Fundamental Research in Nonlinear Random Vibration for Aerospace Applications

摘要

Response and safety of nonlinear structures under random excitations areinvestigated. The excitations can be either external, or parametric, or both. Extensions are made along two directions from the earlier works on exact solutions when the excitations are Gaussian white noises: (1) the excitations are impulsive, but non-Gaussian, (2) the system does not belong to the class of generalized stationary potential, thus, exact solution is not obtainable at the present time. In the first case, the probability density of the structural response is governed by a partial differential equation, with infinite number of terms. A perturbation analysis is devised to obtain approximate solutions. In the second case, a new technique is developed to obtain approximate solutions on the principle of weighted residuals. On the issues of structural safety, two failure modes are investigated: catastrophic failure and fatigue failure. Catastrophic failure occurs when structural response exceeds, for the first time, a critical limit. Fatigue failure is investigated from a fracture mechanics point of view, namely, failure is assumed to occur when a dominant crack is propagated to a critical size.... Random Vibration, Nonlinear Systems.