Vibro-acoustic analysis of multilayered shells of revolution based on a general higher-order shear deformable zig-zag theory

Abstract

This paper presents a semi-analytical approach for predicting the vibration and acoustic responses of an arbitrarily shaped, multilayered shell of revolution immersed in a light or heavy unbounded fluid. A higher-order shear deformable zig-zag shell theory with general shape functions is proposed to describe the displacement field of a multilayered shell with arbitrary curvatures, which provides a theoretical unification of most thin and shear deformable shell theories in the literature. Based on the higher-order zig-zag theory, the structure model of the multilayered shell is formulated by using a modified variational method combined with a multi-segment technique, whereas a Chebyshev spectral Kirchhoff–Helmholtz integral formulation is employed to model the exterior acoustic fluid. The displacement field of the shell and the sound pressure of the fluid are expanded by Fourier series and Chebyshev orthogonal polynomials. Such a treatment reduces the size of the problem and permits a semi-analytical solution for the displacement and acoustic variables. A set of collocation nodes distributed over the roots of Chebyshev polynomials are used to establish the algebraic system of the acoustic integral equations, and the non-uniqueness solution is eliminated by means of interior CHIEF points. Numerical examples are given for vibration and acoustic radiation analyses of multilayered spherical, cylindrical and conical shells. Comparison studies are performed to evaluate the accuracy of various shell theories. The validity of the present method for acoustic analyses of multilayered shells is demonstrated by comparing the results with exact solutions and those obtained from the coupled finite element/boundary element method. Individual contributions of circumferential modes to the radiated sound of multilayered shells are examined.