ANALYTICAL AND NUMERICAL SOLUTION FOR FREE VIBRATIONS OF LAMINATED COMPOSITE PLATES

Vasilije Bojović; Marina Rakočević

doi:10.5937/jaes0-50407

Vasilije Bojović Faculty of Civil Engineering, University of Montenegro, Podgorica, Montenegro
Marina Rakočević Faculty of Civil Engineering, University of Montenegro, Podgorica, Montenegro

DOI: https://doi.org/10.5937/jaes0-50407

Keywords: natural frequencies, free vibrations, analytical solution, numerical solution, laminated composite plates

Abstract

Analytical and numerical free vibration analysis of thick and moderately thick laminated composite plates, with different boundary conditions is performed in this paper. Laminated composite plates with cross-ply and angle-ply orientation of layers are considered. The ply orientation is an angle between the x-axis and the direction of fibres in that ply (layer). Cross-ply laminates are those, which have ply orientations θ of 0° or 90°. Ply orientation of angle-ply laminates is θ and -θ, where 0° ≤ θ ≤ 90°. The analytical and numerical calculation of natural frequencies of vibrations for laminates with symmetric and antisymmetric arrangement of layers is performed. The analytical solution is developed using the Equivalent Single-Layer Theories, the CLPT (Classical Laminated Plate Theory) and the FSDT (First-order Shear Deformation Theory). The numerical calculation is made using the ANSYS software package, which is based on the finite element method. The influence of dimensions, boundary conditions, and ply orientation, on the values of natural frequencies, is analysed. The conducted analysis detected the significant impact of dimensions, boundary conditions, and ply orientation, on the free vibrations of laminated composite plates. Increasing the thickness of the plate, the influence of shear deformation increases. Therefore, in the analysis of thicker plates, the FSDT provides more accurate results, than the CLPT. It is observed that the application of Equivalent Single-Layer Theories (CLPT and FSDT) is justified in the analysis of moderately thick plates, while in the analysis of thick plates, the use of Layerwise theories is recommended.

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