Stationary and Transient Response Statistics

The covariance functions for the transient response of a linear MDOF-system due to stationary time limited exitation with an arbitrary frequency content are related directly to the covariance functions of the stationary response. For rational spectral density functions closed form expressions for the covariance functions are obtained. In case of white noise excitation the expressions simplify considerably, and an approximative method for including the main effects of an actual spectral density function is derived based on a white noise analogy. The theory is applied to a multistorey frame structure, and it is demonstrated that it offers an efficient way to calculate the time-dependent second-order moments. The approximation appears to yield fully adequate results for many practical applications involving lightly damped structures.