Forced stationary vibrations of flexible plates induced by random narrow-band excitations

Abstract

We consider some problems related to the analysis of the modes of forced vibrations of elastic plates induced by random narrow-band excitations. The investigation of nonlinear vibrations of a plate is performed within the framework of a reduced discrete model constructed by using the Hamilton variational principle, finite-element methods, and generalized coordinates. To study the dynamical state of the analyzed structure, we perform numerical simulation of the vibrations induced by a particular realization of narrow-band excitations. Each realization of random narrow-band excitations is obtained with the help of a shaping filter of the second order and describes harmonic oscillations with slowly varying amplitude and phase. We also consider the scenarios of transitions between different modes of vibrations of the plate and estimate the time of its residence in different dynamical states.