基于遗传算法的声子晶体梁振动传输特性优化设计

OPTIMAL DESIGN OF PHONONIC CRYSTAL BEAMS FOR ATTENUATING VIBRATION PROPAGATION

以工程中常用的梁类结构为背景,研究了利用声子晶体带隙来抑制梁中振动传播的设计方法,在考虑附加质量、振幅等约束条件下,用遗传算法来优化设计声子晶体梁的力学参数,从而实现"按需设计"。基于传递矩阵法建立了局域共振声子晶体梁振动传输特性的计算方法,以某频段内的插入损失最大为优化目标,通过建立有效的惩罚函数并选择合适的遗传运算策略,建立了考虑质量、振幅约束条件下局域振子参数的优化设计方法,实现了局域共振声子晶体梁振子参数的优化设计,并分析了优化结果的正确性。所提出的优化设计方法对于将声子晶体应用于抑制结构振动传播的工程实践具有重要的实用价值。

Phononic crystals (PC) are periodic structures or composites exhibiting elastic band gaps within which sound and vibration are all forbidden. For a PC sample with finite periods and finite size, vibration with certain frequency following into the gaps will be significantly attenuated when it propagates along the specimen. Such a property of PCs offers a new approach to control vibrations in engineering structures. However, PC beams with certain frequency gap will bring additional resonances with lower frequency, which are harmful and must be taken into account. Here in, A PC beam with periodically attached local resonators (LR beams) is used to attenuate vibration propagation from its one end to the other. The transfer matrix (TM) of LR beams is formulated and the vibration transmissibility is calculated with TM method. The insertion loss of those attached resonators is used as an indicator for comparison of different designs. The parameters of local resonators are optimized with genetic algorithm to minimize vibration transmission in specified frequency range covering both stopping band (gap) and passing band. In addition, constraint such as add-on mass and displacement limits are also taken into account during the optimization. The optimized results are analyzed for validation. The influences of resonators’ parameters on the vibration transmissibility of LR beams are also investigated and summarized. The proposed optimizing approach and the summarized rules are referable for controlling vibration propagation in beams with PC gaps.