Dynamic instability of shear-deformable laminated plates

The dynamic instability of antisymmetric angle-ply and cross-ply laminated plates, subjected to periodic inplane loads P(t) = P_s + P_d cosωt, is investigated within the high-order shear deformation lamination theory, where the motion is governed by five partial differential equations. Using the method of multiple-scale, analytical expressions for the instability regions are obtained at ω = Ω_j ± Ω_i, where Ω_i are the natural frequencies of the system. It is shown that, besides the principal instability region at ω = 2Ω₁ (Ω₁ is the fundamental frequency), other cases of ω = Ω_i + Ω_j related to the first mode, can be of major importance and yield a significantly enlarged instability region.