CN112130599A - Cable multi-mode vibration control method considering damper performance frequency dependency - Google Patents
Cable multi-mode vibration control method considering damper performance frequency dependency Download PDFInfo
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Abstract
A cable multi-modal vibration control method considering the performance frequency dependence of a damper. The method comprises the following steps: s1: determining the requirement of the minimum damping ratio of the stay cable according to the Scruton number requirement for inhibiting wind and rain vibration of the stay cable, and using the requirement as a control threshold value of the multi-stage modal damping design of the stay cable; s2: testing the rigidity and damping characteristics under different frequency and amplitude conditions through a damper monomer test; s3: according to modal frequencies of orders below 3Hz of the cable, interpolating to obtain the rigidity and damping coefficient of the damper when the cable vibrates in the corresponding mode; s4: analyzing the damping effect of the damper on the mode with the stay rope frequency below 3Hz, judging whether the damping effect meets a set threshold value, if so, keeping the current damping parameter unchanged, if not, adjusting the parameter and the installation position of the damper, and turning to the step S2. Compared with the prior art, the invention has the advantages of effectively determining the performance of the damper, controlling the multi-stage vibration of the stay cable, improving the vibration reduction design precision of the stay cable, ensuring the stability and the service life of the stay cable structure and the like.
Description
Technical Field
The invention belongs to the technical field of vibration control of engineering structures, and relates to a cable multi-mode vibration control method which is characterized in that a damper is arranged near an anchoring point of a cable and the dependency between the performance of the damper and the vibration frequency is considered.
Background
The cable bearing structure is a very important civil construction structure, mainly comprising a cable-stayed bridge, a suspension bridge, a mast/tower structure and the like. Such structures have excellent spanning and shrugging capabilities, with spans or heights still developing and corresponding cables becoming longer and longer. The inhaul cable in the structure bears axial tension, the section size, the mass per unit length and the transverse rigidity of the inhaul cable are small, vibration is easy to occur, and the vibration has the characteristics of multiple modes and multiple mechanisms, so that the inhaul cable is a bottleneck for restricting the development of a cable structure.
At present, the most common control methods for inhaul cable vibration mainly comprise: (1) the surface of the cable sheath is treated by adopting an aerodynamic measure, the aerodynamic measure comprises the modes of winding a spiral line, pressing a pit and the like, and the vibration is reduced mainly by destroying the coupling mechanism of the cable and wind and rain; (2) the cable is additionally provided with a damper at a position close to an anchoring point of the cable, the cable is transversely connected with a structure (such as a tower and a beam) connected with the cable in the span, the energy dissipation capacity of the cable during transverse vibration is increased, and the purposes of vibration reduction and vibration suppression are achieved; (3) and the auxiliary cables are used for connecting the adjacent inhaul cables, so that the overall rigidity and the energy consumption capability of the cables are improved.
In the stay cable vibration reduction scheme, the scheme of comprehensively adopting pneumatic measures and a cable end damper is most widely applied. The damper plays a main energy consumption role and has damping and inhibiting effects on the vibration of different mechanisms and modes of the cable. In the design, a damper is generally arranged at one position between a cable and a beam, and the purpose is to aim at the low-order vibration mode of the cable within the range of 0-3.0 Hz. Since the cable is prone to wind and rain vibrations in this frequency band, the parameters of the damper are therefore optimized for these modes.
Meanwhile, theoretical and experimental researches of various existing dampers show that most of dampers have certain dependence on the performance and the vibration frequency. For example, at a fixed displacement amplitude, the damping coefficient of a viscous shear-type damper decreases and the stiffness coefficient increases as the vibration frequency increases. It is noted that the reduction of the damping coefficient with increasing frequency is advantageous for multi-order vibration control of the cable, since the optimal damping coefficient for high-order vibrations is smaller than the optimal damping coefficient for low-order modes. However, an increase in the stiffness coefficient impairs the damping performance of higher order vibrations. Therefore, the two damper performance indicators need to be considered together in the cable multimode vibration control design because of the different effects of the frequency dependence. The effect is accurately considered, the installation and the support height of the damper can be reduced on the premise of ensuring the cable vibration reduction effect, and the cost and the maintenance difficulty are reduced.
