Study Of Dynamic Characteristics Of Tensioned Strings With Tuned Mass Dampers

As an important force member of cable-stayed bridges,due to its own low stiffness and low damping characteristics,it is very easy to vibrate under external excitation,thus affecting the fatigue life and use safety of cable-stayed bridges,and generally the vibration of cable-stayed bridges can be suppressed by installing dampers on the cablestayed bridges.This paper takes the tensioned strings with tuned mass dampers installed as the research object to study its dynamic characteristics under free vibration state,and the following work is carried out in this paper:(1)The differential equations of free vibration of a tuned mass damper tensioned string system containing any number of tuned mass dampers are dimensionless and unitized to reduce it to a unit tuned mass damper tensioned string system,and the eigenvalue problem of the system is solved by using the Laplace transform method,and the explicit analytical expressions of the eigenfunctions of this type of system and the general form of the system frequency equation are given for the first time.(2)The frequency equation of a tensioned string system with a single tuned mass damper is solved,and the explicit approximate analytical expressions for the complex frequency and modal damping ratio of the system are given.On this basis,the dynamic characteristics of the system in two special cases where the complex frequency is purely real and purely imaginary are discussed,and the effect of the variation of the damper parameters on the modal damping ratio of the system in the damper tensioned string system is studied.(3)In the case that the system contains two tuned mass dampers,the frequency equation of the system is solved approximately,and the variation law of the modal damping ratio of the system under the influence of different parameter settings and values of the two dampers is studied using the approximate solution.(4)The dynamic characteristics of the damper tensioned string system are studied by numerical simulation using the finite element method.To avoid the problems caused by the overall damping matrix of this type of system being non-proportional,the state space finite element method is proposed to convert the eigenvalue problem of the damper tensioned string system into a classical generalized eigenvalue problem for solution.The results of the modal damping ratio of the system given by the approximate analytical solution and the modal damping ratio of the system obtained by the state-space finite element method are compared to verify the correctness of the approximate analytical solution and determine its applicability.The optimization analysis of the single-tuned mass-damper tensioned string system under fifth-order vibration is carried out by using the parameter scan method,and the specific parameter settings are given.The main conclusions obtained in this paper are as follows:(1)The explicit approximate analytical solution given in this paper for the tuned mass damper tensioned string system is significantly better than the results of existing studies in the literature in terms of computational accuracy and applicability.The modal damping ratios of the system given by the approximate solution are consistent with the numerical solutions given by the state space finite element method for almost all the parameters considered in this paper,and the approximate analytical solution is applicable to both the low order and the middle and high order modal damping ratios of the system.(2)Using the variation law of the modal damping ratio of the system with each parameter of the damper,the design of the tuned mass damper can be guided.In general,when the damper frequency is tuned to the system inherent frequency,a better damping effect can be obtained;at the same time,the damper should be installed at the location where the amplitude of the system vibration function is large.