Optimal Design Of Inerter System Based On The Principle Of Maximum Damping-related Velocity Ratio

Inerter system is a new type of structural damping device,which can dissipate seismic energy efficiently.The common design methods of inerter system are mainly aimed at controlling the structural displacement response,which can’t give full play to the energy dissipation effect of inerter system.In the process of deriving the design formula,it is often assumed that the inherent damping of the structure is zero,and the influence of the inherent damping of the structure on the damping effect is ignored.However,when classical numerical optimization algorithm is used to solve the optimization problem of inerter system,it needs complex gradient expression and appropriate initial solution,so the solution effect is not ideal.Therefore,taking the energy dissipation effect as the target to design the inerter system is of practical significance to maximize the energy dissipation effect of the inerter system.In addition,selecting the appropriate optimization algorithm can ensure that the key parameter values of the inerter system can be accurately calculated on the premise of determining the damping performance.In order to make full use of the high energy dissipation characteristic of inerter system,this paper designs the inerter system with the goal of maximizing the energy dissipation rate ratio.Since the multi-scale quantum harmonic oscillator algorithm has strong adaptability,good global convergence,high operation efficiency and easy programming,this paper chooses to use the multi-scale quantum harmonic oscillator algorithm to calculate the key parameter values of inerter system.（1）The research background and significance,common inerter system types,and research status of inerter system are introduced.（2）Based on the random vibration theory,the random vibration response expression of the structure with inerter is derived,and the analytical expression of the energy dissipation rate ratio and the mathematical description of the principle equivalent optimization problem of the maximum energy dissipation rate ratio are given.（3）using the Lagrange multiplier method used for inerter system parameter optimization design formula is deduced,and through the design example of the spoil,let inerter system design principles and design the correctness of the formulas is verified,and validated based on the end,the inherent damping ratio is derived the formula used for inerter system design in the applicability of the inherent damping ratio of structures.（4）The multi-scale quantum harmonic oscillator algorithm was applied to solve the optimal parameters of the inerter system,and the optimization program of the maximum energy dissipation rate ratio of the inerter system based on the multi-scale quantum harmonic oscillator algorithm was compiled in Python language,and the optimal values of the key parameters of the inerter system were calculated（5）The vibration control effect of inerter system designed by design principle and optimization algorithm is analyzed and verified by an example...