Disclosure of Invention
The invention aims to provide a cable multi-mode vibration control method considering the dependency between the performance of a damper and the vibration frequency for installing a viscous shear type damper at a position close to an anchoring point of a cable.
In order to achieve the purpose, the technical scheme of the invention is as follows: a cable multi-modal vibration control method taking into account the frequency dependence of damper performance, comprising the steps of:
s1: determining the minimum damping ratio of the stay cable through a Scruton number as a design threshold;
s2: testing the rigidity and damping characteristics under different frequency and amplitude conditions through a damper monomer test;
s3: according to the frequency of the cable in the mode below 3Hz, interpolating to obtain the rigidity and damping coefficient of the damper when the cable vibrates in the corresponding mode;
s4: comprising the following substeps:
s41, analyzing the damping effect of the damper on each order of vibration; s42, judging whether the damping effect meets the set threshold, if yes, keeping the current damping parameter unchanged, if not, S43 adjusting the damping parameter and the installation position, and going to step S2.
Further, all low-order modes which are easy to generate wind and rain vibration are designed and considered; the vibration frequency of the cable mode is between 0 and 3.0 Hz.
The used damper is firstly subjected to a monomer performance test, and the monomer test is used for testing the mechanical property of the damper under the periodic deformation conditions of different frequencies and amplitudes.
When the damper is tested in a single body mode, at least 4 frequencies are selected between 0.2Hz and 3.0Hz for testing; preferably, the test is carried out under the working conditions of 0.2Hz, 1Hz, 2Hz and 3 Hz.
During the single body test of the damper, after the deformation frequency of the test working condition is determined, at least 4 amplitudes with the amplitude between 0.5mm and 25mm are selected for testing; preferably four amplitudes of 1mm, 5mm, 10mm and 20mm are tested.
The damper is loaded for at least 20 cycles under the periodic forced deformation of determined frequency and amplitude, or the test can be stopped after 2 cycles after the damper output curve is observed to be stable.
And testing the force and displacement time course measured under each working condition (specific frequency and amplitude) according to the performance of the single damper, obtaining a corresponding speed time course according to numerical differentiation, and identifying the rigidity and the damping coefficient of the damper under the working condition by adopting a least square method according to a Kelvin-Voigt model.
During identification, a force-displacement relation time course of a damping force stabilization period in a damper monomer test is adopted, and at least 1 complete cycle of displacement and force-time curves are used.
The obtained rigidity and damping coefficient of the damper under various frequency and amplitude conditions are identified, interpolation is carried out, the rigidity and damping coefficient (interpolation under various amplitude conditions respectively) of the damper under various orders of vibration frequency corresponding to the damper are obtained, and preferably, an exponential interpolation function is selected.
After the rigidity and frequency characteristics of the damper under the vibration condition of each order of the cable are obtained, the additional damping of the damper to the vibration of each order of the cable is analyzed according to a characteristic equation considering the small-sag cable additional belt rigidity viscous damper system.
Further, in step S1, the Scruton number (S)c) The calculation formula of (2) is as follows:
wherein m is the mass per unit length (kg/m) of the cable, zeta is the modal damping ratio, and rho is the air density (kg/m)3) And D is the outer diameter (m) of the stay cable. The minimum scrub number required for stay cables of regular surfaces to suppress wind and rain vibration is Sc>10; for the surface-treated inhaul cable Sc>5. The solved damping ratio threshold value is represented as zetamin。
Further, step S2 includes the following sub-steps:
s21: determining performance parameters and an installation position of a damper;
s22: estimating the cable frequency;
s23: carrying out monomer test according to the substeps and test conditions;
s24: and identifying the rigidity coefficient and the damping coefficient of the damper according to the test result.
Further, in step S21, the damper performance parameters for the viscous shear damper include the viscosity of the selected medium, the thickness of the medium, the shear area, and the like; the viscous damper includes the characteristics of the viscous liquid, the size of the damping hole and the like.
