Acoustic resonance scattering from a submerged functionally graded cylindrical shell

Abstract

An exact treatment based on the inherent background coefficients that describe the background amplitudes in the scattered field is employed to investigate the scattering of time-harmonic plane acoustic waves by an arbitrarily thick hollow isotropic functionally graded cylinder submerged in and filled with non-viscous compressible fluids. The mechanical properties of the graded shell are assumed to vary smoothly and continuously with the change of volume concentrations of the constituting materials (ZrO 2 and Al) across the thickness of the shell according to a power-law distribution. The original inhomogeneous shell is approximated by a laminate model, for which the solution is expected to gradually approach the exact one as the number of layers increases. The transfer matrix ( T-matrix) solution technique, which involves a system global transfer matrix formed as the product of the individual transfer matrices by applying continuity of the displacement and stress components at the interfaces of neighbouring layers, is employed to solve for the modal scattering coefficients. Following the classic acoustic resonance scattering theory (RST), the scattered field and response to surface waves are determined by constructing the partial waves and obtaining the backgrounds (non-resonance) and resonance components from it. Three types of FGM cylindrical shells composed of Al and ZrO 2 are configured and their response spectra to an incident plane wave are calculated. The effects of the FGM interlayer thickness and material compositional gradient (the constituent volume fraction) on the inherent background, global and resonance scattering coefficients are examined. Limiting cases are considered and good agreements with the solutions available in the literature are obtained.