A Novel Approach for Evaluating Nonstationary Response of Dynamic Systems to Stochastic Excitation

The transient state of a dynamic system,such as offshore structures,to random excitation is always nonstationary.Many studies have contributed to evaluating response covariances at the transient state of a linear multi-degree-of-freedom(MDOF)system to random excitations,but a closed-form solution was not available unless the excitation was assumed to be a physically unrealizable white noise process.This study derives explicit,closed-form solutions for the response covariances at the transient state by using a pole-residue(PR)approach operated in the Laplace domain when the excitations are assumed to be stationary random processes described by physically realizable spectral density functions.By using the PR method,we can analytically solve the triple integral in evaluating the nonstationary response covariance.As this approach uses the poles and residues of system transfer functions,rather than the conventional mode superposition technique,the method is applicable to MDOF systems with non-classical damping models.Particular application of the proposed method is demonstrated for multi-story shear buildings to stochastic ground acceleration characterized by the Kanai–Tajimi spectral density function model,and a numerical example is provided to illustrate the detailed steps.No numerical integrations are required for computing the response covariances as the exact closed-form solution has been derived.The correctness of the proposed method is numerically verified by Monte Carlo simulations.

Analyzing Nonstationary Random Response of a SDOF System under the Evolutionary Random Excitation by Wavelet Transform

For evolutionary random excitations, a general method of analyzing nonstationary random responses of systems was presented in this paper. Firstly, for the evolutionary random excitation model, the evolutionary power spectrum density function （EPSD） of a random excitation was given by wavelet transform. Based on the EPSD, the nonstationary responses of a SDOF system subjected to evolutionary random excitations were studied. The application and validity of presented method were illustrated by numerical examples. In numerical examples, the recently developed stochastic models for El Centro （1934） and Mexico City （1985） earthquakes which preserve the nonstationary evolutions of amplitude and frequency content of ground accelerations were used as excitations. The nonstationary random mean-square responses of a SDOF system under these two excitations were evaluated and compared with simulated results.