The Earthquake Engineering Online Archive

An alternative representation of the elastic-viscoelastic analogy

Dasgupta, Gautam; Sackman, Jerome L.

UCB/EERC-75/40, Earthquake Engineering Research Center, University of California, Berkeley, 1975-12, 30 pages (555/D24/1975)

An alternative representation of the elastic-viscoelastic correspondence principle for solids similarly viscoelastic in bulk and shear, and subjected to steady-state harmonic excitation, is derived. This form of the elastic-viscoelastic analogy is particularly useful when the elastic solution is not available in closed form, but is only known numerically, say in tabular form. The analyticity property of the frequency response function is utilized to formulate a Dirichlet problem in the lower half of the complex plane with the elastic solution on the real line as the boundary data. An infinite integral representation for the viscoelastic frequency response function is then obtained, where the elastic frequency response and viscoelastic properties enter in the integrand. This integral may be evaluated numerically using a suitable quadrature formula, and the known discrete numerical values of the elastic frequency response function, to generate an approximation to the viscoelastic frequency response function. The computation can be monotonically refined by the inclusion of more elastic data points. A simple example is presented to illustrate an application of this alternative formulation.

Available online: http://nisee.berkeley.edu/documents/EERC/EERC-75-40.pdf (2 MB)