A semi-analytic model for vibro-acoustic analysis of functionally graded shells of revolution

Abstract

A semi-analytic model with wider applications is developed for vibro-acoustics of submerged functionally graded material (FGM) shells of revolution, and independent or coupled FGM shells are specific cases. For structural model, the shell is divided to many narrow segments treated as conical shells. Materials vary continuously in thickness direction according to the four-parameter power-law distributions about volume fractions of two constituents. Based on the first-order shear deformation theory (FSDT), differential equations are solved via expanding displacements as power series and Fourier series in meridional and circumferential directions, respectively. Continuity and boundary conditions are assembled to vibration governing equation. For acoustic model, Helmholtz integral equation is simplified to one line integral after expanding velocity and acoustic pressure as Fourier series in circumferential direction, and the pressure is further expressed as displacements of the shell. Then, structural and acoustic models are coupled as adding the acoustic pressure to continuity conditions. Through comparing results of developed model with the ones of literature and coupled finite element–boundary element method for some FGM shells, rapid convergence and high accuracy are demonstrated. Furthermore, discrepancies between vibro-acoustic responses of FGM, homogeneous and layered shells are slight, and effects of heavy fluid become more obvious as the volume fraction of the material with large stiffness decreases.