Parametric Excitation of Viscoelastic Plates

TLDR: In this paper, the dynamic instability of rectangular viscoelastic plates subjected to periodic in-plane loads P s + P d cos θt is investigated and the material behavior is given in terms of the Boltzmann superposition principle.

Abstract: The dynamic instability of rectangular viscoelastic plates subjected to periodic in-plane loads P s + P d cos θt is investigated. The material behavior is given in terms of the Boltzmann superposition principle, which allows any linear viscoelastic character. This representation yields an integro-differential equation of motion, for which time-dependent instability regions are determined analytically using the multiple-scales method. It is shown that, due to viscoelasticity, the stability regions are expanded relative to the elastic ones and that a plate which may be initially stable can become unstable after a finite time, unlike in the elastic case. The influence of the static and the dynamic parts of the loads on this region is also investigated.