doi:10.3850/978-981-08-7619-7_P004

ABSTRACT

The dynamic behavior of structural and mechanical systems subjected to uncertain dynamic excitations can be described, in general, through random processes. The probabilistic characterization of these random processes can be extremely complex. However, in specific applications, an incomplete description of stochastic processes corresponding to dynamic structural response may suffice, based on the spectral characteristics of the processes under study. In particular, the so-called non-geometric spectral characteristics (NGSCs) can be employed to evaluate the time-variant central frequency and bandwidth parameters, which characterize in a synthetic way a nonstationary stochastic process (NSSP). In this paper, using the definition of NGSCs for general complex-valued NSSPs, closed-form solutions for the NGSCs of NSSPs representing the response of linear elastic structural models subjected to time-modulated colored noises are obtained. These NGSCs are used in this study to compute exactly, and in closed-form, the time-variant central frequency and bandwidth parameter of the response processes of single-degree-of-freedom (SDOF) and both classically and non-classically damped multi-degree-of-freedom (MDOF) linear elastic systems subjected to colored noise excitation from at rest initial conditions. These closed-form solutions are useful in problems which require the use of complex modal analysis, such as random vibrations of non-classically damped MDOF linear structures, and in structural reliability applications. Monte Carlo simulations have been used to confirm the validity of the proposed solutions.

Keywords: Stochastic processes, Bandwidth parameter, Non-Geometric spectral characteristics, Classically and Non-Classically damped MDOF systems.

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