Radial vibration analysis of single and composite spherical shells by wave approach

This paper presents the wave approach for the analysis of free vibration and transmission response of single and composite spherical shells. From wave standpoint, propagation and refection matrices are combined to obtain the characteristic equation of radial vibration for a single spherical shell with free–free and free–clamped boundary constraints. The corresponding natural frequencies solved by the wave approach are compared with the results by the fundamental analytical solution and classical Bessel solution. Additionally, based on the wave solution, transfer matrix, localization factor, and transmission response of a phononic crystal composite spherical shell are investigated. The predicted attenuation bands by the finite element method (FEM) are exactly the same as the theoretical analytical results. The effect of radial span ratio and inner radius on the attenuation band is also discussed.