Dynamic Stiffness Matrices for Viscoelastic Half Planes

Analytical expressions and numerical results are presented for the complex-valued, dynamic (frequency dependent), flexibility 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 of the half plane, are obtained from solutions of two boundary value problems, associated with harmonically time-varying (e^iωt) stresses uniformly distributed between two adjacent nodal points. Numerical values for these coefficients are presented for a viscoelastic half plane of constant hysteretic material. A method is developed to determine from these results the dynamic stiffness matrix, associated with the nodal points at the base of a surface supported structure, for the half plane. The resulting dynamic stiffness matrix is shown to be superior compared to the one determined from an available procedure, which is based on solutions of displacement boundary value problems for the half plane.