The Earthquake Engineering Online Archive

Frequency dependent stiffness matrices for viscoelastic halfplane foundations

Chopra, Anil K.; Chakrabarti, Parthasarathi; Dasgupta, Gautam

UCB/EERC-75/22, Earthquake Engineering Research Center, University of California, Berkeley, 1975-08, 129 pages (475/C49/1975)

Numerical results are presented for frequency-dependent, complex-valued stiffness influence coefficients for a homogeneous, isotropic, linearly viscoelastic halfspace 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 are included: Voigt solid and constant hysteretic solid. A method is presented to determine from these results the frequency-dependent, complex-valued foundation stiffness matrix associated with the nodal points at the base of the structure. 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 halfspace 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.

Available online: http://nisee.berkeley.edu/documents/EERC/EERC-75-22.pdf (10 MB)