Refined Dynamic Stability Theory of Laminated Isotropic Circular Plates

Hamilton’s variational principle is used for the derivation of transversally isotropic laminated circular plates motion. Nonlinear strain-displacements relations are considered. Linearized dynamic stability equations are obtained for circular plates subjected to the same uniformly distributed periodic radial loads. The effects of transverse shear and rotational inertia are included. The exact solutions of vibrations and buckling problems are given initially in the terms of Bessel, power, and trigonometric functions. The vibrational modal functions are used then as a basis in the Galerkin method that reduced the study of dynamic stability to investigation of bounds of instability of Mathieu’s equations. Analytic expressions for the bounds of both principal and combination-type instability regions are obtained using the methods of Bolotin and Tamir. A new effect—sensitivity of certain instability regions to slight imperfections in the symmetry of lamination—is found out and discussed here.