Nonlinear analysis of viscoelastic rectangular plates subjected to harmonic in-plane load compression

Resumo

In this work, based on Kelvin-Voigt mechanical model, the viscoelastic damping on the dynamic
instability of axially loaded rectangular plates is studied. A thin stainless-steel rectangular plate with linear
rotational springs at the edges is considered. The non-linear Von-Kármán relations are used to describe the
deformation relations of plates and the system of non-linear dynamic equilibrium equations is found through the
Hamilton principle by application of the Rayleigh-Ritz method, which are in turn, solved by the fourth-order
Runge-Kutta method. The bifurcation diagrams, the phase portraits and the Poincaré maps are obtained for the
principal and secondary instability regions. For lower values of axial loading, the non-trivial solutions analyzed
in the secondary region of dynamic instability are characterized by two periodic responses of period 1T, at the
principal instability region, a periodic solution of period 2T is observed. 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.