Three-Dimensional Vibration Analysis of Rectangular Laminated Composite Plates with Combination of Clamped and Free Boundary Conditions

고정과 자유경계조건의 조합을 고려한 직사각형 복합적층판의 3차원 진동해석

  • Received : 2006.01.13
  • Accepted : 2006.03.14
  • Published : 2006.04.27

Abstract

paper presents the results of a three-dimensional study of the natural vibration of laminated composite rectangular plates with various combinations of clamped and free boundaries. The Ritz method was used to obtain the stationary values of the associated Lagrangian, with displacements approximated using mathematicaly complete, characteristic orthogonal polynomials. The correctness of the three-dimensional model was established through a convergence study of the non-dimensional frequencies, followed by a comparison of the analytical findings in the existing literature. The wide scope of additional three-dimensional frequency results explains the influence of a number of geometrical and material parameters for angle-ply and cross-ply laminated plates, namely aspect ratio (${\mathcal{a/b}}$), thickness ratio (${\mathcal{a/h}}$), orthotropy of material, number of plies (${\mathcal{N}}$), fiber orientation angle (${\theta}$), and stacking sequence.

본 논문은 고정과 자유 경계의 다양한 조합을 갖는 직사각형 복합적층판의 고유진동에하고 있다. 본 연구에서는 수학적으로 완전한 특성직교다항식으로 표현되는 근사변위와 Ritz법을 이용하여 Lagrange 범함수의 정상값을 구하였다. 3차원 모델의 정확성이 무차원 진동수의 수렴도를 검토하여 이루어졌으며, 또한 기존 문헌상의 해석결과와의 비교를 통하여 진동수의 정확성을 검토하였다. 본 논문에서 제시된 3차원 진동수의 결과를 이용하여 복합적층판의 기하 및 재료에 관한 매개변수 즉, 형상비(${\mathcal{a/b}}$), 폭두께비(${\mathcal{a/h}}$), 재료의 직교이방성, 플라이 수(${\mathcal{N}}$), 섬유배향각(${\theta}$) 및 적층순서가 미치는 효과를 설명하였다.

Keywords

Acknowledgement

Supported by : Semyung University

References

  1. Bhumbla, R., Kosmatka, J.B., and Reddy, J.N. (1990) Free Vibration Behavior of Spinning Shear Deformable Plates Composed of Composite Materials, AIAA Journal, Vol. 28, pp. 1962-1970 https://doi.org/10.2514/3.10505
  2. Chai, G.B. (1994) Free Vibration of Generally Laminated Composite Plates with Various Edge Support Conditions, Composite Structures, Vol. 29, pp. 249-258 https://doi.org/10.1016/0263-8223(94)90022-1
  3. Chihara, T.S. (1978) An Introduction to Orthogonal Polynomials, Gordon and Breach Science Publishers, London
  4. Craig, T.J. and Dawe, D.J. (1986) Flexural Vibration of Symmetrically-laminated Composite Rectangular Plates Including Transverse Shear Effects, International Journal of Solids and Structures, Vol. 22, pp. 155-169 https://doi.org/10.1016/0020-7683(86)90005-3
  5. Kabir, H.R.H. (2004) On Free Vibration Response and Mode Shapes of Arbitrarily Laminated Rectangular Plates, Composite Structures, Vol. 65, pp. 13-27. https://doi.org/10.1016/j.compstruct.2003.10.001
  6. Kim, J.W. and Jung, H.Y. (2001) Three Dimensional Vibration Analysis of Cantileverd Laminated Composite Plates, Journal of the Computational Structural Engineering Institute of Korea, Vol. 14, No. 1, pp. 299-308
  7. Leissa, A.W. (1981) Advances in Vibration, Buckling and Postbuckling Studies on Composite Plates, In Composite Structures, Edited by I.H. Marshall, Applied Science Pub., London
  8. Leissa, A.W. and Baharlou, B. (1987) Vibration and Buckling of Generally Laminated Composite Plates with Arbitrary Edge Conditions, International Journal of Mechanical Sciences, Vol. 29, pp. 545-555. https://doi.org/10.1016/0020-7403(87)90026-9
  9. Liew, K.M. (1996) Solving the Vibration of Thick Symmetric Laminates by Reissner/Mindlin Plate Theory and P-Ritz Method, Journal of Sound and Vibration, Vol. 198, pp. 343-360 https://doi.org/10.1006/jsvi.1996.0574
  10. Noor, A.K. (1973) Free Vibration of Multi-layered Composite Plates, AIAA Journal, Vol. 11, pp. 1038-1039 https://doi.org/10.2514/3.6868
  11. Narita, Y. and Leissa, A.W. (1992) Frequencies and Mode Shapes of Cantilevered Laminated Composite Plates, Journal of Sound and Vibration, Vol. 154, pp. 161-172 https://doi.org/10.1016/0022-460X(92)90410-Y
  12. Shi, J.W., Nakatani, A., and Kitagawa, H. (2004) Vibration Analysis of Fully Clamped Arbitrarily Laminated Plate, Composite Structures, Vol. 23, pp. 115-122
  13. Srinivas, S. and Rao, A.K. (1970) Bending, Vibration and Buckling of Simply Supported Thick Orthotropic Rectangular Plates and Laminates, International Journal of Solids and Structures, Vol. 6, pp. 1463-1481 https://doi.org/10.1016/0020-7683(70)90076-4
  14. Vinson, J.R. and Sierakowski, R.L. (1986) The Behavior of Structures Composed of Composite Materials, Dordrecht: Martinus Nijhoff, 1986
  15. Whitney, J.M. and Pagano, N.J. (1976) Deformation in Hereogeneous Anistropic Plates, ASME Journal of Applied Mechanics, Vol. 37, pp. 1031-1036 https://doi.org/10.1115/1.3408654