A spectral element approach for response spectrum estimation of frame structures with uncertain parameters subjected to stationary stochastic excitations

Determination of the response spectra of structures under excitation is crucial for vibration control, reliability analysis, fatigue life prediction, and optimization design of structures. However, available methods can be time-consuming and even erroneous when dealing with structural uncertainty, making them difficult to apply to actual complex structures. This paper proposes a spectral element approach for response spectrum estimation of structures with uncertain parameters subjected to stationary stochastic excitations. First, the spectral element method and Karhunen-Loève expansion technology are utilized to represent the response spectra of structures with uncertain parameters to reduce computation cost. Then, a dimension-reduction technology of random variables is utilized to simplify the numerical computations while retaining accuracy. Based on the above, the method for the envelope response spectrum with practical applicability is proposed in this study. The method can accurately and efficiently estimate the response spectrum of structures with uncertain parameters. The proposed approach is validated by comparison with the Monte Carlo method using three numerical examples.