Further, in step S22, the vibration frequency of the low-order vibration is 0 to 3.0Hz, specifically:
fn0≤3.0Hz
wherein f isn0In the vibration frequency of the cable in the state where no damper is installed (subscript 0 indicates the state where no damper is installed in the cable), n is an integer of 1,2,3, …, and indicates the mode order of the cable vibration. When the stay cable is long, the vibration frequency of the stay cable is calculated through a tension string model, and the method specifically comprises the following steps:
wherein H is the cable force (kN), and l is the total length (m) of the stay cable string; (m is the mass per unit length of the cable (kg/m), n is an integer of 1,2,3 and … and represents the modal order of cable vibration.)
When the cable length is longer, the influence of cable sag needs to be considered. Correspondingly, the odd-order vibration mode dimensionless circular frequency of the stay cable is passed through
As an initial value, iteration solution is carried out by adopting a fixed point or a Newton method, which specifically comprises the following steps:
wherein the content of the first and second substances,
the dimensionless circular frequency of the stay cable vibrating without the damper;
the dimensionless frequency of the even order vibration mode is:
in the calculation of dimensionless frequencies of odd-order vibration modes, λ2For dimensionless parameters related to the sag of the inhaul cable, the specific calculation formula is as follows:
wherein θ is an inclination angle (°) of the cable, E is an elastic modulus (GPa) of the cable, and a is an effective cross-sectional area (m) of the cable2) G is the acceleration of gravity (9.81 m/s)2)，LeThe length (m) of the stay cable after being stressed and extended is as follows:
sag parameter lambda of stay cable used in current cable-stayed bridge2The value of (2) is between 0 and 2.5, the sag mainly affects the first order vibration of the cable, and the first order vibration frequency in the cable surface affected by the sag is as follows:
further, in the step S23, a constant amplitude sine forced vibration test should be adopted; the single test for setting all the stay cable vibration frequencies as much as possible; selecting at least 4 frequencies between 0.2Hz and 3.0Hz for testing, and optimally selecting at least 0.2Hz, 1Hz, 2Hz and 3Hz working conditions for testing; setting a comparison test of different vibration amplitude working conditions under the same frequency, wherein the amplitude interval is 0.5-25 mm; at least 4 amplitudes are selected within the interval of 0.5-25 mm for testing, and four amplitudes of 1mm, 5mm, 10mm and 20mm are optimally selected. The total number N of the test working conditions is as follows:
N＝n1×n2
wherein n is1Number of vibration frequencies, n2Is the number of vibration amplitudes.
In order to stabilize the resistance curve in the test, the damper is loaded for at least 20 cycles under the periodic forced deformation of determined frequency and amplitude, or the test can be stopped after 2 cycles after the damper output curve is observed to be stable.
Further, in step S24, for the test result obtained in step S23, the dynamic characteristics of the damper are identified according to the Kelvin-Voigt model, and the resistance formula is as follows:
wherein k isdIs damper stiffness (kN/m), cdIs the damping coefficient (kN/m/s), v (t) is the damper deformation position (m),
the deformation velocity (m/s) can be obtained by numerically differentiating the displacement time course. In order to ensure the accuracy, the sampling frequency of the displacement measurement is not less than 100 Hz.
Further, in step S3, it is proposed that the interpolation formula takes an exponential form, for example:
wherein q isc,qkFrequency coefficients of damping coefficient and stiffness coefficient estimated values, bc,bkAre respectively a damping systemThe indexes of the numerical and rigidity coefficient estimated values are dimensionless and can be fitted by a least square method; c. CeThe damping coefficient obtained for the fitting has the unit (kN/m/s), keThe stiffness coefficient obtained for the fit is in units of (kN/m). During identification, a force-displacement relation time course of a damping force stabilization period in a damper monomer test is adopted, and at least 1 complete cycle of displacement and force-time curves are used.
Further, step S4: analyzing the damping effect of the damper on each order of vibration, judging whether the damping effect meets a set threshold value, and if so, keeping the current damping parameter unchanged; if not, the damping parameters are adjusted, and the process goes to step S2.
