Three-dimensional free and transient vibration analysis of composite laminated and sandwich rectangular parallelepipeds: Beams, plates and solids

This paper presents an efficient method for predicting the free and transient vibrations of multilayered composite structures with parallelepiped shapes including beams, plates and solids. The exact three-dimensional elasticity theory combined with a multilevel partitioning hierarchy, viz., multilayered parallelepiped, individual layer and layer segment, is employed in the analysis. The continuity constraints on common interfaces of adjacent layer segments are imposed by a modified variational principle, and the displacement components of each layer segment are assumed in the form of orthogonal polynomials and/or trigonometric functions. Numerical studies are given for free vibrations of composite laminated and sandwich beams, plates, and solids. Some in-plane shear vibration modes missed in previous elasticity solutions for multilayered plates are examined. The natural frequencies derived from Reddy's high-order shear deformation theory and layerwise theory for soft-core sandwich plates show significant deviation from elasticity solutions. Transient displacement and stress responses for angle-ply laminated and sandwich plates under four types of impulsive loads (including rectangular, triangular, half-sine and exponential pulses) are obtained by the Newmark integration procedure. The present solutions may serve as benchmark data for assessing the accuracy of advanced structural theories and new developments in numerical methods.