CN112000144A - Stress belt bridge vehicle-induced vibration control method based on eddy current tuned mass damper - Google Patents

Stress belt bridge vehicle-induced vibration control method based on eddy current tuned mass damper Download PDF

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CN112000144A
CN112000144A CN202010817753.7A CN202010817753A CN112000144A CN 112000144 A CN112000144 A CN 112000144A CN 202010817753 A CN202010817753 A CN 202010817753A CN 112000144 A CN112000144 A CN 112000144A
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肖祥
张贺
余俊伟
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Wuhan University of Technology WUT
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Abstract

The invention relates to the technical field of bridge engineering, in particular to a stress belt bridge vehicle-induced vibration control method based on an eddy current tuned mass damper, which comprises the following steps: respectively solving dynamic responses in an uncontrolled state and a controlled state aiming at a vehicle stress belt bridge system; the controlled state is that a vehicle stress belt bridge system is added with a vortex tuned mass damper; the uncontrolled state is that no eddy current tuned mass damper is added in the stress belt bridge system of the vehicle; establishing a response surface model based on the eddy current tuned mass damper; constructing a damper parameter optimization objective function according to the peak values of the dynamic response in the uncontrolled state and the controlled state; optimizing the target function and the response surface model by using the damper parameters, optimizing the damper parameters and determining the optimal damper parameters; and setting the stress belt bridge system of the vehicle according to the optimal damper parameters. The invention is suitable for a nonlinear coupling system, and achieves a better bridge vibration control effect by using the eddy current tuned mass damper.

Description

Stress belt bridge vehicle-induced vibration control method based on eddy current tuned mass damper
Technical Field
The invention relates to the technical field of bridge engineering, in particular to a stress belt bridge vehicle-induced vibration control method based on an eddy current tuned mass damper.
Background
Currently, there is work focused on linear vibration control using conventional tuned mass dampers for the vibration control of stressed vehicular belt bridges, and this method assumes vibration control of a linear vehicular belt bridge system, and studies the response in this case. The above method has two problems: firstly, the method is not suitable for vibration control of a nonlinear vehicle bridge system, and the system control efficiency is poor. And secondly, the response measured at the same time cannot reflect the actual situation, and the error brought by analysis under a specific condition is larger.
Disclosure of Invention
In order to solve the technical problems, the stress belt bridge vehicle-induced vibration control method based on the eddy current tuned mass damper is suitable for a nonlinear coupling system, and achieves a better bridge vibration control effect by using the eddy current tuned mass damper.
The invention provides a stress belt bridge vehicle-induced vibration control method based on an eddy current tuned mass damper, which is characterized by comprising the following steps of:
respectively solving dynamic responses in an uncontrolled state and a controlled state aiming at a vehicle stress belt bridge system; the controlled state is that a vehicle stress belt bridge system is added with a vortex tuned mass damper; the uncontrolled state is that no eddy current tuned mass damper is added in the stress belt bridge system of the vehicle;
establishing a response surface model based on the eddy current tuned mass damper;
constructing a damper parameter optimization objective function according to the peak values of the dynamic response in the uncontrolled state and the controlled state;
optimizing the target function and the response surface model by using the damper parameters, optimizing the damper parameters and determining the optimal damper parameters;
and setting the stress belt bridge system of the vehicle according to the optimal damper parameters.
Further, the respectively solving the dynamic responses in the uncontrolled state and the controlled state for the vehicle stress belt bridge system specifically includes:
establishing an incremental equation of motion of a stress belt bridge system of the vehicle;
setting damper parameters in a preset range, constructing a response solution iterative algorithm, and solving an incremental motion equation of the vehicle stress belt bridge system so as to respectively obtain dynamic responses in an uncontrolled state and a controlled state.
Still further, the dynamic response includes: bridge displacement, bridge acceleration, and vehicle acceleration.
Still further, the incremental equation of motion of the vehicle stress belt bridge system is as follows:
Figure BDA0002633333600000021
in equation (1), wherein M, C and K represent the mass, damping and stiffness matrices of the vehicle stress belt bridge system, respectively; q, F and Fr represent the degree of freedom, load and resistance vectors of the vehicle stress belt bridge system, respectively;
when the vehicle stress belt bridge system is in an uncontrolled state, matrices M, C and K, and vectors q, F, and Fr are as follows:
Figure BDA0002633333600000022
Figure BDA0002633333600000023
in equations (2) and (3), subscript v represents a vehicle moving on the bridge, b represents a bridge, and d represents a damper.