Comprising the following substeps:
s41: analyzing the damping effect of the damper on each order of vibration;
s42: judging whether the damping effect meets a set threshold value or not;
s43: damper parameters are adjusted, and damper position can also be adjusted if desired.
Further, in the step S41, the damper damping ratio ζ isnThe calculation formula is as follows:
ζn＝Im(βnl)/|βnl|
wherein ζnIs damping ratio of nth order vibration of the stay cable, n is order of the stay cable, betanThe wave number of the nth order vibration of the stay cable. For quasi-symmetric (n ═ 1,3, …) modes, βnThe solving formula of (2) is as follows:
where a' l-a is the distance between the damper and the distal cable anchor point. Considering that the damper is generally close to the cable anchoring end (generally, the distance of the cable from the nearest anchoring point is between 1% and 3% of the cable length), the following approximate formula can be found:
wherein a is the distance (m) between the damper installation position and the nearest anchoring end;
the wave number of the nth order vibration of the guy cable under the undamped condition,
λ2is a dimensionless parameter related to the sag of the stay cable; mu, eta and alpha are dimensionless quantities related to the rigidity coefficient and the damping coefficient,
wherein
In units of imaginary numbers. For antisymmetric-like modes (n-2, 4, …), βnThe solving formula of (2) is as follows:
also considering the damper located near the end point of the cable, approximately
Further, in the steps S42 and S43, the modal damping ratio ζ obtained by the damper-mounted wire is analyzed for all modes in which the vibration frequency of the wire is 3Hz or lowernAnd threshold value ζminComparison, if ζn≥ζminThen the design is finished; otherwise, the damper parameters and the installation position are adjusted, and the step S2 is returned.
The beneficial effects of the invention include:
(1) the method considers the frequency dependence of the damper performance, and realizes accurate estimation of the vibration mode vibration attenuation effect of the damper on the cable vibration frequency between 0Hz and 3 Hz.
(2) The accurate consideration of the frequency dependence of the damper performance can reduce the installation height of the damper, facilitate the installation and maintenance of the damper and reduce the manufacturing cost of the damper bracket.
(3) Meanwhile, the method is suitable for multi-mode vibration reduction of a newly-built inhaul cable structure and treatment of low-order vibration of an in-service inhaul cable-damper system.
Drawings
FIG. 1 is a flow chart of a cable multi-modal vibration control design method that takes into account the frequency dependence of damper performance.
Fig. 2(a) is a resistance-displacement diagram obtained by a damper single body test.
FIG. 2(b) is a resistance-velocity diagram obtained from the damper cell test.
FIG. 3 is a schematic diagram of the Kelvin-Voigt model.
Fig. 4(a) is a comparison graph of the measured value and the interpolation of the stiffness coefficient of the damper.
FIG. 4(b) is a comparison graph of the measured damping coefficient and the interpolation of the damper.
FIG. 5 is a comparison graph of multi-modal additional damping values obtained by considering frequency dependence of damper parameters and actual measurements.
Detailed Description
The invention is described in detail below with reference to the figures and specific embodiments.
The invention provides a practical cable multi-mode vibration control design method considering the performance frequency dependency of a damper, as shown in figure 1, comprising the following steps:
s1: determining the minimum damping ratio of the stay cable through a Scruton number as a design threshold;
s2: testing the rigidity and damping characteristics under different frequency and amplitude conditions through a damper monomer test;
s3: according to the frequency of the cable in the mode below 3Hz, interpolating to obtain the rigidity and damping coefficient of the damper when the cable vibrates in the corresponding mode;
s4: s41, analyzing the damping effect of the damper on each order of vibration, S42 judging whether the damping effect meets a set threshold, if so, keeping the current damping parameter unchanged, if not, S43 adjusting the damping parameter, and turning to the step S2.
