Analysis of parametrically excited laminated shells

The dynamic stability of a shear-deformable circular cylindrical shell subjected to a periodic axial loading P(t) = P_s + P_d cos ωt is investigated. The simply-supported laminated shell of finite length is analyzed within Love's first-approximation theory, with the addition of transverse shear deformation and rotary inertia. Using the method of multiple scales, analytical expressions for the instability regions are obtained at ω = Ω_j ± Ω_i, where Ω_i are the natural frequencies of the shell. Yet, it is shown that instability cannot occur for the case ω = Ω_j - Ω_i due to the symmetric properties of the problem. It is also shown that, besides the principal instability region at ω = 2Ω₁ (Ω₁ is the fundamental frequency), other cases of ω = Ω_i + Ω_j can be of major importance and yield a significantly enlarged instability region.