弹性地基上随机失谐周期加固管的波动局部化特性研究

STUDY ON WAVE LOCALIZATION IN RANDOMLY DISORDERED PERIODICALLY STIFFENED PIPES ON ELASTIC FOUNDATIONS

基于弹性地基上均匀管梁的横向波动微分方程,推导了周期加固管中各胞元的动态刚度矩阵,进而利用传递矩阵法建立了相邻胞元间的传递矩阵。将随机失谐参数引入到周期加固管中,根据Wolf算法,采用局部化因子计算了结构参数对弯曲波动局部化特性的影响。通过对周期加固管的一系列算例分析表明,弹性地基上的均匀管路存在一个临界频率,当波动频率小于该临界频率时,弯曲波的传播始终是衰减的。弹性地基可以抑制弯曲波动在特定频率范围内的传播。同时,几何尺寸变化和随机失谐对周期加固管路的频带特性和局部化程度影响不同,可以调整结构的尺寸或选择不同的变异系数来改变结构的波传播特性。最后,采用有限元模拟验证了所提出周期加固管波传播模型的正确性。

By using the differential equation governing the flexural vibration of a uniform pipe-beam on elastic foundations, the dynamic stiffness matrix of each cell in a periodically stiffened pipe is obtained and the transfer matrix between the adjacent cells is derived based on the transfer matrix method. A random disorder is introduced in the disordered periodically stiffened pipe, and the localization factors are calculated to examine the wave localization using Wolf's algorithm. The effects of various controlling parameters on the wave localization characteristics of the disordered periodic pipes are assessed through a comprehensive set of numerical case studies. The obtained results show that the flexural wave is always attenuated when the frequency is less than some critical frequency of a uniform pipe on elastic foundations. For certain frequency ranges, the elastic foundations can restrict the propagation of flexural waves. The frequency bands and the degree of the localization are different for various geometric dimensions and disordered configurations of the periodically stiffened pipes, so wave propagation in the structure can be altered by tuning structural parameters and the disorder level. The validity of the proposed methodology of wave propagation in the periodically stiffened pipe is verified by finite element simulations.