Nonlinear vibrations of viscoelastic rectangular plates

Nonlinear vibrations of viscoelastic thin rectangular plates subjected to normal harmonic excitation in the spectral neighborhood of the lowest resonances are investigated. The von Kármán nonlinear strain–displacement relationships are used and geometric imperfections are taken into account. The material is modeled as a Kelvin–Voigt viscoelastic solid by retaining all the nonlinear terms. The discretized nonlinear equations of motion are studied by using the arclength continuation and collocation method. Numerical results are obtained for the fundamental mode of a simply supported square plate with immovable edges by using models with 16 and 22 degrees of freedom and investigating solution convergence. Comparison to viscous damping and the effect of neglecting nonlinear viscoelastic damping terms are shown. The change of the frequency–response with the retardation time parameter is also investigated as well as the effect of geometric imperfections.