Further, in step S1, the Scruton number (S)c) The calculation formula of (2) is as follows:
wherein m is the mass per unit length (kg/m) of the cable, zeta is the damping ratio, and rho is the air density (kg/m)3) And D is the outer diameter (m) of the stay cable. Minimum Scruton number (S) required for stay cables of regular surface to suppress wind and rain vibrationc) Is Sc>10; for the surface-treated inhaul cable Sc>5. Damping ratio threshold is expressed as ζmin。
Further, step S2 includes the following sub-steps:
s21: determining performance parameters and an installation position of a damper;
s22: estimating the cable frequency;
s23: carrying out monomer test according to the substeps and test conditions;
s24: and identifying the rigidity coefficient and the damping coefficient of the damper according to the test result.
Further, in step S21, the damper performance parameters for the viscous shear damper include the viscosity of the selected medium, the thickness of the medium, the shear area, and the like; the viscous damper includes the characteristics of the viscous liquid, the size of the damping hole and the like.
Further, in step S22, the vibration frequency of the low-order vibration is 0 to 3.0Hz, specifically:
fn0≤3.0Hz
wherein f isn0In the vibration frequency of the cable (subscript 0 indicates a state where the cable is not provided with any damper), n is an integer of 1,2,3, …, and indicates the mode order of the cable vibration. When the stay cable is long, the vibration frequency of the stay cable is calculated through a tension string model, and the method specifically comprises the following steps:
wherein H is the cable force (kN) and l is the total length (m) of the stay cable string.
When the cable length is longer, the influence of cable sag needs to be considered. Correspondingly, the odd-order vibration mode dimensionless circular frequency of the stay cable is passed through
As an initial value, iteration solution is carried out by adopting a fixed point or a Newton method, which specifically comprises the following steps:
wherein the content of the first and second substances,
the dimensionless circular frequency of the stay cable vibrating without the damper;
the dimensionless frequency of the even order vibration mode is:
in the calculation of dimensionless frequencies of odd-order vibration modes, λ2For dimensionless parameters related to the sag of the inhaul cable, the specific calculation formula is as follows:
wherein θ is an inclination angle (°) of the cable, E is an elastic modulus (GPa) of the cable, and a is an effective cross-sectional area (m) of the cable2) G is the acceleration of gravity (9.81 m/s)2)，LeThe length (m) of the stay cable after being stressed and extended is as follows:
sag parameter lambda of stay cable used in current cable-stayed bridge2The value of (2) is between 0 and 2.5, the sag mainly affects the first order vibration of the cable, and the first order vibration frequency in the cable surface affected by the sag is as follows:
further, in the step S23, the monomer test should adopt a constant amplitude sine forced vibration test; the single test for setting all the stay cable vibration frequencies as much as possible; selecting at least 4 frequencies between 0.2Hz and 3.0Hz for testing, and optimally selecting at least 0.2Hz, 1Hz, 2Hz and 3Hz working conditions for testing; setting a comparison test of different vibration amplitude working conditions under the same frequency, wherein the amplitude interval is 0.5-25 mm; at least 4 amplitudes are selected within the interval of 0.5-25 mm for testing, and four amplitudes of 1mm, 5mm, 10mm and 20mm are optimally selected. The total number N of the test working conditions is as follows:
N＝n1×n2
wherein n is1Number of vibration frequencies, n2Is the number of vibration amplitudes. The test results are shown in fig. 2(a) and 2 (b).
Further, as shown in fig. 2(a) and 2(b), in order to stabilize the resistance curve in the test, the damper is loaded for at least 20 cycles under the periodic forced deformation of determined frequency and amplitude, or the test can be stopped after 2 cycles after the damper output curve is observed to be stable.
Further, in step S24, for the test result obtained in step S23, the dynamic characteristics of the viscous shear-type damper are identified according to the Kelvin-Voigt model, as shown in fig. 3, and the resistance formula is as follows:
wherein k isdIs damper stiffness (kN/m), cdIs the damping coefficient (kN/m/s), v (t) is the damper deformation position (m),
the deformation velocity (m/s) can be obtained by numerically differentiating the displacement time course. In order to ensure the accuracy, the sampling frequency of the displacement measurement is not less than 100 Hz. The coefficient recognition results are schematically shown in fig. 4(a) and 4 (b).
