Wave propagation in periodic shells with tapered wall thickness and changing material properties

Abstract

A theoretical method based on the Transfer Matrix Formulation and Wavelet Transforms is developed in order to effectively investigate the influence of periodicity, variable geometry and material properties on the wave propagation characteristics of axis-symmetric shells. Several experiments have been conducted to verify the numerical predictions and to demonstrate that the Wavelet Transform is a very powerful tool to uniquely identify and compare the energy distribution both in the time and frequency domain. Thin shells are modeled as two-dimensional wave-guides, where the propagation of the longitudinal waves is coupled with the flexural (radial) waves. Variations of the wall thickness, medium radius and element length of the shell can effectively filter out/stop undesirable bands of frequencies from the longitudinal and/or the transverse wave characteristics. The principal parameter that influences the width and location of the stop bands is the ratio between the cross sections at the two ends of the shell element. Sophisticated exponential profiles and simpler linear taper are implemented and compared. Functionally graded materials (FGM) are also investigated as an alternative way to influence the parameters of the stop bands. Combinations of the FGM and geometric taper give the flexibility needed for some very demanding applications. Different types of periodic taper configurations have complementary effects on the wave characteristics. Combinations of these complex geometries (bi-periodic tapered cells) are presented and shown to produce the most effectual energy redistribution.