CN102789547B - Stay cable force calculation method taking actions of vibration attenuation damper into account - Google Patents
Stay cable force calculation method taking actions of vibration attenuation damper into account Download PDFInfo
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- CN102789547B CN102789547B CN201210242817.0A CN201210242817A CN102789547B CN 102789547 B CN102789547 B CN 102789547B CN 201210242817 A CN201210242817 A CN 201210242817A CN 102789547 B CN102789547 B CN 102789547B
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Abstract
The invention relates to a stay cable force calculation method taking actions of a vibration attenuation damper into account. The method comprises the following steps: measuring the vibration frequency f2 of a stay cable after the installation of the vibration attenuation damper; simplifying the vibration attenuation damper as an elastic support, and taking the actions of the elastic support into account in load items of a motion equation taking bending stiffness into account in the stay cable surface; calculating the equivalent stiffness value of the vibration attenuation damper; substituting the equivalent stiffness value of the vibration attenuation damper, the installation position, the self-characteristic value of the stay cable and the estimated stay cable force value into the motion equation taking bending stiffness into account in the stay cable surface, and solving by using a finite difference numerical method to obtain a computed vibration frequency f3 of the stay cable; if the difference between the computed vibration frequency f3 and the measured frequency f2 is not within the allowed error band, then regulating the estimated stay cable force value, and computing again until the difference between the computed vibration frequency f3 and the measured frequency f2 is within the allowed error band; and regulating an estimated stay cable force value which is the actual stay cable force value. The method is beneficial to improving the accuracy of the computed result of the stay cable force.
Description
Technical field
The present invention relates to Design of Cable-Stayed Bridge technical field, particularly a kind of stay cable force computing method considering damper effect.
Background technology
Existing cable-stayed bridge generally applies damper to avoid the significantly vibration of suspension cable.The installation of damper can change the actual measurement fundamental frequency of suspension cable, but can not change the actual Suo Li of suspension cable.Therefore, in the Suo Li computation process of suspension cable, the effect of damper should be considered.By considering the effect of damper in the damping term of the suspension cable equation of motion, obtained the actual Suo Li of suspension cable by this equation of motion of Numerical Methods Solve of complex eigenvalues.Because this kind of method is comparatively loaded down with trivial details, therefore, the approximate formula method that in engineering, conventional equivalent rope is long calculates the inclined cable force value considering damper, namely before and after supposing damper installation, Suo Li computing formula is constant, and after utilizing adjustment, the Equivalent Calculation rope length of suspension cable and the suspension cable practical frequency after installing damper calculate the actual rope force value of suspension cable.Along with the development of computing technique particularly numerical computation method, if need to obtain more accurate rope force value, the suspension cable equation of motion of Numerical Methods Solve consideration damper effect just should be adopted.
Summary of the invention
The object of the present invention is to provide a kind of stay cable force computing method considering damper effect, the method is conducive to the accuracy improving stay cable force result of calculation.