Further, in step S3, it is proposed that the interpolation formula takes an exponential form, for example:
wherein q isc,qkFrequency coefficients of damping coefficient and stiffness coefficient estimated values, bc,bkThe indexes of the damping coefficient estimation value and the stiffness coefficient estimation value are respectively dimensionless and can be fitted by a least square method; c. CeThe damping coefficient obtained for the fitting has the unit (kN/m/s), keThe stiffness coefficient obtained for the fit is in units of (kN/m). During identification, a force-displacement relation time course of a damping force stabilization period in a damper monomer test is adopted, and at least 1 complete cycle of displacement and force-time curves are used. The coefficient interpolation results are shown in fig. 5.
Further, step S4: analyzing the damping effect of the damper on each order of vibration, judging whether the damping effect meets a set threshold value, and if so, keeping the current damping parameter unchanged; if not, the damping parameters are adjusted, and the process goes to step S2.
Comprising the following substeps:
s41: analyzing the damping effect of the damper on each order of vibration;
s42: judging whether the damping effect meets a set threshold value or not;
s43: damper parameters are adjusted, and damper position can also be adjusted if desired.
Further, in step S41, the damper damping ratio calculation formula is as follows:
ζn＝Im(βnl)/|βnl|
wherein ζnIs damping ratio of nth order vibration of the stay cable, n is order of the stay cable, betanThe wave number of the nth order vibration of the stay cable. For quasi-symmetric (n ═ 1,3, …) modes, βnThe solving formula of (2) is as follows:
where a' l-a is the distance between the damper and the distal cable anchor point. Considering that the damper is generally close to the cable anchoring end (generally, the distance of the cable from the nearest anchoring point is between 1% and 3% of the cable length), the following approximate formula can be found:
wherein a is the distance (m) between the damper installation position and the nearest anchoring end;
the wave number of the nth order vibration of the guy cable under the undamped condition,
λ2is a dimensionless parameter related to the sag of the stay cable; mu, eta, alpha are dimensionless quantities related to stiffness coefficient and damping coefficient
Wherein
In units of imaginary numbers. For antisymmetric-like modes, betanThe solving formula of (2) is as follows:
the approximation is:
further, in the steps S42 and S43, the analyzed damping ratio ζ isnAnd threshold value ζminComparison, if ζn≥ζminThen the design is finished; otherwise, the damper parameters and the installation position are adjusted, and the step S2 is returned.
Examples of the embodiments
The design of a viscous shear damper is carried out on one stay cable of a large-span cable-stayed bridge. The inhaul cable parameters are as follows:
l＝454.1m,m＝77.7kg/m,H＝5099.0kN,A＝9275mm2
θ＝27°,λ2＝1.5,D＝139mm
for the purpose of safety, the damping effect of the pneumatic measure on the surface of the cable is not considered, and the Scruton number m zeta/(rho D)2)>10 calculate the minimum damping ratio ζ required for the cable to suppress wind and rain vibrationmin. Wherein the air density rho is 1.225kg/m3Calculating to obtain the minimum damping ratio requirement of the stay cable as zetamin＝0.30％。
The frequency of the cord is calculated as follows
The cable length is large, the influence of cable sag is considered in the first-order frequency, and an equation is solved
So as to obtain the compound with the characteristics of,
further obtaining the frequency f when the damper is not arranged on the inhaul cable1＝0.299Hz,f2＝0.564Hz,f30.846Hz, …. A viscous shear damper is designed to be installed at a position 2.36% of the cable length away from the anchor point at the beam end of the cable.
Obtaining a resistance curve through a damper monomer test, and identifying the dynamic characteristic of the viscous shear type damper according to a Kelvin-Voigt model, wherein a resistance formula is as follows:
the damper stiffness coefficient and the damping coefficient were identified and the results are shown in fig. 4. Then interpolation is carried out to obtain the result of the damper under the condition of corresponding different vibration frequencies of the stay cable, and an exponential form is adopted in an interpolation formula, such as:
the interpolation function in this example is calculated as:
ce＝85.98ω-0.7132
ke＝648.4ω0.4141
the interpolation results are shown in fig. 4, and the stiffness and damping coefficient of the specific damper are shown in table 1. Because the damper amplitude is small in subsequent measurements, around 2mm, table 1 lists the results of interpolation based on the 2mm displacement amplitude test. Subsequently, in step S41, the damping effect ζ under different amplitude conditions of each order of frequency is analyzednAlso shown in Table 1.