Still further, the constructing a response solution iterative algorithm to solve the incremental equation of motion of the vehicle stress belt bridge system specifically includes:
rewriting the incremental motion equation based on a Wilson-theta method and a Taylor formula;
and (5) setting an iteration condition, and solving the rewritten incremental motion equation.
Still further, the rewritten incremental equation of motion is:
Figure BDA0002633333600000024
k in formula (4)tThe effective tangential stiffness matrix is obtained by:
Figure BDA0002633333600000025
the iteration condition is as follows:
Figure BDA0002633333600000026
in formula (6), | q | non-woven phosphor∞Represents the infinite norm of the vector, and η is a convergence coefficient.
In the above technical solution, the dynamic response expressions in the uncontrolled state and the controlled state are:
Figure BDA0002633333600000031
in the formula (7), the first and second groups,
Figure BDA0002633333600000032
preferably, the response surface model is:
Figure BDA0002633333600000033
in the formula (8), the first and second groups,
Figure BDA0002633333600000034
a2＝2a0，
Figure BDA0002633333600000035
and x represents a damper parameter vector to be optimized.
Preferably, the peak of the dynamic response comprises: the peak value of bridge displacement, the peak value of bridge acceleration and the peak value of vehicle acceleration;
the damper parameter optimization objective function is as follows:
Max(J(χ))＝Max(β1Jby+β2Jba+β3Jba) (9)
in formula (9), betaj(j-1-3) represents a weighting factor satisfying β1+β2+β3＝1；Jby、JbaAnd JvaRespectively representing the target functions of bridge displacement, bridge acceleration and vehicle acceleration.
Preferably, the expression of the objective function of the bridge displacement, the bridge acceleration and the vehicle acceleration is as follows:
Figure BDA0002633333600000036
Figure BDA0002633333600000037
Figure BDA0002633333600000038
in the formulae (10) to (12), n1Number of bridge displacement test points, n2Representing the number of bridge acceleration test points, n3Representing the number of vehicle acceleration test points; gamma raybyiIs a control target function of bridge displacement, gammabaiIs a control target function of bridge acceleration, gammavaiFor a control objective function of vehicle acceleration, the expression is as follows:
Figure BDA0002633333600000039
Figure BDA00026333336000000310
Figure BDA00026333336000000311
in the formulae (13) to (15), ybi、abiAnd aviRespectively representing a bridge displacement peak value, a bridge acceleration peak value and a vehicle acceleration peak value in an uncontrolled state;
Figure BDA00026333336000000312
and
Figure BDA00026333336000000313
respectively representing the displacement peak value of the bridge, the acceleration peak value of the bridge and the acceleration peak value of the vehicle in a controlled state.
In the invention, the vehicle stress belt bridge system is a nonlinear coupling system, and parameters of a damper (vortex tuned mass damper) are optimized by establishing a related incremental motion equation and a response calculation method on the basis of the vehicle stress belt bridge system, so that the damper can achieve a better bridge vibration control effect.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the drawings without creative efforts.
FIG. 1 is a schematic flow chart of a method according to an embodiment of the present invention;
FIG. 2(a) is a graph comparing bridge displacements in an embodiment of the present invention;
FIG. 2(b) is a graph comparing bridge accelerations according to an embodiment of the present invention;
FIG. 3 is a graph comparing vehicle acceleration in the embodiment of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
A stress belt bridge system for a vehicle is composed of a stress belt bridge and a vehicle running on the stress belt bridge. The vehicle stress belt bridge system belongs to a nonlinear coupling system due to elasticity of a vehicle and tension of a stress belt bridge.
The embodiment controls the vibration of the stress belt bridge system of the vehicle by arranging an eddy current tuned mass damper (hereinafter referred to as a damper) on the stress belt bridge.
As shown in fig. 1, the method for controlling stress band bridge vehicle-induced vibration based on an eddy current tuned mass damper provided in this embodiment includes:
101. respectively solving dynamic responses in an uncontrolled state and a controlled state aiming at a vehicle stress belt bridge system;
the controlled state is that a vehicle stress belt bridge system is added with a vortex tuned mass damper; the uncontrolled state is that no eddy current tuned mass damper is added to the vehicle stress belt bridge system.
