Acoustic scattering from functionally graded cylindrical shells

Abstract

In this paper, the method of wave function expansion is adopted to study the scattering of a plane harmonic acoustic wave incident upon an arbitrarily thick-walled, functionally graded cylindrical shell submerged in and filled with compressible ideal fluids. A laminate approximate model and the so-called state space formulation in conjunction with the classical transfer matrix (T-matrix) approach, are employed to present an analytical solution based on the three-dimensional exact equations of elasticity. Three models, representing the elastic properties of FGM interlayer are considered. In all models, the mechanical properties of the graded shell are assumed to vary smoothly and continuously with the change of volume concentrations of the constituting materials across the thickness of the shell. In the first two models, the rule of mixture governs. The main difference between them is the set of elastic constants (e.g., Lamé’s constants in model I and Young’s modulus and Poisson’s ratio in Model II) which are governed by the rule of mixtures. In the third model, an elegant self-consistent micromechanical model which assumes an interconnected skeletal microstructure in the graded region is employed. Particular attention is paid to backscattered acoustic response of these models in a wide range of frequency and for different shell wall-thicknesses. The results reveal a technical comparison between these models. In addition, by examining various cases (i.e., different shell wall-thicknesses, various profiles of variations and different volume concentration of constituents), the impact of the overall volume concentration of constituents and also the profile of variations, on the resonant response of the graded shell is investigated. Limiting cases are considered and good agreement with the solutions available in the literature is obtained.