For achieving the above object, the technical solution used in the present invention is: a kind of stay cable force computing method considering damper effect, comprise the following steps:
Step 1: install before damper at suspension cable, measures the vibration frequency f1 installing suspension cable before damper, and by calculating the rope force value T installing suspension cable before damper; After installing damper, again measure the vibration frequency f2 installing suspension cable after damper;
Step 2: for the suspension cable installing damper, is reduced to resiliency supported by described damper, and considers the effect of described resiliency supported in the load item of suspension cable in-plane moving equation considering bending stiffness;
Step 3: assuming that constant in the rope force value of installing described suspension cable before and after damper, and preset the equivalent stiffness value of damper, the rope force value of the segmented numbers such as the default rigidity value of damper, installation site, suspension cable elastic modulus, suspension cable area of section, suspension cable external diameter, suspension cable line density, suspension cable level inclination, inclined cable length, suspension cable and suspension cable is substituted into the suspension cable in-plane moving equation considering bending stiffness, and utilize the numerical method of finite difference to solve, obtain the calculated rate f3 of Inclined Cable Vibration; Calculate the difference between the calculated rate f3 of described Inclined Cable Vibration and the vibration frequency f2 of actual measurement, if described difference exceeds error allowed band, then adjust the default rigidity value of damper, and recalculate the calculated rate of Inclined Cable Vibration, until the difference of the calculated rate f3 of Inclined Cable Vibration and the vibration frequency f2 of actual measurement drops in error allowed band, thus obtain the equivalent stiffness value of damper;
Step 4: stay cable force is estimated, by the segmented numbers such as the equivalent stiffness value of described damper, installation site, suspension cable elastic modulus, suspension cable area of section, suspension cable external diameter, suspension cable line density, suspension cable level inclination, inclined cable length, suspension cable and the suspension cable in-plane moving equation estimating rope force value substitution consideration bending stiffness, and utilize the numerical method of finite difference to solve, obtain the calculated rate f4 of Inclined Cable Vibration;
Step 5: calculate the difference between the calculated rate f4 of described Inclined Cable Vibration and the vibration frequency f2 of actual measurement, if described difference exceeds error allowed band, then rope force value is estimated in adjustment, and return step 4, recalculate the calculated rate of Inclined Cable Vibration, until the difference of the calculated rate f4 of Inclined Cable Vibration and the vibration frequency f2 of actual measurement drops in error allowed band;
Step 6: the difference of the calculated rate f4 of Inclined Cable Vibration and the vibration frequency f2 of actual measurement is dropped on and estimates the actual rope force value that rope force value is exactly suspension cable in error allowed band.
The invention has the beneficial effects as follows the accuracy and precision that can improve stay cable force result of calculation, and can consider that suspension cable self bendind rigidity is on the impact of stay cable force measurement result.
Below in conjunction with drawings and the specific embodiments, the present invention is described in further detail.
Accompanying drawing explanation
Fig. 1 is the geometric configuration schematic diagram that the embodiment of the present invention is provided with the suspension cable of damper.
Fig. 2 is the discrete model schematic diagram that the embodiment of the present invention is provided with the suspension cable of damper.
Fig. 3 is the workflow diagram of the embodiment of the present invention.
Embodiment
The present invention considers the stay cable force computing method of damper effect, as shown in Figure 3, comprises the following steps:
Step 1: install before damper at suspension cable, measures the vibration frequency f1 installing suspension cable before damper, and by calculating the rope force value T installing suspension cable before damper; After installing damper, again measure the vibration frequency f2 installing suspension cable after damper;
Step 2: for the suspension cable installing damper, is reduced to resiliency supported by described damper, and considers the effect of described resiliency supported in the load item of suspension cable in-plane moving equation considering bending stiffness;
Step 3: assuming that constant in the rope force value of installing described suspension cable before and after damper, and preset the equivalent stiffness value of damper, the rope force value of the segmented numbers such as the default rigidity value of damper, installation site, suspension cable elastic modulus, suspension cable area of section, suspension cable external diameter, suspension cable line density, suspension cable level inclination, inclined cable length, suspension cable and suspension cable is substituted into the suspension cable in-plane moving equation considering bending stiffness, and utilize the numerical method of finite difference to solve, obtain the calculated rate f3 of Inclined Cable Vibration; Calculate the difference between the calculated rate f3 of described Inclined Cable Vibration and the vibration frequency f2 of actual measurement, if described difference exceeds error allowed band, then adjust the default rigidity value of damper, and recalculate the calculated rate of Inclined Cable Vibration, until the difference of the calculated rate f3 of Inclined Cable Vibration and the vibration frequency f2 of actual measurement drops in error allowed band, the difference of the calculated rate f3 of Inclined Cable Vibration and the vibration frequency f2 of actual measurement is dropped on and in error allowed band, estimates the equivalent stiffness value that rigidity value is exactly the damper obtained required for us;
Step 4: stay cable force is estimated, by the segmented numbers such as the equivalent stiffness value of described damper, installation site, suspension cable elastic modulus, suspension cable area of section, suspension cable external diameter, suspension cable line density, suspension cable level inclination, inclined cable length, suspension cable and the suspension cable in-plane moving equation estimating rope force value substitution consideration bending stiffness, and utilize the numerical method of finite difference to solve, obtain the calculated rate f4 of Inclined Cable Vibration;
Step 5: calculate the difference between the calculated rate f4 of described Inclined Cable Vibration and the vibration frequency f2 of actual measurement, if described difference exceeds error allowed band, then rope force value is estimated in adjustment, and return step 4, recalculate the calculated rate of Inclined Cable Vibration, until the difference of the calculated rate f4 of Inclined Cable Vibration and the vibration frequency f2 of actual measurement drops in error allowed band;
Step 6: the difference of the calculated rate f4 of Inclined Cable Vibration and the vibration frequency f2 of actual measurement is dropped on and estimates the actual rope force value that rope force value is exactly suspension cable in error allowed band.
