Three-dimensional elasticity solution for vibration analysis of composite rectangular parallelepipeds

• Vibrations of composite rectangular parallelepipeds with arbitrary boundary conditions are analyzed.
• Theoretical model is formulated using a modified variational principle based on 3-D elasticity theory.
• Free vibration solutions are given for isotropic and composite beams, plates, and solids.
• Composite parallelepipeds under rectangular, triangular, half-sine and exponential pulses are examined.

A three-dimensional elasticity solution is proposed for determining the free and transient vibrations of composite rectangular parallelepipeds with arbitrary combinations of boundary constraints. The theoretical model is formulated by means of a modified variational principle in conjunction with a multi-segment partitioning procedure based on the three-dimensional linear elasticity theory. The displacement components of each parallelepiped segment are expanded by a triplicate series of orthogonally polynomial functions i.e., the Chebyshev orthogonal polynomials of first and second kind and the Legendre orthogonal polynomials of first kind. To demonstrate the reliability and accuracy of the present methodology, a considerable number of free vibration solutions are given for isotropic and composite rectangular parallelepipeds (including beams, plates, and solids) with different combinations of free, simply-supported, clamped and elastic-supported boundary conditions. The present results are compared with existing experimental and analytical results published in the literature as well as those solutions obtained from finite element analyses. New benchmark solutions are also obtained for composite parallelepipeds. With regard to the transient vibration analyses, composite rectangular parallelepipeds subjected to several time-dependent impulsive loads, including a rectangular pulse, a triangular pulse, a half-sine pulse and an exponential pulse, are investigated. The effects of the fiber orientation, boundary condition as well as the type of impulsive load on the transient responses of composite parallelepipeds are also discussed in detail.