ABSTRACT
Many engineering systems are subjected to loads that are essentially random processes, e.g., random functions. Examples include the wings of an airplane under gust loads, the hull of a ship under wave loads or an automobile’s suspension on a rough terrain. Moreover, the properties of many systems, such as their strength (stress at failure) are also random and vary in time. In random vibration analysis, one of the objectives is to determine the statistics of the system response and the probability of failure due to the response. Tools for time invariant reliability problems, such as first-order and second-order reliability methods (FORM and SORM), are not directly applicable to random vibration analysis. Probabilistic analysis of a dynamic system under loads that are random processes
involves the following steps:
1. Construct probabilistic models of the excitations using data obtained from measurements and experience. Using the stationarity assumption (described later in the chapter), the excitations are characterized using their means, autocorrelations and cross-correlations.