The 101 specifically includes:
1011. establishing an incremental equation of motion of a stress belt bridge system of the vehicle;
10111. an incremental equation of motion can be established based on a virtual working principle; the incremental equation of motion of the vehicle stress belt bridge system is as follows:
Figure BDA0002633333600000051
in equation (1), wherein M, C and K represent the mass, damping and stiffness matrices of the vehicle stress belt bridge system, respectively; q, F and Fr represent the degree of freedom, load and resistance vectors of the vehicle stress belt bridge system, respectively;
when the vehicle stress belt bridge system is in an uncontrolled state, matrices M, C and K, and vectors q, F, and Fr are as follows:
Figure BDA0002633333600000052
Figure BDA0002633333600000053
in equations (2) and (3), subscript v represents a vehicle moving on the bridge, b represents a bridge, and d represents a damper.
In the present embodiment, the subscript contains v as data related to the vehicle, b as data related to the bridge, and d as data related to the damper. In the process of solving the dynamic response under the uncontrolled state and the controlled state, if the dynamic response is under the uncontrolled state, the element or the matrix of which the subscript contains d is not considered in the matrix. In the uncontrolled case, M is solveddd，Cdd，Cbd，Cdb，Kdd，KdbAnd KbdThese several items are set to 0.
1012. Setting damper parameters in a preset range, constructing a response solution iterative algorithm, and solving an incremental motion equation of the vehicle stress belt bridge system so as to respectively obtain dynamic responses in an uncontrolled state and a controlled state. The dynamic response comprises: bridge displacement, bridge acceleration, and vehicle acceleration.
For solving the dynamic response under controlled conditions:
firstly, setting parameters of a damper (ECTMD) in a preset range; the following description will be given by taking the added ith damper as an example:
setting the damper parameters of the ith damper in a preset range as follows: m isi、ci、ki(ii) a After the damper is added, M to the formula (2) is finally formeddd，Cdd，Cbd，Cdb，Kdd，KdbAnd KbdIn the submatrix, the relationship is expressed as follows:
Figure BDA0002633333600000054
Figure BDA0002633333600000055
in equations (18) and (19), NxRepresenting a displacement field function.
The method for constructing the response solution iterative algorithm and solving the incremental motion equation of the vehicle stress belt bridge system specifically comprises the following steps:
10121. rewriting the incremental motion equation based on a Wilson-theta method and a Taylor formula;
assuming that both systems M, C and K are constant in each incremental time step Δ t, the incremental equations of motion for the vehicle's stressed bridged system are rewritten as follows using the nonlinear algebraic equation of Wilson- θ method:
Figure BDA0002633333600000061
Figure BDA0002633333600000062
Figure BDA0002633333600000063
in the equations (20) to (21),
Figure BDA0002633333600000064
a2＝2a0，
Figure BDA0002633333600000065
and theta is a Wilson parameter of 1.4.
Assuming that the solution at the (k-1) iteration is known, the vector R can be expanded according to the Taylor formula by the series of this known solution:
Figure BDA0002633333600000066
in equation (23), R represents a residual vector. The modified incremental equation of motion obtained after the high-order term is ignored:
Figure BDA0002633333600000067
k in formula (4)tThe effective tangential stiffness matrix is obtained by:
Figure BDA0002633333600000068
10122. setting iteration conditions, and solving the rewritten incremental motion equation;
iterative solution is performed until two successive result vectors satisfy the following iteration condition:
Figure BDA0002633333600000069
in formula (6), | q | non-woven phosphor∞Represents the infinite norm of the vector, and η is a convergence coefficient.
The dynamic response expressions under the uncontrolled state and the controlled state are obtained through calculation:
Figure BDA00026333336000000610
in the formula (7), the first and second groups,
Figure BDA00026333336000000611
according to the dynamic response of the stress belt bridge system of the vehicle in a controlled state and an uncontrolled state, a control target function expression is obtained as follows:
Figure BDA0002633333600000071
in equation (24), y represents the peak dynamic response of the vehicle stress belt bridge system in an uncontrolled state (no damper);
Figure BDA0002633333600000072
representing the peak of the dynamic response of the vehicle stress belt bridge system under controlled conditions (with dampers).
In the present embodiment, the vibration control is aimed at minimizing the vibration response, and for the vehicle stress belt bridge system vibration control, the bridge vibration and the vehicle vibration are the most important evaluation indexes. For bridges, displacement and acceleration responses are two direct indicators for evaluating bridge vibrations. On the aspect of vehicles, the running performance of the vehicles described by the acceleration response is also an important index for indirectly evaluating the vibration of the bridge. Therefore, the displacement and acceleration of the key position are selected as vibration control targets of the bridge; representative vehicle acceleration is selected as a vibration control target of the vehicle.
