The effects of earthquake wave dispersion on the response of simple dynamic structural models

Abstract

The extent and means by which the dispersive properties of the site geology influence the structural response to the ground shaking is examined. Based on linear wave propagation assumptions, the maximum possible response of a dynamic system is calculated along with the dispersion function, called the critical dispersion, necessary to produce this maximum or critical response. For linear systems, the critical response can be calculated from an integration on the fourier amplitude of acceleration times the critical response transfer function. The dependence of the response upon the dispersion is fairly frequency independent, and for the particular cases examined the critical dispersion induced maximum response was roughly a factor of two greater than the response derived from sets of synthetic accelerograms which included dispersion effects. The response of multi-degree of freedom linear systems is derived from the single degree of freedom, SDOF, results except that they depend on all of the natural frequencies of the system. Finally, the response of a SDOF elastoplastic system is examined in a similar manner. The critical dispersion is now amplitude dependent because the response frequency, hence the dominant excitation frequency, is also amplitude dependent. For a range of frequencies the critical response for the nonlinear system is as much as a factor of ten greater than the calculated response from realistic dispersion functions, indicating a stronger dependence of the response upon the dispersion than for the linear systems.