Effect of support conditions on nonlinear parametric vibrations of a viscoelastic anisotropic reinforced composite plate

This study considers the nonlinear dynamics of a rectangular reinforced plate made of glass-reinforced plastic subjected to a periodic compressive load along one pair of edges. The model is based on a refined Timoshenko-type theory, which retains transverse shear and rotary inertia, and it includes geometric nonlinearity together with Boltzmann–Volterra hereditary viscoelasticity governed by the weakly singular Koltunov–Rzhanitsyn kernel. The anisotropy of the structure is described by transformed reduced stiffnesses at an arbitrary reinforcement angle. Applying the Bubnov–Galerkin method reduces the problem to a system of nonlinear integro-differential equations, which are integrated numerically once the singularity of the kernel has been removed. Two sets of boundary conditions are considered: simple support and clamping of all edges, with the material, geometry, rheological parameters, and loading law kept identical, which makes it possible to attribute the difference in the results to the type of support. The sensitivity of the response to the reinforcement angle is shown to be governed by the support conditions: for simple support, rotating the fibers from 0° to 45° reduces the deflection at the midpoint by roughly a factor of three, whereas for clamping the same rotation changes the amplitude by about 10% and in the opposite direction. Taking hereditary properties into account turns undamped vibrations into a decaying process without external damping, in the same way for both types of support. The clamped plate is found to require nine retained modes compared with four for simple support, and the reason for the difference is identified.