Sound radiation from finite cylindrical coated shells, by means of asymptotic expansion of three-dimensional equations for coating

Abstract

This work presents the mathematical analysis and numerical results about sound radiation from a finite cylindrical coated shell. The shell motion is obtained using the classical Donnell operator, whereas the layer motion is described by means of the three-dimensional Navier equations. Since there are no exact solutions allowing simple coupling to the supporting shell and to the outer acoustic medium, displacement solutions of Navier’s equations are expressed using asymptotic expansions in the layer thickness. In this analysis, provided that the thickness layer divided by the dilatation wavelength in the compliant layer (e/λ0) remains small compared to unity, one can develop the layer displacement field in powers of ε truncated at order S. The general formulation truncated at order S is presented as well as the numerical application of the method truncated at order 2. Numerical results are shown that exhibit the influence of the coating layer on the vibroacoustic behavior of the shell.