On the parametric instability of laminated plates modeled within a high-order shear-deformation theory

The parametric instability of cross-ply laminated plates, subjected to periodic in-plane loads P(t)=P_s+P_d cos τt, is investigated. Within the high-order shear deformation lamination theory the motion is governed by three coupled partial differential equations, which are nonsymmetric in their nature. Using the method of multiple-scale, analytical expressions for the instability regions are obtained at θ=Ω_j±Ω_i, where Ω_i are the natural frequencies of the system. It is shown that beside the principal instability region at θ=2 Ω₁, other instability regions can exist for the first mode, and their significance is examined by various parameters such as the length-to-thickness ratio and the modulus ratio.