Damping Enhancement Mechanism And Meta-heuristic Optimal Design Of Inerter System

Inerter system is a new type of structural vibration control device for damping systems.It can absorb vibration energy efficiently and amplify the deformation of its internal energy dissipating device（EDD）,thereby improving the EDD’s efficiency of energy dissipation and response mitigation.This is called the characteristic of damping enhancement,which is the key mechanism of the inerter system and can be used as a concise design principle for the inerter system.However,the existing damping-enhancement formulae for the design of inerter systems are complicated and inconvenient to apply.Therefore,under the framework of the design theory of damping enhancement of inerter system,this paper deduces the analytical form of inerter system based on the design principle of giving full play to the damping enhancement characteristics of inerter system and meeting the performance requirements as the direct goal.The closed-form design formulae of inerter systems.is simplified,The design principle and design parameters are verified by a design example,which proves the correctness and effectiveness of the design method in this paper.Subsequently,to optimize the insufficiency of non-inderent-damping assumption in the process of deriving the analytical design formula,on this basis,the metaheuristic algorithm with high solidity is further used to optimize the structure with an inerter system.Calculation accuracy and calculation efficiency of damping parameters of the structure with an inerter system.The main research contents are as follows:（1）According to the mechanical characteristics of the inerter system,establish the mechanical model of the single-degree-of-freedom（SDOF）structure with an inerter system,based on the theory of random vibration,the analytical formulae of the mean-square responses for an SDOF structure with an inerter system are obtained under the white noise excitation.To give full play to the damping enhancement of inerter system,under the goal of meeting the performance requirements,the design principle of "maximum damping enhancement" is proposed,and the mathematical description of the optimal design of maximum damping enhancement is discussed.（2）According to the mathematical description of the maximum damping enhancement,combined with the extremum conditions and the non-inderent-damping assumption,the random vibration response formula is appropriately simplified,and the closed-form design formulae of the inerter system with a concise form and reasonable precision is derived.Based on the closed-form design formulae,the design process of the structure with inerter system based on the principle of maximum damping enhancement is discussed.（3）Based on the closed-form design formulae and design process of the maximum damping enhancement of the structure with an inerter system,design a variety of the structure with inerter system examples with different shock absorption requirements.The dynamic time-history analysis is carried out,and the validity and correctness of the principle of maximum damping enhancement of damped structure with inerter system and its closedform design formulae are verified by comparison with the classical fixed-point theory.（4）To further obtain more accurate parameters of the structure with inerter system and optimize the non-inderent-damping assumption when deriving the closed-form design formula,the particle swarm algorithm with good robustness,simple principle,and easy programming is used for meta-heuristic algorithm.It carries out the optimal design of the maximum damping enhancement of the inerter system.At the same time,the adaptive penalty weight is introduced into the particle swarm algorithm to consider the constraints,and the adaptively adjusted inertia weight is used to improve the solution efficiency.Based on the Python language,an adaptive weight particle swarm algorithm program was developed to solve the design problem of the maximum damping enhancement of the structure with inerter system.The solution process of the design example reflects the effectiveness of the adaptive weighted particle swarm algorithm for solving the optimization design problem of the structure with inerter system.The dynamic time history analysis results show that the design parameters meet the preset damping performance requirements.