A modified Fourier solution for vibration analysis of moderately thick laminated plates with general boundary restraints and internal line supports

• A unified vibration analysis method is developed for thick composite laminated plates.
• The proposed method is appropriate for arbitrary boundary conditions.
• New results for laminated plates with elastic restraints.
• New results for internal line supported laminated plates.
• Influence of the location of a line support is investigated.

In this investigation, a modified Fourier solution based on the first-order shear deformation theory is developed for the free vibration problems of moderately thick composite laminated plates with general boundary restraints and internal line supports. In this solution approach, regardless of boundary conditions, the displacements and rotation components of the plate are invariantly expressed as a new form of trigonometric series expansions in which several supplementary terms introduced to ensure and accelerate the convergence of the series expansion. All the unknown coefficients are treated as the generalized coordinates and determined using the Raleigh–Ritz method. A systematic comparison including classical boundaries, elastic restraints, and internal line supports between the current solutions and numerical results published by other researchers is carried out to validate the excellent accuracy, reliability and feasibility of the proposed method. Excellent agreements are achieved. Comprehensive studies on the effects of elastic restraint parameters, layout schemes and locations of line supports are also reported. New results are obtained for plates subjected to elastic boundary restraints and arbitrary internal line supports in both directions, which may serve as benchmark solutions for future researches.