NONLINEAR ANALYSIS OF VISCOELASTIC RECTANGULAR PLATES

Resumo

In this work, the non linear vibrations of thin, viscoelastic and isotropic clamped
rectangular plates, subjected to concentrated harmonic load are studied. The Von Karman
non linear strains relations are used and to describe the clamped boundary conditions,
rotational springs are considered. The viscoelastic material is described as the Kelvin-Voigt
model and the Raylrigh Ritz method is used to obtain a system of non linear dynamic
equilibrium equations with 39 degrees of freedom which is solved, in turn, by the Runge-Kutta
tnethod. A parametric detailed analysis is performed to study the influence of axial load,

viscosity parameter and geometry on the non linear response of the plate. The frequency-
amplitude relation and resonance curves were plotted. The frequency-amplitude curves

showed that as the viscosity parameter is increased, the maximum amplitudes and the degree
of nonlinearity are reduced, it was also observed that when both the dimentions of the plate
and external load are increased, the frequency-amplitude relations are quasi linear, The
resonance curves showed that the plate has a typical hardening behavior with two coexisting
atractors with high sensitivity to initial conditions.