Study On Parameter Optimization Of Nonlinear Tuned Mass Damper System Based On Perturbation Analysis Method

As society pays increasing attention to the reliability of large infrastructure facilities such as bridges,high-rise buildings and dams,structural vibration control technology is gradually gaining attention.Structural vibration control technology is an emerging vibration control technology with multidisciplinary and multi-disciplinary intersection,which is of great significance to protect people’s life and property safety and other aspects by installing some active,semi-active or passive energy dissipation devices on the structure to change the parameters of stiffness,damping and mass of the structure or provide active control force to achieve the desired vibration control effect.In this paper,the optimal design and evaluation of nonlinear tuned mass dampers are carried out to reduce unnecessary structural vibration in the context of structural vibration control.The research work has yielded good results and several innovative scientific findings.The research work and main contributions of the thesis are:(1)Starting from a two-degree-of-freedom model of a linear controlled structure coupled with a nonlinear tuned damper,the differential equations for the dynamics of the two-degree-of-freedom nonlinear tuned mass damper system are established,and the set of differential equations is simplified by omitting the higher order minima according to the Taylor series,followed by the derivation of the modulation-demodulation equations for the system response using the complex variable averaging method to provide the theoretical basis for the analysis in the subsequent sections.(2)The accuracy of the steady-state response results of the complex variable averaging method is verified by using the Longe-Kutta method,and the numerical calculation results show that the accuracy of the approximate solution results is good.(3)Set other initial conditions to zero,change only the initial displacement of the controlled structure,and study the effect of the initial conditions on the static bifurcation by numerical time course method.It is found that zero initial displacement corresponds to the high branch of the static bifurcation and large initial displacement corresponds to the low branch of the static bifurcation.(4)A parametric study is carried out based on the results of the approximate steady-state response of the nonlinear tuned mass damper system,and a multivalued solution discriminant based on the complex variable averaging method in the case of 1:1 resonance is proposed.The numerical method is used to verify that the arithmetic example shows that it can accurately determine whether the response is multivalued or single-valued when the system is subjected to periodic excitation,and a study on the optimized design of the mass damper frequency based on the minimum displacement ratio is carried out.(5)Based on the nonlinear controlled structure-nonlinear tuned mass damper coupled two-degreeof-freedom model,the nonlinear system of equations for the structural response is derived using the complex variable averaging method,and the system of equations can effectively reduce the time of numerical calculations.