DOI: 10.5937/jaes0-50407
This is an open access article distributed under the CC BY 4.0
Volume 22 article 1184 pages: 245-252
In this paper, a comprehensive analysis of the free vibration characteristics of laminated composite plates (LCP) with different thicknesses, is conducted using both analytical and numerical methods. The study encompasses various boundary conditions and considers laminates with cross-ply and angle-ply orientations. The ply orientation, defined as the angle between the x-axis and the fibre direction within each ply, is a key focus of the investigation. Cross-ply laminates are characterized by ply orientations θ of 0° or 90°, while angle-ply laminates exhibit ply orientations of 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 Single-Layer Theories, including the CLPT (Classical Laminated Plate Theory) and the FSDT (First-order Shear Deformation Theory). The numerical calculation is made using the finite element-based software ANSYS. 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 the considered plates. Increasing the thickness of the plate leads to an increase in shear deformation. Therefore, in the analysis of thicker plates, it is noted that the FSDT yields more accurate results compared to the CLPT. It has been established that the application of Equivalent Single-Layer Theories (CLPT and FSDT) is justified in the analysis of moderately thick plates. In contrast, for the analysis of thick plates, the use of Layerwise theories is recommended.
1. Reddy, J.N. (2003). Mechanics of laminated composite plates and shells – Theory and Analysis, II edition. CRC Press, Boca Raton, DOI: 10.1201/b12409.
2. Reddy, J.N., Khdeir, A.A. (1989). Buckling and Vibration of Laminated Composite Plates Using Various Plate Theories. AIAA Journal, vol. 27, no. 12, 1808-1817, DOI: 10.2514/3.10338.
3. Liew, K.M., Huang, Y.Q., Reddy, J.N. (2003). Vibration analysis of symmetrically laminated plates based on FSDT using the moving least squares differential quadrature method. Computer Methods in Applied Mechanics and Engineering, vol. 192, no. 19, 2203-2222, DOI: 10.1016/S0045-7825(03)00238-X.
4. Sharma, A.K., Mittal, N.D. (2010). Review on stress and vibration analysis of composite plates. Journal of Applied Sciences, vol. 10, no. 23, 3156-3166, DOI: 10.3923/jas.2010.3156.3166.
5. Sharma, A.K., Mittal, N.D., Sharma, A. (2011). Free vibration analysis of moderately thick anti-symmetric cross-ply laminated rectangular plates with elastic edge constraints. International Journal of Mechanical Sciences, vol. 53, no. 9, 688–695, DOI: 10.1016/j.ijmecsci.2011.05.012.
6. Vuksanović, Đ. (2000). Linear analysis of laminated composite plates using single layer higher-order discrete models. Composite Structures, vol. 28, 205-211, DOI: 10.1016/S0263-8223(99)00096-3.
7. Marjanović, M., Vuksanović, Đ. (2014). Layerwise solution of free vibrations and buckling of laminated composite and sandwich plates with embedded delaminations. Composite Structures, vol. 108, 9-20, DOI: 10.1016/j.compstruct.2013.09.006.
8. Vuksanović, Đ., Marjanović, M. (2014). Free vibrations of delaminated composite and sandwich plates. The 5th international conference Civil engineering – science and practice, 363-370.
9. Bojović, V., Rakočević, M. (2022). Free vibration analysis of symmetric cross-ply laminated composite plates. The 8th international conference Civil engineering – science and practice, 101-109.
10. Bojović, V. (2021). Stress strain analysis of laminated composite plates. Master thesis, Faculty of Civil engineering, University of Montenegro, Podgorica.
11. Rakočević, M., Bojović, V. (2021). Analysis of symmetric angle-ply laminated composite plates. Researches 2020 - Special issue of the Journal Istraživanja/Researches, on the occasion of the 40th anniversary of the Faculty of Civil Engineering in Podgorica, 1980-2020, 147-156.
12. Rakočević, M. (2016). Analytical solution for simply supported laminated composite plate based on Partial layerwise theory. Journal of Applied Engineering Science, vol. 14 no. 1, 102-108, DOI: 10.5937/jaes14-10470.
13. Rakočević, M., Popović, S., Ivanišević, N. (2017). A computational method for laminated composite plates based on layerwise theory. Composites Part B, vol. 122, 202-218, DOI: 10.1016/j.compositesb.2017.03.044.
14. Rakočević, M., Popović, S. (2018). Bending analysis of simply supported rectangular laminated composite plates using a new computation method based on analytical solution of layerwise theory. Archive of Applied Mechanics, vol. 88, 671-689, DOI: 10.1007/s00419-017-1334-x.
15. ANSYS Inc. Ansys Mechanical User’s Guide.
16. ANSYS Inc. (2009). Verification Manual for the Mechanical APDL Application – Release 12.1.