Dynamic instability of antisymmetric laminated plates

The dynamic instability of antisymmetric angle-ply and cross-ply laminated plates, subjected to periodic in-plane loads P(t) = P₀ + P₁ cos θt, is investigated. Within the classical lamination theory, the motion is governed by three partial differential equations. By using the method of multiple scales, analytical expressions for the instability regions are obtained at θ = Ω_i + Ω_j, where Ω_i are the natural frequences of the system. It is shown that in some cases, beside the principal instability region at θ = 2Ω₁, where Ω₁ is the fundamental frequency, other cases of θ = Ω_i + Ω_j can be of major importance, and the final instability regions are significantly enlarged.