State augmentation method for non-stationary/non-Gaussian vibrations of multi degree-of-freedom linear systems

The basic assumptions of stationary/Gaussian excitations and temporal independence in linear systems are commonly employed in stochastic dynamic analyses, facilitating various engineering investigations. However, in certain scenarios such as wind-induced vibrations under non-synoptic extreme wind, these assumptions may lead to unreliable predictions. The excitations exhibit significant non-stationary/non-Gaussian features due to the inherent non-synopticity of the flow. Moreover, when accounting for motion-induced forces, the coupled aerodynamic-mechanical system is modeled as a linear time-varying system marked by time-dependent aerodynamic damping and stiffness. This study aims to introduce a state augmentation method for examining the multi-modal vibrations of a long-span bridge excited by non-synoptic winds. Both unsteady motion-induced forces and non-stationary/non-Gaussian turbulence-induced forces are considered to predict the buffeting response. Based on stochastic calculus theory and the stars and bars method, we derive equations governing the statistical moments of all orders for the response of a dynamic system with multiple degrees of freedom. A comprehensive buffeting analysis of the model bridge to all wind segments of Typhoon Hagupit is conducted by using the proposed method, showing potentially greater responses when considering the non-synoptic features of the wind.