Elastic perfectly plastic oscillator under random loads: Linearization and response power spectral density

Abstract

The randomly-excited elastic-perfectly-plastic oscillator—hysteretic bilinear oscillator with zero secondary stiffness—has been extensively researched. The vast majority of the work on that system has investigated the time-domaine statistics of the response. No studies have focused on the power spectral densities. This study specifically examines the system's velocity power spectral density—the system's displacement is nonstationary—under wide-band random excitations by means of a statistical linearization/stochastic averaging technique that is developed in one existing and two new procedures, one with constant, the other with amplitude-dependent parameters. The three procedures are evaluated against Monte Carlo simulation and classical Gaussian linearization in terms of the velocity average power, the peak frequency of the power spectral density, its peak value, its bandwidth, and its overall shape around the main frequency. The best predictions were yielded by the new procedure with amplitude-dependent parameters, which combines an extended amplitude-phase transformation, a linearization with random parameters into a Maxwell system, a correlation-function-based criterion, the conditional power spectral density concept, and a power conservation correction step. The new procedures can be adapted to apply to other hysteretic systems.