Dynamic Stiffness Matrices for Viscoelastic Half-Plane Foundations

Abstract

Numerical results are presented for complex-valued dynamic (frequency-dependent) stiffness influence coefficients for a homogeneous isotropic linearly viscoelastic half-space in plane strain or generalized plane stress. These influence coefficients, defined for uniformly spaced nodal points at the surface, are obtained from solutions of two boundary value problems, associated with unit harmonic displacements prescribed separately in each of the two-degrees-of-freedom of one nodal point with all other nodal points kept fixed. Results for two viscoelastic models, Voigt solid and constant hysteretic solid, are included. Utilizing the results of this work, the earthquake response of a structure, idealized as a two-dimensional finite element system, on the surface of a viscoelastic half-space in plane strain or generalized plane stress can be analyzed by the substructure method. Because the boundary value problems were solved for unit displacements at individual nodal points on the surface of the foundation, it would not be necessary to limit the base of the structure to a rigid plate.