Análise não linear de placas retangulares compostas de material viscoelástico - Dias, Phablo Veríssimo Inácio (2020)
Based on Kelvin-Voigt mechanical model, in this work the viscoelastic damping in nonlinear vibrations and dynamic instability of transversally and axially loaded rectangular plates is studied. Rectangular plates with initial geometric imperfections and with linear rotational springs at the edges are admitted in order to consider clamped boundary conditions. The non-linear Von-Kármán relations are used to describe the deformation relations of the plates and the system of non-linear dynamic equilibrium equations is found through the Hamilton principle by way of application of the Rayleigh-Ritz method, being solved later through of the fourth-order Runge-Kutta method. Initially, using the frequency-amplitude relations the influence of the viscoelasticity parameter on the plate’s non-linear mechanical behavior is investigated, observing that with the increase in the viscoelasticity parameter, the maximum amplitudes and non-linearity of the response decrease. The resonance curves, the post-critical path, the bifurcation diagrams, the attraction basins, the phase plans and the Poincaré maps were obtained for two different plates under distinct loading conditions. It is shown that, for all the amplitudes of the transverse loading studied, the plate presents periodic solutions of period 1T. When the plate is analyzed with higher levels of axial loading, this response may have periods of high order, and quasi-periodic and chaotic responses are also found. In all cases, a behavior of hardening of the plate is observed, however, in the study of effect of initial geometric imperfections, the response may become initially softened for high levels of imperfection. Finally, a nonlinear damping model is also used, which is compared with an equivalent viscous damping model.