I am investigating an engineering problem that relates to the dynamic stability of a beam-like structure under the action of a stochastic excitation (say, e.g., a marine structure acted by waves or a tall building acted by wind). My excitation is described by a wide-band band spectrum such as the ones here (typical spectrum depicted below).
I want to investigate the stability of the response of my structural finite element model, composed of beam elements. From my reading of Xie, Dynamic Stability of Structures, and Ibrahim, Parametric Random Vibration, I understand that most of the techniques available relate to the analysis of Itô differential equations, e.g., through moment stability of Lyapunov exponents.
- My immediate question is whether these techniques require my excitation to be approximated by a Gaussian white noise process, and if it is legitimate to do so given the spectral density I showed above.
- Having a multiple degree-of-freedom system (my finite element model) described by a set of ODEs (weak formulation of the equilibrium equations) that are written in matrix form as M $\ddot{\textbf{x}}$ + D $\dot{\textbf{x}}$ + K $\textbf{x}$ = $\textbf{P}$(t) , how successful can I expect to be in applying the analytical techniques to assess the response stability?
