CRITICAL SEISMIC VECTOR RANDOM EXCITATIONS FOR MULTIPLY SUPPORTED STRUCTURES

Abstract

A method for determining critical power spectral density matrix models for earthquake excitations which maximize steady response variance of linear multiply supported extended structures and which also satisfy constraints on input variance, zero crossing rates, frequency content and transmission time lag has been developed. The optimization problem is shown to be non-linear in nature and solutions are obtained by using an iterative technique which is based on linear programming method. A constraint on entropy rate as a measure of uncertainty which can be expected in realistic earthquake ground motions is proposed which makes the critical excitations more realistic. Two special cases are also considered. Firstly, when knowledge of autospectral densities is available, the critical response is shown to be produced by fully coherent excitations which are neither in-phase nor out-of-phase. The critical phase between the excitation components depends on structural parameters, but independent of the auto-spectral densities of the excitations. Secondly, when the knowledge of autospectral densities and phase spectrum of the excitations is available, the critical response is shown to be produced by a system dependent coherence function representing neither fully coherent nor fully incoherent ground motions. The applications of these special cases are discussed in the context of land-based extended structures and secondary systems such as nuclear piping assembly. Illustrative examples on critical inputs and response of sdof and a long-span suspended cable which demonstrated the various features of the approach developed are presented.