分级周期梁结构的振动带隙特性优化研究

针对分级周期梁结构，进行了振动带隙特性优化研究，以期提高结构的减振性能。采用谱元法计算分级周期梁的频响曲线，并结合传递矩阵法计算结构的色散关系，将两种方法相结合来研究结构的振动带隙特性。构建带隙占比函数作为优化目标函数，将单胞结构的尺寸作为优化参数进行带隙特性优化。经过优化，使得在研究频段内带隙特性大大提高。通过与有限元法和振动实验相对比，验证了谱元法计算和优化结果的正确性。研究内容对于提高周期结构的振动带隙特性和减振应用提供有益参考。

Optimization of band-gap characteristics of hierarchical periodic beam

In order to improve the vibration reduction performance of hierarchical periodic beam, the vibration band-gap characteristics are optimized. The spectral element method (SEM) is used to calculate the frequency response curves of the periodic beam, the dispersion relation curves of the structure is calculated by the transfer matrix method and the two methods are combined to study the vibration band-gap characteristics of the structure. The band-gap ratio function is constructed as the optimization objective function, and the sizes of the unit-cell are used as the optimization parameters to optimize the band-gap characteristics. After optimization, the band-gap characteristics in the considered frequency ranges are greatly improved. Compared with the finite element method (FEM) and vibration experiment, the correctness of the calculation results of the SEM is verified. The research content provides a useful reference for improving the vibration band-gap characteristics of periodic structures and the application of vibration reduction.