The geometric configuration of the suspension cable of damper is installed as shown in Figure 1.Definition coordinate system (x, z) be global coordinate system, coordinate system (x*, z*) be overall secant coordinate system, namely x direction is horizontal direction, z direction is vertical direction, x* direction is suspension cable two end point connecting line direction, z* direction is vertical with x* direction and with suspension cable at same plane, described damper is installed on the certain position of described suspension cable two ends respectively, does not consider damping effect of damper, only considers its supporting effect, described damper is reduced to the linear elasticity with certain support stiffness to support, by linear elasticity anchorage force F
dx(t) and F
dzt () substitutes into the suspension cable dimensionless equation of motion considering bending stiffness, obtain suspension cable dimensionless equation of motion (1) and (2) of considering damper effect:
(1)
(2)
By described suspension cable along tangential n decile, the effect of described damper is reduced to a linear elasticity concentrated force, act on the node of the subdivisions such as suspension cable, the position of Operational node and the installation site of corresponding described damper, discrete model as shown in Figure 2, finite difference discrete processes is carried out to equation (1) and (2), can obtain:
(3)
(4)
In formula (1), (2), (3), (4),
,
,
,
x* be edge
x* direction coordinate,
z* be edge
z* direction coordinate,
salong suspension cable length direction coordinate,
lfor the distance between suspension cable two-end-point,
for suspension cable level inclination,
dimensionless axially extra dynamic tension,
,
axial extra dynamic tension,
hthe horizontal component of cable tension,
dimensionless axial tensile force,
, T is suspension cable axial tensile force,
,
, u*, w* be
x*with
z*the dynamic displacement in direction,
the ratio of suspension cable axial rigidity and horizontal pull,
,
the ratio of bending stiffness and axial rigidity,
, E is suspension cable elastic modulus, and A is suspension cable cross-sectional area, and I is suspension cable bendind rigidity,
,
dimensionless time,
the single order circular frequency without the oblique string of sag,
,
be the component of suspension cable initial tension along x* direction, m is suspension cable line density,
the parameter quoted in formulation process,
,
it is the extra dynamic tension edge of suspension cable
x* the component in direction, i be suspension cable discrete after section number (as shown in Figure 2), t is the time; N is the number of damper,
dirac delta function,
,
that i-th damper acts on respectively
the longitudinal damping power at place and horizontal damping force,
,
,
represent i-th damper longitudinal damping power stiffness coefficient,
the linear deformation size of i-th damper,
represent i-th damper horizontal damping force stiffness coefficient,
represent the transversely deforming size of i-th damper;
Thus obtain discrete after movement difference equations matrix form KW=P, solving of eigenwert and proper vector is carried out to matrix K, calculated rate and the vibration shape of suspension cable can be calculated.