Table 1 interpolation based on test results to obtain the rigidity and damping coefficient (displacement amplitude 2mm) of the damper under different frequency conditions
In order to check the accuracy of the analysis result, a damper field test is performed. The field test results are similar to the analysis results, see fig. 5, and the specific results are shown in table 2 below.
Table 2 results of field measurements of example guy cables
As a result, the damper designed by the invention meets the threshold standard zetamin0.30 percent, and meets the design requirement.
The embodiments described above are intended to facilitate one of ordinary skill in the art in understanding and using the present invention. It will be readily apparent to those skilled in the art that various modifications to these embodiments may be made, and the generic principles described herein may be applied to other embodiments without the use of the inventive faculty. Therefore, the present invention is not limited to the above embodiments, and those skilled in the art should make improvements and modifications within the scope of the present invention based on the disclosure of the present invention.
Claims (14)
1. A cable multi-mode vibration control method considering damper performance frequency dependency is characterized by comprising the following steps:
s1: determining the requirement of the minimum damping ratio of the stay cable as a design threshold value according to the Scruton number of the stay cable;
s2: testing the rigidity and damping characteristics under different frequency and amplitude conditions through a damper monomer test;
s3: according to the frequency of the vibration mode of the cable frequency below 3Hz, the rigidity and the damping coefficient of the damper when the cable vibrates in the corresponding mode are obtained by adopting an interpolation method;
s4: analyzing the damping effect of the damper on each order of modal vibration with the stay rope frequency below 3Hz, judging whether each order of damping effect meets a set threshold value, if so, keeping the current damper parameter and the installation position unchanged, if not, adjusting the damping parameter and the installation position, and turning to the step S2.
2. The cable multimode vibration control method considering damper performance frequency dependence according to claim 1, characterized in that: design considerations dictate that all low-order modes are prone to wind and rain vibration.
3. The cable multimode vibration control method considering damper performance frequency dependence according to claim 2, characterized in that: the vibration frequency of the cable mode is between 0 and 3.0 Hz.
4. The cable multimode vibration control method considering damper performance frequency dependence according to claim 1, characterized in that: the used damper is firstly subjected to a monomer performance test, and the monomer test is used for testing the mechanical property of the damper under the periodic deformation conditions of different frequencies and amplitudes.
5. The cable multimode vibration control method considering damper performance frequency dependence according to claim 3, characterized in that: when the damper is tested in a single body mode, at least 4 frequencies are selected between 0.2Hz and 3.0Hz for testing.
6. The cable multimode vibration control method considering damper performance frequency dependence according to claim 5, characterized in that: the test is carried out by selecting the working conditions of 0.2Hz, 1Hz, 2Hz and 3 Hz.
7. The cable multimode vibration control method considering damper performance frequency dependence according to claim 3, characterized in that: in the single damper test, at least 4 amplitudes with the amplitude between 0.5mm and 25mm are selected for testing after the deformation frequency of the test working condition is determined.
8. The cable multimode vibration control method considering damper performance frequency dependence according to claim 7, characterized in that: four amplitudes of 1mm, 5mm, 10mm and 20mm were selected for testing.
9. The cable multimode vibration control method considering damper performance frequency dependence according to claim 3, characterized in that: the damper is loaded for at least 20 cycles under the periodic forced deformation of determined frequency and amplitude, or the test can be stopped after 2 cycles after the damper output curve is observed to be stable.
10. The cable multimode vibration control method considering damper performance frequency dependence according to claim 3, characterized in that: and testing the force and displacement time courses measured under each working condition according to the performance of the single damper, obtaining the corresponding speed time course according to numerical differentiation, and identifying the rigidity and the damping coefficient of the damper under the working condition by adopting a least square method according to a Kelvin-Voigt model.
