A fast Chebyshev spectral approach for vibroacoustic behavior analysis of heavy fluid-loaded baffled rectangular plates with general boundary conditions

Abstract

A computationally efficient Chebyshev spectral approach is proposed to solve the vibroacoustic response of heavy fluid-loaded baffled rectangular plates. The governing equations for the displacements of motion in rectangular plates and the sound pressure in the Helmholtz integral are formulated using high-order, first-class Chebyshev polynomial expansions. This formulation is combined with Gauss-Chebyshev-Lobatto sampling. The quadruple integral encountered in solving the work done by the heavy fluid on the plate is reformulated into the configuration of a tensor product. The approach significantly reduces the computation time for solving the acoustic equations, bringing the vibration response of fluid-loaded plates closer to that of vacuum plates and limiting it to just a few seconds. The elastic boundary conditions of the rectangular plates are simulated using linear and rotational springs. Predictions of vibroacoustic behavior, including plate velocity, sound pressure, sound power, and radiation efficiency, are validated against literature results. The accuracy and efficiency of the Chebyshev spectral approach for the vibroacoustic coupling systems are demonstrated by the presence of exemplary agreements. Furthermore, this study investigates the effect of boundary conditions, geometric characteristics, and damping variables on the vibroacoustic behavior of rectangular plates.