Response of uncertain dynamic systems. II

摘要

This paper deals with structural and mechanical systems that can be modeled as single-degree-of-freedom oscillators, the knowledge of whose mass, damping, and stiffness parameters is uncertain. In conformity with usual engineering practice, it is assumed that knowledge of only the upper and lower limits within which these uncertain parameters lie is available. Excitations generated by a) external forces such as wind loads, and b) base accelerations such as those caused by strong earthquake ground shaking are both considered. The statistics of the response of such systems are obtained for the following three types of excitations. 1.1) Harmonic excitations, yielding the statistics of the transfer function of the system. Here it is shown that Monte Carlo simulaiton require large sample sizes to obtain results close to those analytically deduced.2.2) Deterministic time histories of excitation, yielding the statistics of the transient response of the system. This is done by Fourier decomposition using the transfer function results obtained above.3.3) Random stationary excitations, yielding the statistics of the power spectal density of the response.Thus the paper presents the results of the response “random system” subjected to harmonic excitations, deterministic transient excitations, and random stationary excitations.