A semi-analytic method for vibro-acoustic responses of functionally graded cylindrical shells

A semi-analytic method is developed to study vibro-acoustic responses of functionally graded cylindrical shells with arbitrary boundary conditions. Material properties vary continuously in thickness direction according to the four-parameter power-low distributions in terms of volume fractions of two constituents. The shell is firstly divided into many narrow strips. By employing first-order shear deformation theory and expanding displacement as the exponent functions and Fourier series in axial and circumferential directions, five displacements and five forces at any cross-sections are expressed as 10 unknown coefficients. Surface Helmholtz integral equation is reduced to line integral through expanding surface pressure and velocity as Fourier series in circumferential direction, and the pressure can be further represented by displacement functions of strips via meshing the line integral to some 3-node isoparameter elements and utilizing the relationship between displacement and velocity. Continuity conditions, which contain effects of acoustic pressure, and boundary conditions are orderly assembled to the final governing equation. By comparing vibro-acoustic results of present method with the ones in the reference or calculated by FEM/BEM, rapid convergence and high accuracy are demonstrated. Furthermore, effects of external fluid and material parameters are studied.