Mixed mode nonlinear response of rectangular plates under static and dynamic compression

The paper deals with the nonlinear response of thin rectangular plates subjected to in-plane compressive harmonic load. The excitation frequency is equal to the natural frequency for an unloaded plate. The equations of motion based on classical theory are solved by Galerkin integrals. The novel part of the research is the consideration of two and/or three simultaneous mode shapes in deflection function. By performing numerical integration using the Runge–Kutta procedure, the dynamic responses of the plates have been analyzed based on in-time plate maximal deflection, phase portraits, and Poincaré maps. The dynamic buckling has been estimated by employing Volmir or Budiansky–Hutchinson criteria. The influence of mixed mode on plate behavior in dynamic load has been analyzed. Additionally, the effect of mixed mode for equilibrium path determination has been investigated for plates under static load. The problems are verified in a numerical way by employing the finite element method (FEM) - ANSYS software.