Formulation of enriched macro elements using trigonometric shear deformation theory for free vibration analysis of symmetric laminated composite plate assemblies

The formulation of an enriched macro element suitable to analyze the free vibration response of composite plate assemblies is presented in this article. Based on the Trigonometric Shear Deformation Theory (TSDT) and the use of Gram–Schmidt orthogonal polynomials as enrichment functions a finite macro element is developed. In the TSDT framework, shear stresses are vanished at the top and bottom surfaces of the plates and shear correction factors are no longer required. The Principle of Virtual Work is applied to derive the governing equations of motion. A special connectivity matrix is obtained; so that hierarchically enriched global stiffness matrix and mass matrix of general laminated plate structures are derived, allowing to study generally coplanar plate assemblies by combining two or more macro elements. This procedure gives a matrix-eigenvalue problem that can be solved with optimum efficiency. Results of free vibration analysis for symmetric laminated plates of different thickness ratios, geometrical planform shapes and boundary conditions are presented. The accuracy of the formulation is ensured by comparing some numerical examples with those available in the literature.