A spectral global matrix method for modelling the response of a fluid-loaded multilayered cylindrical shell excited by an acoustic plane wave

Abstract

This paper proposes a numerically stable method for modelling a fluid-loaded multilayered cylindrical shell excited by a plane wave, which solves the fd instability problem that is usually observed when using the well-known transfer matrix method (TMM). In the considered modelling, each layer can be either a viscoelastic coating described by a general three-dimensional (3D) elasticity model or an intermediate perfect fluid layer. The transfer matrix of each layer relating the state vector at the layer's two interfaces is estimated with an appropriate standard method. Instead of multiplying together the layer transfer matrices in order to deduce the transfer matrix of the multilayer cylinder, we propose an alternative approach. This one consists in writing the continuity relations at each interface of the considered systems and in building a global matrix that can be solved to obtain the system response. As shown by numerical applications on typical naval test cases, the proposed global matrix assembly procedure as opposed to the classical TMM provides numerical stability over both a wide range of axial wavenumbers and circumferential orders, but also the ability to consider intermediate fluid layers. Besides, this model is well-suited to describe elastic solid layers of any anisotropy as illustrated by an additional case considering a transverse isotropic layer.