Defining the control objective functions of bridge displacement, bridge acceleration and vehicle acceleration as follows:
Figure BDA0002633333600000073
Figure BDA0002633333600000074
Figure BDA0002633333600000075
in the formulae (13) to (15), ybi、abiAnd aviRespectively representing the displacement peak value of the bridge, the acceleration peak value of the bridge and the acceleration of the vehicle under the uncontrolled stateA degree peak value;
Figure BDA0002633333600000076
and
Figure BDA0002633333600000077
respectively representing the displacement peak value of the bridge, the acceleration peak value of the bridge and the acceleration peak value of the vehicle in a controlled state.
102. Establishing a response surface model based on the eddy current tuned mass damper; the response surface model is as follows:
Figure BDA0002633333600000078
in the formula (8), the first and second groups,
Figure BDA0002633333600000079
a2＝2a0，
Figure BDA00026333336000000710
and x represents a damper parameter vector to be optimized.
In this embodiment, the parameters of the damper are set as follows: m isdj、cdjAnd kdj；
x＝{md1 md2 md3 cd1 cd2 cd3 kdl kd2 kd3} (25)
In the formula (25), mdjDenotes the mass of the jth damper, cdjDenotes the damping coefficient, k, of the jth damperdjThe spring rate of the jth damper is shown.
103. Constructing a damper parameter optimization objective function according to the peak values of the dynamic response in the uncontrolled state and the controlled state;
in this embodiment, the peak of the dynamic response includes: the peak value of bridge displacement, the peak value of bridge acceleration and the peak value of vehicle acceleration; the expressions of the target functions of the bridge displacement, the bridge acceleration and the vehicle acceleration are as follows:
Figure BDA00026333336000000711
Figure BDA0002633333600000081
Figure BDA0002633333600000082
in the formulae (10) to (12), γbyiAs a control objective function of bridge displacement, gammabaiAs a control objective function of bridge acceleration, gammavaiA control objective function that is a vehicle acceleration; n is1Number of bridge displacement test points, n2Representing the number of bridge acceleration test points, n3Indicating the number of vehicle acceleration test points.
In the parameter optimization process, the control objective function is constrained in the following region:
0≤γbai≤1，0≤γvai≤1，0≤γbyi≤1
to narrow the solution range, the following restrictions are placed on the damper parameters (j ═ 1-3):
0≤mdj≤d，0≤cdj≤c，0≤kdj≤k
the damper parameter optimization objective function is as follows:
Max(J(χ))＝Max(β1Jby+β2Jba+β3Jba) (9)
in formula (9), betaj(j-1-3) represents a weighting factor satisfying β1+β2+β3＝1；Jby、JbaAnd JvaRespectively representing the target functions of bridge displacement, bridge acceleration and vehicle acceleration.
104. Optimizing the target function and the response surface model by using the damper parameters, optimizing the damper parameters and determining the optimal damper parameters;
105. and setting the stress belt bridge system of the vehicle according to the optimal damper parameters.
To verify the effectiveness of the method of this embodiment, two identical two-axle vehicles with a distance of 5m were moved from the left end to the right end of the bridge at a speed v of 40km/h for the actual stressed belt bridge, and the vehicle parameters are listed in table one:
TABLE 1 Dual axle vehicle parameters
Figure BDA0002633333600000083
The bridge span and sag were 150m and 4.25m, respectively, and the density and axial stiffness of the objects studied were 1.70 × 103kg/m and EA 0.93 × 108kN, respectively, and the initial horizontal tension of the stress zone was 50.56 × 103 kN. Considering the bridge structure to be symmetrical relative to the midspan, the damper (ECTMD) parameter settings of two key points are identical, namely md1＝md3,cd1＝cd3And kd1＝kd3. Thus, the number of ECTMD parameters to be optimized in the stress band bridge is np＝6。
In the ECTMD parameter optimization, the peak displacement and acceleration of the positions of 1/4 span and 3/4 span in the span are selected as the control response of a bridge, and the peak acceleration of each vehicle body is selected as the control response of a vehicle. Thus, six bridge responses and two vehicle responses are used in the optimization analysis in total, and the number of objective functions is q 8. Using the algorithm described in this embodiment, a series of response samples for the vehicle stress belt bridge system at different sample points are calculated using the ECTMD parameters.