In step 1, before installing damper, the computing method of the rope force value T of suspension cable comprise the following steps:
Step 11: the vibration of suspension cable is measured, and spectrum analysis is carried out to measurement result, obtain the vibration frequency f1 surveyed; Stay cable force is estimated, obtains estimating rope force value;
Step 12: by the segmented numbers such as suspension cable elastic modulus, suspension cable area of section, suspension cable external diameter, suspension cable line density, suspension cable level inclination, inclined cable length, suspension cable and the suspension cable in-plane moving equation estimating rope force value substitution consideration bending stiffness, and utilize the numerical method of finite difference to solve, obtain the calculated rate of Inclined Cable Vibration;
Step 13: calculate the difference between the calculated rate of Inclined Cable Vibration and the vibration frequency of actual measurement, if described difference is in error allowed band, then judge to estimate the actual rope force value that namely rope force value is suspension cable, algorithm terminates; If described difference exceeds error allowed band, then rope force value is estimated in adjustment, and return step 12 and carry out loop iteration, until the difference of the calculated rate of Inclined Cable Vibration and the vibration frequency of actual measurement drops in error allowed band, after adjustment, estimate the actual rope force value that rope force value is suspension cable;
When calculating the calculated rate of Inclined Cable Vibration, only consider equation linear term and do not consider external force, considering that the suspension cable dimensionless equation of motion of bending stiffness and sag is:
(5)
(6)
Finite difference discrete processes is carried out to equation (5) and (6), can obtain:
(7)
(8)
In formula (5), (6), (7), (8),
,
,
,
x* be edge
x* direction coordinate,
z* be edge
z* direction coordinate,
salong suspension cable length direction coordinate,
lfor the distance between suspension cable two-end-point,
for suspension cable level inclination,
dimensionless axially extra dynamic tension,
,
axial extra dynamic tension,
hthe horizontal component of cable tension,
dimensionless axial tensile force,
, T is suspension cable axial tensile force,
,
, u*, w* be
x*with
z*the dynamic displacement in direction,
the ratio of suspension cable axial rigidity and horizontal pull,
,
the ratio of bending stiffness and axial rigidity,
, E is suspension cable elastic modulus, and A is suspension cable cross-sectional area, and I is suspension cable bendind rigidity,
,
dimensionless time,
the single order circular frequency without the oblique string of sag,
,
be the component of suspension cable initial tension along x* direction, m is suspension cable line density;
the component of the extra dynamic tension of suspension cable along x* direction, i be suspension cable discrete after section number, t is the time;
Thus obtain the suspension cable equation of motion discrete after matrix form be: KW=P, solving of eigenwert and proper vector is carried out to matrix K, calculated rate and the vibration shape of Inclined Cable Vibration can be calculated.
Be more than preferred embodiment of the present invention, all changes done according to technical solution of the present invention, when the function produced does not exceed the scope of technical solution of the present invention, all belong to protection scope of the present invention.
Claims (2)
1. consider stay cable force computing method for damper effect, it is characterized in that: comprise the following steps:
Step 1: install before damper at suspension cable, measures the vibration frequency f1 installing suspension cable before damper, and by calculating the rope force value T installing suspension cable before damper; After installing damper, again measure the vibration frequency f2 installing suspension cable after damper;
Step 2: for the suspension cable installing damper, is reduced to resiliency supported by described damper, and considers the effect of described resiliency supported in the load item of suspension cable in-plane moving equation considering bending stiffness;
