Nonstationary random vibration analysis of structures with uncertain parameters based on a polynomial dimensional decomposition

Abstract

AbstractBased on polynomial dimensional decomposition (PDD), a novel method for analysing nonstationary random vibration of structures with uncertain parameters is proposed in this paper. The uncertain structural parameters are assumed to be independent random variables, with certain types of probability distributions; thus, the nonstationary random vibration responses of the structures become stochastic functions of these uncertain parameters. A dimensional decomposition and Fourier expansion were applied to calculate the statistical characteristics of the nonstationary random vibration responses of the structures. To calculate the conditional power spectral density (CPSD) and conditional standard deviation (CSD) of the nonstationary random vibration responses, CPSD and CSD were explicitly expressed using expansion coefficients and polynomial basis. Subsequently, the probability distributions of the structural responses can be effectively calculated in terms of these explicit expressions. Dimension‐reduction integration and Gauss numerical integration were applied to calculate expansion coefficients. The validity of the proposed method was verified by numerical examples, including a single‐degree‐of‐freedom system and a multi‐degree‐of‐freedom system (reinforced concrete shear wall). The results indicate that the proposed method is as accurate as Monte Carlo simulation (MCS), whereas the proposed method requires considerably smaller number of nonstationary random vibration analyses than MCS. Moreover, the nonstationary random vibration analysis of a long‐span cable‐stayed bridge demonstrates that the proposed method is feasible for quantifying the uncertainties of the nonstationary random vibration responses of complex engineering structures with uncertain parameters.