To further verify the effectiveness of the proposed optimization procedure, three cases were considered in the following analysis.
The first condition is as follows: the stress belt bridge structure is not controlled;
case two: the stress belt bridge structure is controlled, and a damper with linear design parameters is considered;
case three: the stress band bridge structure is controlled and the damper with the best parameters is considered.
Fig. 2(a) shows the vertical displacement of the bridge span, and the peak responses of the three cases are found to be 2.61mm, 2.38mm and 2.05mm respectively. The control efficiency of the system with the optimal parameter damper can reach about 21.4 percent, which is obviously greater than that of linear design ECTMDS (8.9 percent). Fig. 2(b) shows the vertical acceleration of the bridge span, and it can also be seen that the system with the optimal parameter damper achieves better control effect. Fig. 3 is a graph comparing the acceleration of the vehicle body in three cases. It can also be found that the linear design is 12.2% for the control efficiency of the vehicle body, and the control efficiency can reach 45.7% by using the method described in the embodiment.
These observations indicate that ECTMD with optimal parameters can effectively suppress vibration of the entire nonlinear vehicle stress belt bridge system. Therefore, the parameter optimization method based on the ECTMDS can effectively control vibration of the actual stress belt bridge system of the vehicle, and the effectiveness of the optimization method is verified.
It should be understood that the specific order or hierarchy of steps in the processes disclosed is an example of exemplary approaches. Based upon design preferences, it is understood that the specific order or hierarchy of steps in the processes may be rearranged without departing from the scope of the present disclosure. The accompanying method claims present elements of the various steps in a sample order, and are not intended to be limited to the specific order or hierarchy presented.
In the foregoing detailed description, various features are grouped together in a single embodiment for the purpose of streamlining the disclosure. This method of disclosure is not to be interpreted as reflecting an intention that the claimed embodiments of the subject matter require more features than are expressly recited in each claim. Rather, as the following claims reflect, invention lies in less than all features of a single disclosed embodiment. Thus, the following claims are hereby expressly incorporated into the detailed description, with each claim standing on its own as a separate preferred embodiment of the invention.
The previous description of the disclosed embodiments is provided to enable any person skilled in the art to make or use the present invention. To those skilled in the art; various modifications to these embodiments will be readily apparent, and the generic principles defined herein may be applied to other embodiments without departing from the spirit or scope of the disclosure. Thus, the present disclosure is not intended to be limited to the embodiments shown herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.
What has been described above includes examples of one or more embodiments. It is, of course, not possible to describe every conceivable combination of components or methodologies for purposes of describing the aforementioned embodiments, but one of ordinary skill in the art may recognize that many further combinations and permutations of various embodiments are possible. Accordingly, the embodiments described herein are intended to embrace all such alterations, modifications and variations that fall within the scope of the appended claims. Furthermore, to the extent that the term "includes" is used in either the detailed description or the claims, such term is intended to be inclusive in a manner similar to the term "comprising" as "comprising" is interpreted when employed as a transitional word in a claim. Furthermore, any use of the term "or" in the specification of the claims is intended to mean a "non-exclusive or".
The above-mentioned embodiments are intended to illustrate the objects, technical solutions and advantages of the present invention in further detail, and it should be understood that the above-mentioned embodiments are merely exemplary embodiments of the present invention, and are not intended to limit the scope of the present invention, and any modifications, equivalent substitutions, improvements and the like made within the spirit and principle of the present invention should be included in the scope of the present invention.

Claims (10)

1. A stress belt bridge vehicle-induced vibration control method based on an eddy current tuned mass damper is characterized by comprising the following steps:
respectively solving dynamic responses in an uncontrolled state and a controlled state aiming at a vehicle stress belt bridge system; the controlled state is that a vehicle stress belt bridge system is added with a vortex tuned mass damper; the uncontrolled state is that no eddy current tuned mass damper is added in the stress belt bridge system of the vehicle;
establishing a response surface model based on the eddy current tuned mass damper;
constructing a damper parameter optimization objective function according to the peak values of the dynamic response in the uncontrolled state and the controlled state;
optimizing the target function and the response surface model by using the damper parameters, optimizing the damper parameters and determining the optimal damper parameters;
and setting the stress belt bridge system of the vehicle according to the optimal damper parameters.
