Random Vibration and Reliability Analysis of Primary-Secondary Structural Systems

Keywords: Primary-Secondary Systems, Linear Random Vibration, Random Vibration Analysis, Earthquake Resistant Design, FORM/SORM, Gaussian Excitation, Dynamic Analysis, Structural Systems, Secondary Systems, and Seismic Behavior.

Abstract: Primary-secondary structural systems do not generally have classical modes of vibration and are characterized by large differences in masses and stiffnesses associated with various degrees of freedom. Considerable research has been directed at finding efficient and robust techniques for the dynamic analysis of these systems. Methods have also been developed for approximate analysis of primary-secondary system. A variety of approximate methods of analysis, such as cascade analysis, perturbation methods and component mode method, have extensively been applied. In addition, there are several exact methods of analysis that circumvent the associated eigenvalue problem of a primary-secondary system. Most of these methods focus on stationary responses. In this work, a methodology is proposed for calculating second moment characteristics of response processes and the probability of failure for linear primary-secondary systems with uncertain parameters subject to non-stationary Gaussian excitation. The proposed method is based on methods of linear random vibration, crossing theory of Gaussian processes, and First-and Second-Order Reliability methods (FORM/SORM). The random vibration analysis follows the state space approach in which excitation is modeled as the output of a linear filter subjected to a uniformly modulated white noise process. Mean crossing rates of responses are used to approximate conditional failure probabilities for a given set of system parameters. The analysis is relatively simple because conditional responses are Gaussian processes. FORM/SORM algorithms are used to approximate unconditional system failure probabilities.