Transient Nonlinear Vibration of Randomly Excited Cylindrical Shallow Panels in Non Aging Viscous Medium

Abstract

In this paper, the nonlinear transient vibration of a cylindrical shallow panel under lateral white noise excitation is studied. The panel is in contact with a non aging viscoelastic medium. Since the external load is a time varying random wide band process, deterministic and conventional approaches cannot be used. Instead, the evolution of the probability density function of the response is investigated. To compute the density function, the famous Monte Carlo simulation is employed while its correctness for this specific application is validated with another work in literature. The governing equation is rewritten to a non dimensional format; so that the results can be applied to a wide range of panels. Specifically, the transient behavior is investigated with respect to the quasi slenderness ratio and the non dimensional mean value of lateral load. As expected, both the simple damped oscillation and unstable jumping phenomenon are seen relative to the values of prescribed parameters. Finally, the joint probability density function of the response is drawn that give someone an idea about the quality of the response in the phase plane.