside Suo Li-plane by the natural frequency of vibration outside the actual measurement plane:

1) carries out the model analysis of plane rope leverage finite element model, determine computational length outside the plane;

2) natural frequency of vibration outside the plane of actual measurement plane rope leverage;

3) according to the natural frequency of vibration outside the multistage plane of actual measurement, bendind rigidity outside the identification plane;

4) set up the relation formula of the natural frequency of vibration outside Suo Li-plane;

5) calculate Suo Li.

2. frequency method outside the plane of test plane rope leverage Suo Li according to claim 1 is characterized in that

1) computational length l outside the plane is determined in the model analysis of stepping parallel planes rope leverage finite element model _wMethod of operating be: select the cable elements and the bar unit that satisfy requirement of engineering precision for use, set up the finite element model of plane rope leverage; Take into full account non-linear and stress and just changed effect, determine corresponding different Suo Li T by model analysis ⁽ⁱ⁾The plane outside the self-vibration fundamental frequency

Fitting formula: Determine computational length l outside the plane _wIn the formula, m is the line density of drag-line, C _mBe cord clip node mass coefficient, l _wBe computational length outside the plane of drag-line in the plane rope leverage,

Be and Suo Li T ⁽ⁱ⁾Self-vibration fundamental frequency outside the corresponding plane.

3. frequency method outside the plane of test plane rope leverage Suo Li according to claim 1 is characterized in that the 2nd) method of operating of the outer natural frequency of vibration in plane of step actual measurement plane rope leverage is: adopt vibro-pickup to survey the natural frequency of vibration outside the plane of plane rope leverage; The layout of vibro-pickup should be avoided equinox, quartile, eight branches and the rope head of drag-line; The vibration measuring direction should be perpendicular to plane, rope leverage place.

4. frequency method outside the plane of test plane rope leverage Suo Li according to claim 1, it is characterized in that the 3rd) method of operating of step according to bendind rigidity outside the outer natural frequency of vibration identification plane, the multistage plane of actual measurement be: according to the principle of " the calculating Suo Li T that surveys each order frequency correspondence should equate ", with natural frequency of vibration substitution formula outside the drag-line plane of surveying: Can identify bendind rigidity outside the plane of drag-line; In the formula, K _wBe bendind rigidity outside the plane of drag-line in the plane rope leverage, m is the line density of drag-line, C _mBe cord clip node mass coefficient, l _wBe computational length outside the plane of drag-line in the plane rope leverage, f _Wn1And f _Wn2Be respectively corresponding n ₁Rank and n ₂Rank (n ₁≠ n ₂) the actual measurement plane outside the natural frequency of vibration.

5. frequency method outside the plane of test plane rope leverage Suo Li according to claim 1 is characterized in that

4) going on foot the method for operating of setting up natural frequency of vibration relation formula outside Suo Li-plane is: the exact formulas that adopts natural frequency of vibration relation outside Suo Li-plane:

For the plane rope leverage of large span, can ignore the influence of bendind rigidity outside the plane, directly with anchor-hold length as computational length outside the plane, the formula of reduction that adopts the outer natural frequency of vibration in Suo Li-plane to concern:

In the formula, T is Suo Li, K _wBe bendind rigidity outside the plane of drag-line in the plane rope leverage, m is the line density of drag-line, C _mBe cord clip node mass coefficient, l _wBe computational length outside the plane of drag-line in the plane rope leverage.