2. The stress belt bridge vehicle-induced vibration control method based on the eddy current tuned mass damper as claimed in claim 1, wherein the respectively solving the dynamic responses in the uncontrolled state and the controlled state for the vehicle stress belt bridge system specifically comprises:
establishing an incremental equation of motion of a stress belt bridge system of the vehicle;
setting damper parameters in a preset range, constructing a response solution iterative algorithm, and solving an incremental motion equation of the vehicle stress belt bridge system so as to respectively obtain dynamic responses in an uncontrolled state and a controlled state.
3. The method of claim 2, wherein the dynamic response comprises: bridge displacement, bridge acceleration, and vehicle acceleration.
4. The method of claim 3, wherein the incremental equation of motion of the vehicle stress band bridge system is:
Figure FDA0002633333590000011
in equation (1), wherein M, C and K represent the mass, damping and stiffness matrices of the vehicle stress belt bridge system, respectively; q, F and Fr represent the degree of freedom, load and resistance vectors of the vehicle stress belt bridge system, respectively;
when the vehicle stress belt bridge system is in an uncontrolled state, matrices M, C and K, and vectors q, F, and Fr are as follows:
Figure FDA0002633333590000012
Figure FDA0002633333590000013
in equations (2) and (3), subscript v represents a vehicle moving on the bridge, b represents a bridge, and d represents a damper.
5. The stress belt bridge vehicle-induced vibration control method based on the eddy current tuned mass damper as claimed in claim 4, wherein the building of a response solution iterative algorithm to solve the incremental motion equation of the vehicle stress belt bridge system specifically comprises:
rewriting the incremental motion equation based on a Wilson-theta method and a Taylor formula;
and (5) setting an iteration condition, and solving the rewritten incremental motion equation.
6. The method of claim 5, wherein the rewritten incremental equation of motion is:
Figure FDA0002633333590000021
k in formula (4)tThe effective tangential stiffness matrix is obtained by:
Figure FDA0002633333590000022
the iteration condition is as follows:
Figure FDA0002633333590000023
in formula (6), | q | non-woven phosphor∞Represents the infinite norm of the vector, and η is a convergence coefficient.
7. The method for controlling stress band bridge induced vibration based on eddy current tuned mass damper according to claim 6, wherein the dynamic response expressions in the uncontrolled state and the controlled state are as follows:
Figure FDA0002633333590000024
in the formula (7), the first and second groups,
Figure FDA0002633333590000025
8. the method of claim 7, wherein the response surface model is:
Figure FDA0002633333590000026
in the formula (8), the first and second groups,
Figure FDA0002633333590000027
a2＝2a0，
Figure FDA0002633333590000028
and x represents a damper parameter vector to be optimized.
9. The method of claim 8, wherein the peak value of the dynamic response comprises: the peak value of bridge displacement, the peak value of bridge acceleration and the peak value of vehicle acceleration;
the damper parameter optimization objective function is as follows:
Max(J(χ))＝Max(β1Jby+β2Jba+β3Jba) (9)
in formula (9), betaj(j-1-3) represents a weighting factor satisfying β1+β2+β3＝1；Jby、JbaAnd JvaRespectively representing the target functions of bridge displacement, bridge acceleration and vehicle acceleration.
10. The method for controlling stress band bridge induced vibration based on the eddy current tuned mass damper according to claim 9, wherein the expression of the objective function of bridge displacement, bridge acceleration and vehicle acceleration is as follows:
Figure FDA0002633333590000031
Figure FDA0002633333590000032
Figure FDA0002633333590000033
in the formulae (10) to (12), n1Number of bridge displacement test points, n2Representing the number of bridge acceleration test points, n3Representing the number of vehicle acceleration test points; gamma raybyiIs a control target function of bridge displacement, gammabaiIs a control target function of bridge acceleration, gammavaiFor controlling acceleration of vehicleAnd (3) making an objective function, wherein the expression is as follows:
Figure FDA0002633333590000034
Figure FDA0002633333590000035
Figure FDA0002633333590000036
in the formulae (13) to (15), ybi、abiAnd aviRespectively representing a bridge displacement peak value, a bridge acceleration peak value and a vehicle acceleration peak value in an uncontrolled state;
Figure FDA0002633333590000037
and
Figure FDA0002633333590000038
respectively representing the displacement peak value of the bridge, the acceleration peak value of the bridge and the acceleration peak value of the vehicle in a controlled state.
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