振子质量非均布的有限结构梁减振频带优化

Optimization of damping frequency band in finite structure beam with uneven mass distribution of oscillator

对有限结构的声子晶体梁,首先结合传递矩阵法和有限结构的边界约束条件,在理论上计算了其振动传递特性,从而得到减振频带的频率范围和衰减深度。然后通过有限元法和样件试验得到的加速度传递函数验证了计算方法的准确性。进而分析了不同周期数对振动传递特性的影响,发现一定周期布置后的声子晶体梁减振频带已趋向稳定。最后,以振子总质量和减振频带总宽度为优化目标,通过NSGA-Ⅱ算法对6周期布置的有限结构声子晶体梁的各个振子质量进行优化。保持减振频带宽度不变时,以振子质量最小进行优化,振子总质量减小50.3%。综合平衡振子质量和减振频带宽度进行优化,优化后振子质量减小27%,减振频带宽度增加120%。该方法为声子晶体的工程应用与优化提供了参考和指导。

First,the vibration transfer characteristic is theoretically calculated by combining the transfer matrix method and the constraint boundary of finite structure.Through the acceleration response function obtained from the finite element method and the experiment,the accuracy of the method is verified.Second,the influence of period on vibration transfer characteristic is discussed.The width of damping frequency band is constant with specific periodic oscillators.Finally,taking the oscillators'mass and damping frequency band's width as the objective of optimation,the NSGA-Ⅱalgorithm is used to optimize the quality of each oscillator in the limited structure local resonance beam.After optimization,the total mass of oscillator can be reduced by 50.3% while the width of band is unchanged.What's more,total mass of oscillator is reduced by 27% and the width of damping frequency band is increased by 120%.This method provides reference and guidance for engineering application and optimization of phononic crystals.