Stochastic Frame Response using Modal Truncation

Abstract

This paper describes a computationally simplified procedure for calculating the covariance matrix of building frame displacements when the structure is excited by multiple correlated stationary forcing functions. Normal mode truncation procedures are used to enable the analyst to obtain an approximate covariance matrix of response to any desired degree of accuracy. Plots are given for normal coordinate receptance coefficients with 2% and 5% critical damping. Comments are made with respect to the importance of auto-power and cross-power spectral densities and frequency bands in which their values must be accurately calculated.