A hybrid method for analysing stationary random vibration of structures with uncertain parameters

This paper presents a new hybrid polynomial dimensional decomposition-pseudo excitation method (PDD-PEM) for analysing stationary random vibration of structures with uncertain parameters. The power spectral density (PSD) of the structural random response is expressed as a function of uncertain parameters using the PEM and a finite hierarchical expansion is performed using the component functions of the PDD. The component functions are then represented by approximate Fourier-polynomial expansions with orthonormal polynomial bases and expressions are given for calculating the first two moments of the PSD of random structural responses, using the coefficients of the expansion. Considering that calculating the coefficients requires difficult multi-dimensional integration, a dimension-reduction integration method and a Gaussian numerical integration method are introduced to effectively reduce the computational efforts of the calculation of the coefficients. The results of five numerical examples indicate that the proposed method is nearly as accurate as but more efficient than the Monte Carlo simulation method.

Automated summary

This paper introduces a new method for analyzing stationary random vibration of structures with uncertain parameters. The method involves polynomial decomposition and Fourier-polynomial expansion of component functions to calculate the PSD of random structural responses efficiently. The use of dimension-reduction integration and Gaussian numerical integration methods helps reduce the computational efforts required for calculating the coefficients.