Step 3: assuming that constant in the rope force value of installing described suspension cable before and after damper, and preset the equivalent stiffness value of damper, the rope force value of the segmented numbers such as the equivalent stiffness value of damper, installation site, suspension cable elastic modulus, suspension cable area of section, suspension cable external diameter, suspension cable line density, suspension cable level inclination, inclined cable length, suspension cable and suspension cable is substituted into the suspension cable in-plane moving equation considering bending stiffness, and utilize the numerical method of finite difference to solve, obtain the calculated rate f3 of Inclined Cable Vibration; Calculate the difference between the calculated rate f3 of described Inclined Cable Vibration and the vibration frequency f2 of actual measurement, if described difference exceeds error allowed band, then adjust the default rigidity value of damper, and recalculate the calculated rate of Inclined Cable Vibration, until the difference of the calculated rate f3 of Inclined Cable Vibration and the vibration frequency f2 of actual measurement drops in error allowed band, thus obtain the equivalent stiffness value of damper;
Step 4: stay cable force is estimated, by the segmented numbers such as the equivalent stiffness value of described damper, installation site, suspension cable elastic modulus, suspension cable area of section, suspension cable external diameter, suspension cable line density, suspension cable level inclination, inclined cable length, suspension cable and the suspension cable in-plane moving equation estimating rope force value substitution consideration bending stiffness, and utilize the numerical method of finite difference to solve, obtain the calculated rate f4 of Inclined Cable Vibration;
Step 5: calculate the difference between the calculated rate f4 of described Inclined Cable Vibration and the vibration frequency f2 of actual measurement, if described difference exceeds error allowed band, then rope force value is estimated in adjustment, and return step 4, recalculate the calculated rate of Inclined Cable Vibration, until the difference of the calculated rate f4 of Inclined Cable Vibration and the vibration frequency f2 of actual measurement drops in error allowed band;
Step 6: the difference of the calculated rate f4 of Inclined Cable Vibration and the vibration frequency f2 of actual measurement is dropped on and estimates the actual rope force value that rope force value is exactly suspension cable in error allowed band;
Wherein, definition coordinate system (x, z) be global coordinate system, coordinate system (x*, z*) be overall secant coordinate system, described damper is installed on the certain position of described suspension cable two ends respectively, described damper is reduced to the linear elasticity with certain support stiffness and supports, by linear elasticity anchorage force F
dx(t) and F
dzt () substitutes into the suspension cable dimensionless equation of motion considering bending stiffness, obtain suspension cable dimensionless equation of motion (1) and (2) of considering damper effect:
(1)
(2)
By described suspension cable along tangential n decile, the effect of described damper is reduced to a linear elasticity concentrated force, act on the node of the subdivisions such as suspension cable, the position of Operational node and the installation site of corresponding described damper, finite difference discrete processes is carried out to equation (1) and (2), can obtain:
(3)
(4)
In formula (1), (2), (3), (4),
,
,
,
salong suspension cable length direction coordinate,
lfor the distance between suspension cable two-end-point,
θfor suspension cable level inclination,
dimensionless axially extra dynamic tension,
,
axial extra dynamic tension,
hthe horizontal component of cable tension,
dimensionless axial tensile force,
, T is suspension cable axial tensile force,
,
, u*, w* be
x*with
z*the dynamic displacement in direction,
k 2the ratio of suspension cable axial rigidity and horizontal pull,
,
δthe ratio of bending stiffness and axial rigidity,
, E is suspension cable elastic modulus, and A is suspension cable cross-sectional area, and I is suspension cable bendind rigidity,
ι=
ω 0 t,
ιdimensionless time,
ω 0the single order circular frequency without the oblique string of sag,
, H* is the component of suspension cable initial tension along x* direction, and m is suspension cable line density, and h* is the extra dynamic tension edge of suspension cable
x* the component in direction, i be suspension cable discrete after section number, t is the time; N is the number of damper,
dirac delta function,
f dxi ,
f dzi that i-th damper acts on respectively
x=
x d the longitudinal damping power at place and horizontal damping force,
,
,
k dxi represent i-th damper longitudinal damping power stiffness coefficient,
u di the linear deformation size of i-th damper,
k dzi represent i-th damper horizontal damping force stiffness coefficient,
w di represent the transversely deforming size of i-th damper;
Thus obtain discrete after movement difference equations matrix form KW=P, solving of eigenwert and proper vector is carried out to matrix K, calculated rate and the vibration shape of Inclined Cable Vibration can be calculated.
