The problem of determining optimal power spectral density models for earthquake excitation which satisfy constraints on total average power, zero crossing rate and which produce the highest response variance in a given linear system is considered. The solution to this problem is obtained using linear programming methods. The resulting solutions are shown to display a highly deterministic structure and, therefore, fail to capture the stochastic nature of the input. A modification to the definition of critical excitation is proposed which takes into account the entropy rate as a measure of uncertainty in the earthquake loads. The resulting problem is solved using calculus of variations and also within linear programming framework. Illustrative examples on specifying seismic inputs for a nuclear power plant and a tall earth dam are considered and the resulting solutions are shown to be realistic. Copyright

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Journal Earthquake Engineering and Structural Dynamics
Manohar, C.S. (C. S.), & Sarkar, A. (1995). Critical earthquake input power spectral density function models for engineering structures. Earthquake Engineering and Structural Dynamics, 24(12), 1549–1566. doi:10.1002/eqe.4290241202