Dispersion Relations and Mode Shapes for Waves in Laminated Viscoelastic Composites by Finite Difference Methods.

摘要

Dispersion relations and mode shapes for wave propagation in a laminated,infinite viscoelastic composite are obtained by finite difference methods. A complex modulus formulation is used. Free vibrations are studied for which the frequency is complex and the wave number real. Floquet theory is applied. Discretization of the governing differential equations and quasi periodic boundary conditions leads to a generalized eigenvalue problem for a large,sparse complex matrix. This is solved by a method involving permutation of the matrix into a convenient banded form and by writing recursion relations for the determinant. As an example,numerical results are obtained for a two medium composite with the filament material elastic and the matrix material modelled as elastic in dilatation and a standard linear solid in shear. The method proves to be very efficient and accurate for calculating frequencies as well as mode shapes. (Author)