Thermally induced vibrations of cross-ply laminated shallow shells

An exact analytical solution of the dynamic response of cross-ply laminated shallow shells subject to rapid heating is presented. The classical theory (based on Love-Kirchhoff assumption), involving three coupled partial differential equations, is used. The solution is applicable to shells whose parallel edges are simply supported and the remaining ones are clamped. A generalized modal approach is used to obtain the solution. The equations of motion are converted into a single-order system of equations by using state variables. The biorthogonality conditions of principal modes of the original and adjoint eigenfunctions are used to decouple the state space equation. Histories of deflection of graphite-reinforced aluminum shell panels are presented through numerical examples.King Saud Universit