2. the stay cable force computing method of consideration damper according to claim 1 effect, is characterized in that: in step 1, and before installing damper, the computing method of the rope force value T of suspension cable comprise the following steps:
Step 11: the vibration of suspension cable is measured, and spectrum analysis is carried out to measurement result, obtain the vibration frequency f1 surveyed; Stay cable force is estimated, obtains estimating rope force value;
Step 12: by the segmented numbers such as suspension cable elastic modulus, suspension cable area of section, suspension cable external diameter, suspension cable line density, suspension cable level inclination, inclined cable length, suspension cable and the suspension cable in-plane moving equation estimating rope force value substitution consideration bending stiffness, and utilize the numerical method of finite difference to solve, obtain the calculated rate of Inclined Cable Vibration;
Step 13: calculate the difference between the calculated rate of Inclined Cable Vibration and the vibration frequency of actual measurement, if described difference is in error allowed band, then judge to estimate the actual rope force value that namely rope force value is suspension cable, algorithm terminates; If described difference exceeds error allowed band, then rope force value is estimated in adjustment, and return step 12 and carry out loop iteration, until the difference of the calculated rate of Inclined Cable Vibration and the vibration frequency of actual measurement drops in error allowed band, after adjustment, estimate the actual rope force value that rope force value is suspension cable;
When calculating the calculated rate of Inclined Cable Vibration, only consider equation linear term and do not consider external force, considering that the suspension cable dimensionless equation of motion of bending stiffness and sag is:
(5)
(6)
Finite difference discrete processes is carried out to equation (5) and (6), can obtain:
(7)
(8)
In formula (5), (6), (7), (8),
,
,
,
salong suspension cable length direction coordinate,
lfor the distance between suspension cable two-end-point,
θfor suspension cable level inclination,
dimensionless axially extra dynamic tension,
,
axial extra dynamic tension,
hthe horizontal component of cable tension,
dimensionless axial tensile force,
, T is suspension cable axial tensile force,
,
, u*, w* be
x*with
z*the dynamic displacement in direction,
k 2the ratio of suspension cable axial rigidity and horizontal pull,
,
δthe ratio of bending stiffness and axial rigidity,
, E is suspension cable elastic modulus, and A is suspension cable cross-sectional area, and I is suspension cable bendind rigidity,
ι=
ω 0 t,
ιdimensionless time,
ω 0the single order circular frequency without the oblique string of sag,
, H* is the component of suspension cable initial tension along x* direction, and m is suspension cable line density; H* is the component of the extra dynamic tension of suspension cable along x* direction, i be suspension cable discrete after section number, t is the time;
Thus obtain the suspension cable equation of motion discrete after matrix form be: KW=P, solving of eigenwert and proper vector is carried out to matrix K, calculated rate and the vibration shape of Inclined Cable Vibration can be calculated.
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| CN105674895B (en) * | 2016-04-19 | 2018-11-27 | 福州大学 | The calculation method of non-cpntact measurement drag-line Nonlinear Dynamic strain |
| CN107014543A (en) * | 2017-05-02 | 2017-08-04 | 中铁大桥科学研究院有限公司 | A kind of cord force of cable-stayed bridge method of testing |
| CN107766676B (en) * | 2017-11-13 | 2021-05-11 | 东南大学 | Stay cable equivalent elastic modulus calculation method considering sag effect |
| CN111783201B (en) * | 2020-06-21 | 2022-07-01 | 西北工业大学 | Rapid analysis method for dynamic characteristics of three-span self-anchored suspension bridge |
| CN112050984B (en) * | 2020-08-07 | 2022-03-08 | 中铁大桥勘测设计院集团有限公司 | Method for obtaining stay cable tension calculation parameter K value |
| CN112130599B (en) * | 2020-08-28 | 2022-02-25 | 同济大学 | Cable multi-mode vibration control method considering damper performance frequency dependency |
| CN112651072B (en) * | 2021-01-06 | 2023-08-22 | 华南理工大学 | Suspension bridge double-sling parameter identification method based on cable network model |
| CN114741767B (en) * | 2022-04-24 | 2024-01-19 | 河海大学 | Stay cable force calculation method considering sag inclination angle bending rigidity at the same time |
| CN115217235B (en) * | 2022-08-23 | 2023-07-21 | 武汉理工大学 | Intelligent vibration reduction system and method for round shell structure |
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| CN101586996A (en) * | 2009-06-26 | 2009-11-25 | 贵州师范大学 | Cable force prediction method of cable stayed bridge based on artificial neural network |
| CN101762346B (en) * | 2009-12-31 | 2011-07-13 | 北京市建筑工程研究院 | Method for measuring rope force of multi-span steel stay rope by using multi-frequency method |
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