Free vibration analysis of composite, circular annular membranes using wave propagation approach

Abstract

This paper presents the wave propagation approach for free vibration analysis of non-uniform annular and circular membranes. Literature reviews reveal that most bodies analyzed by this approach are one dimensional waveguide structures. From wave standpoint, vibration propagates, reflects and transmits in a structure. Firstly, the propagation, reflection and transmission matrices for non-uniform annular and circular membranes are derived. Then, these matrices are combined to provide a concise and systematic approach for obtaining the natural frequencies of non-uniform annular and circular membranes. The solution obtained by this approach is exactly the same as those derived by the classical method. Moreover, a set of benchmark results is presented for various geometric parameters. Finally, the behavior of propagation, reflection and transmission matrices is studied by defining their important parameters. The obtained hints are useful for the analysis of energy transmission in micro/nano devices.