The damping enhancement effect of the inerter system means that its energy dissipation efficiency can be improved with respect to the traditional dampers. Energy dissipation efficiency have been considered as the optimal design principle of the inerter system, however, the solution for optimized key parameters is difficult because of the special mechanical behavior of the inerter. A modified float-point encoding genetic algorithm is proposed in this study to realize the optimal design of the inerter system with maximized energy dissipation efficiency effectively and robustly. A novel and simple crossover strategy termed differential crossover is proposed and applied in the classical genetic algorithm to optimize the inerter system more effectively. The differential crossover strategy means that a new individual is generated based on the difference between two randomly selected individuals in the population. The mathematical expression for the optimization problem of the inerter system corresponding to the maximum energy dissipation efficiency design principle is established. Following the performance-oriented design concept, performance demand is taken as the constrained condition of the optimization problem. Case design confirms that the modified genetic algorithm can successfully solve the optimization problem of the inerter system and perform a better solving ability over the original genetic algorithms.
An inerter system can amplify the deformation of its internal energy dissipation device, thereby improving the efficiency of energy dissipation and shock absorption. This is the so-called damping enhancement mechanism, one of the key mechanisms of the inerter system. Although the theoretical framework for damping enhancement of inerter systems has been established, the implementation of this principle for the design of an inerter system requires solving a complicated constrained optimization problem, which is not easy to be figured out using traditional approaches. To obtain valid design results through a lucid and robust method, it is proposed to optimize the damping parameters through a metaheuristic algorithm named harmony search algorithm in order to maximize the damping enhancement degree of the inerter system with the satisfaction of structural performance. First, the closed-form seismic response solutions of a single-degree-of-freedom (SDOF) structure with an inerter system are derived based on the theory of random vibration. Then, the mathematical expression of the constrained optimization problem is established. Due to the inefficiency of the original harmony search algorithm to solve the constrained optimization problem, the algorithm is modified by introducing a new harmony generating method and an adaptive strategy for parameter adjustment. The modified harmony search algorithm is compiled to solve the optimal design problem of the inerter system. The algorithm is verified by designing a structure with an inerter system. It is found that the number of iterations and time consumption until convergence required by the modified harmony search algorithm can be reduced by about 20%∼90% compared with the original algorithm, which confirms the effectiveness of the modified algorithm. The results of dynamic analyses show that the structure have achieved the preset performance demands under different cases and the damping enhancement characteristic of the inerter system is fully utilized.
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