11. The cable multimode vibration control method considering damper performance frequency dependence according to claim 10, characterized in that: during identification, a force-displacement relation time course of a damping force stabilization period in a damper monomer test is adopted, and at least 1 complete cycle of displacement and force-time curves are used.
12. The cable multimode vibration control method considering damper performance frequency dependence according to claim 10, characterized in that: and identifying the rigidity and damping coefficient of the damper under the conditions of various frequencies and amplitudes, and interpolating to obtain the rigidity and damping coefficient of the damper under various orders of vibration frequencies of the corresponding cable of the damper.
13. The cable multimode vibration control method considering damper performance frequency dependence according to claim 12, characterized in that: an interpolation function in the form of an exponent is selected.
14. The cable multimode vibration control method considering damper performance frequency dependence according to claim 12, characterized in that: after the rigidity and frequency characteristics of the damper under the vibration condition of each order of the cable are obtained, the additional damping of the damper to the vibration of each order of the cable is analyzed according to a characteristic equation considering the small-sag cable additional belt rigidity viscous damper system.
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Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN113375789A (en) * | 2021-06-09 | 2021-09-10 | 北京科技大学 | Structural damping ratio identification method based on free vibration |
| CN116448362A (en) * | 2023-04-20 | 2023-07-18 | 中冶检测认证有限公司 | Vibration control method, vibration control device, and storage medium for multi-layered frame structure |
Citations (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102789547A (en) * | 2012-07-14 | 2012-11-21 | 福州大学 | Stay cable force calculation method taking actions of vibration attenuation damper into account |
| CN103410092A (en) * | 2013-07-24 | 2013-11-27 | 东南大学 | Semi-active control method for vibration of inclined stay cable |
| CN106092534A (en) * | 2016-06-08 | 2016-11-09 | 中国航空动力机械研究所 | Blade modal damping assay method |
| CN107165048A (en) * | 2017-05-16 | 2017-09-15 | 同济大学 | Damp type drag-line |
| CN109869438A (en) * | 2019-03-11 | 2019-06-11 | 中铁大桥科学研究院有限公司 | Multiple tuned mass dampers and hoist cable oscillation damping method |
| CN110704905A (en) * | 2019-09-16 | 2020-01-17 | 东南大学 | Optimal design method for viscous damper for stay cable multistage modal vibration control |
-
2020
- 2020-08-28 CN CN202010884222.XA patent/CN112130599B/en active Active
Patent Citations (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102789547A (en) * | 2012-07-14 | 2012-11-21 | 福州大学 | Stay cable force calculation method taking actions of vibration attenuation damper into account |
| CN103410092A (en) * | 2013-07-24 | 2013-11-27 | 东南大学 | Semi-active control method for vibration of inclined stay cable |
| CN106092534A (en) * | 2016-06-08 | 2016-11-09 | 中国航空动力机械研究所 | Blade modal damping assay method |
| CN107165048A (en) * | 2017-05-16 | 2017-09-15 | 同济大学 | Damp type drag-line |
| CN109869438A (en) * | 2019-03-11 | 2019-06-11 | 中铁大桥科学研究院有限公司 | Multiple tuned mass dampers and hoist cable oscillation damping method |
| CN110704905A (en) * | 2019-09-16 | 2020-01-17 | 东南大学 | Optimal design method for viscous damper for stay cable multistage modal vibration control |
Non-Patent Citations (1)
| Title |
|---|
| 陈林: "《用于阻尼器试验的斜拉索等效模型建模》", 《工程力学（增刊II）》 * |
Cited By (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN113375789A (en) * | 2021-06-09 | 2021-09-10 | 北京科技大学 | Structural damping ratio identification method based on free vibration |
| CN113375789B (en) * | 2021-06-09 | 2023-03-14 | 北京科技大学 | Structural damping ratio identification method based on free vibration |
| CN116448362A (en) * | 2023-04-20 | 2023-07-18 | 中冶检测认证有限公司 | Vibration control method, vibration control device, and storage medium for multi-layered frame structure |
| CN116448362B (en) * | 2023-04-20 | 2024-02-27 | 中冶检测认证有限公司 | Vibration control method, vibration control device, and storage medium for multi-layered frame structure |
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