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

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.