Wave propagation and damping in linear viscoelastic laminates

Abstract

This analysis is concerned with wave propagation and damping in linear viscoelastic laminates. A spectral finite-element method is developed and used to calculate the dispersion properties of the first few wave types of a given laminate; the proposed approach provides a robust and numerically efficient alternative to the transfer matrix method in certain applications. The proposed approach is also well suited to the calculation of the wave types of sections whose material properties vary continuously throughout the thickness of the section. A one-dimensional finite-element mesh is used to describe the through-thickness deformation of the laminate, and the dispersion equation for plane-wave propagation is formulated as a linear algebraic eigenvalue problem in wave number at each frequency of interest. The resulting eigenvectors and eigenvalues can be computed using standard numerical routines and used to investigate the dispersion characteristics of the propagating wave types of the section. The damping loss factor of each wave type is estimated from the cross-sectional strain energy distribution of the laminate. The proposed approach is well suited to modeling the structural-acoustic response of sandwich panels, constrained layer damping treatments, and general viscoelastic laminate sections in statistical energy analysis (SEA) codes.