Stochastic transient response of dynamical systems to multisupport, multicomponent seismic excitation

Exact analytical solutions for the stochastic response of a general multiple degree of freedom system, supported at multiple points, to non-stationary, colored, vector valued, multi-component excitation are obtained by using a state space time domain random vibration formulation.; The non-whiteness of excitation is achieved by passing a white noise through a new class of filter. Besides other attractive advantages it has over the previous ones, this filter is capable of producing any arbitrary power spectral density function with as many peaks as desired. The non-stationarity of excitation is achieved via a modulating piecewise linear function which practically encompasses all other modulating functions used by previous researchers, and is generated to match the desired excitation. Here, one can directly prescribe the time history of RMS values and cross correlation coefficients of any desired excitation.; Availability of all cross terms of time-dependent variances, makes it possible to prescribe all correlation coefficients of excitation, directly. This, in turn, facilitates the analysis of multiple support excitation which plays an important role in analysis of long bridges and light equipment supported on heavier structures.; The modal equations of system are used in their general form and therefore, all three approaches, namely absolute displacement, pseudo static displacement, and relative displacement approach can be handled by present formulation. It is also shown that a multiple component excitation can be modeled and solved with no addition in the present formulation.