Parametric vibrations of a clamped reinforced viscoelastic composite plate

The study focuses on the nonlinear dynamic behavior of an anisotropic fiber-reinforced viscoelastic rectangular plate made of fiberglass with fully clamped edges, subjected to a parametric load applied along one of its sides. The mathematical formulation describing the plate’s dynamic response is developed within the framework of the generalized Timoshenko plate theory, which accounts for transverse shear deformation as well as rotary inertia effects. To incorporate the viscoelastic nature of the material, the integral representation of the Boltzmann-Volterra hereditary theory is employed, allowing the time-dependent stress relaxation of the material to be taken into account. A parametric analysis is performed to investigate how the geometric characteristics of the plate and the viscoelastic properties of the composite material influence its dynamic response. The obtained results may be useful for the design and analysis of composite structural elements operating under dynamic and parametric loading conditions. The considered problem is directly related to vibration analysis and dynamic stability of engineering structures, which is within the scope of vibroengineering applications.