An exact spectral-dynamic stiffness method for free flexural vibration analysis of orthotropic composite plate assemblies - Part I: Theory

A spectral-dynamic stiffness method (S-DSM) for exact free vibration analysis of general orthotropic composite plate-like structures is presented in the paper. The method combines the advantages of the classical dynamic stiffness method (DSM) with those of the spectral method, and it resembles the finite element and the boundary element methods. The formulation is based on the exact general solution of the governing differential equation, which provides complete flexibility to describe any arbitrary boundary conditions. The dynamic stiffness formulation is essentially accomplished through a mixed-variable approach in a symbolic form with explicit expressions rendering physical meanings. Then a systematic procedure for plate assemblies under arbitrary boundary constraints is described. Finally, a set of novel techniques are proposed to enhance the Wittrick Williams algorithm by resolving the fully-clamped plate problem. The validation of the theory and its applications to a wide range of engineering structures are demonstrated in Part II of this two-part paper. (C) 2015 Elsevier Ltd. All rights reserved.