Single domain Chebyshev spectral method for analyses of the vibroacoustic characteristics of baffled irregularly shaped plates

Abstract

In this study a Chebyshev spectral method is introduced to analyse the vibroacoustic characteristics of plates with arbitrary shape. This approach involves a unique expansion of the governing equations for plate displacements using Chebyshev polynomials, coupled with Gauss-Chebyshev-Lobatto sampling. A significant advancement in computational efficiency is the use of a tensor product configuration. To manage irregular shapes, the elements of the inner product matrix corresponding to the open regions were set to zero. For precise shape representation, a substantial number of Chebyshev-Gauss-Lobatto points, surpassing the polynomial truncation count, are carefully selected. the elastic boundary conditions of the plate were simulated by applying artificial spring techniques at different points. The prediction accuracy of the vibroacoustic phenomena, including those of the mean square velocity and sound power, were rigorously confirmed through comprehensive comparisons with results from previous studies and those obtained using the finite element method. Furthermore, the accuracy and versatility of the method are demonstrated through a variety of numerical examples encompassing plates with geometries shaped like rectangules, triangules, clouds, and pigs geometries, and different boundary conditions.