Three-Dimensional Vibration Analysis of Cantilevered Laminated Composite Plates

캔틸레버 복합 적층판의 3차원 진동해석

  • 김주우 (세명대학교 건축공학과) ;
  • 정희영 (서울시립대학교 토목공학과)
  • Published : 2001.09.01

Abstract

This paper presents the three-dimensional (3-D) study of the natural vibration of cantilevered laminated composite plates. The Ritz method is used to obtain stationary values of the associated Lagrangian functional with displacements approximated by mathematically complete polynomials satisfying the boundary conditions at the clamped edge exactly. The accuracy of the 3-D model is established through a convergence study of non-dimensional frequencies followed by a comparison of the converged 3-D solutions with analytical and experimental findings in the existing literature. A wide scope of 3-D frequency results explain the influence of a number of geometrical and material parameters for cantilevered laminated plates, namely aspect ratio (a/b), width-to-thickness ratio (a/h), orthotropy of material, number of plies (NP), fiber orientation angle(θ), and stacking sequence.

본 논문은 캔틸레버 복합 적층판의 고유진동에 대하여 3차원으로 해석한 연구를 제시하고 있다. 본 연구에서는 고정단에서의 경계조건을 엄밀히 만족하고 수학적으로 완전한 다항식으고 표현되는 근사 변위와 Ritz 방법을 이용하여 Lagrangian범함수의 정상값을 구하였다. 3차원 모델의 정확도는 무차원 진동수의 수렴연구를 통하여 이루어졌으며, 또한 기존 문헌상의 해석 및 실험 결과와의 비교를 통하여 본 연구 결과의 정확성을 검토하였다. 본 논문에서 제시된 3차원 진동수의 결과를 이용하여 캔틸레버 복합 적층판의 기하학 및 재료 매개변수 즉, 형상비(a/b), 폭두께비(a/h), 재료의 직교 이방성, 플라이 수(NP), 섬유 배향각(θ), 및 적층 순서가 미치는 효과를 설명하였다.

Keywords

References

  1. Journal of Composite Materials v.13 The natural modes of graphite/epoxy cantilever plates and shells Crawley.E.F.
  2. Journal of Sound and Vibration v.72 Frequency determination and non-dimensionalization for composite cantilever plates Crawley,E.F.;Dugundji,J.
  3. AIAA Journal v.22 Frequency determination technique for cantilevered plates with bending-torsion coupling Jensen,D.W.;Crawley,E.F.
  4. International Journal of Mechanical Sciences v.29 no.8 Vibration and buckling of generally laminated composite plates with arbitrary edge conditions Baharloy,B.;Leissa,A.W.
  5. Journal of Sound and Vibration v.154 no.1 Frequencies and mode shapes of cantilevered laminated composite plates Narita,Y.;Lessa,A.W.
  6. Composite Structures Advances in vibration buckling and postbuckling studies on composite plates Leissa,A.W.;I.H.Marshall(ed.)
  7. Mechanics of Composite Materials Jones,R.M.
  8. The Behavior of Structures Composed of Composite Materials Vinson,J.R.;Sierakowski,R.L
  9. Journal of Sound and Vibration v.49 Free vibration analysis of cantilever plates by the method of superposition Gorman,D.J.