Vibration Analysis of Three Layer Sandwich Beam

3층 샌드위치보의 진동해석

  • 박철휴 (경상대학교 해양산업연구소) ;
  • 김원철 (경상대학교 해양산업연구소) ;
  • 양보석 (부경대학교 공과대학 기계공학과)
  • Published : 1998.02.01

Abstract

This paper proposes a new technique to formulate the finite element model of a sandwich beam by using GHM (Golla-Hughes-McTavish) internal auxiliary coordinates to account for frequency dependence. Through the use of auxiliary coordinates, the equation of motion of undamped mass and stiffness matrix form is extended to encompass viscoelastic damping matrix. However, this methods all suffer from an increase in order of the final finite element model which is undesirable in many applications. Here we propose to combine the GHM method with model reduction techniques to remove the objection of increased model order.

본 연구에서는 진동수에 종속된 GHM (Golla-Hughes-McTavish) 내부보조좌표를 사용하여, 3층 샌드위치보의 유한요소모델을 정식화하는 새로운 기법을 제안하였다. 내부보조좌표를 3층 샌드위치보에 사용하면, 비감쇠질량과 강성행렬의 운동방정식은 정성감쇠행렬이 포함되므로써 행렬의 요소들이 복잡하게 확장되어 진다. 따라서 이 방법은 실제의 많은 응용에 있어서 바람직하지 못한 유한요소모델의 행렬요소들의 증가에 따른 많은 단점을 갖게 된다. 따라서, 본 논문에서는 행렬요소들의 증가에 따른 여러 단점들을 제거하기 위하여, 행렬요소 감소방법을 GHM방정식과 합성된 운동방정식을 유도하는 새로운 방법을 제안한다.

Keywords

References

  1. AIAA Journal v.21 no.5 Fractional Calculus - A Different Approach to the Analysis of Viscoelastically Damped Structures Bagley, R.L.;Torvik, P.J.
  2. Trans. ASME. Journal of Applied Mechanics v.58 On Damping Mechanisms in Beams Banks, H. T.;Inman, D. J.
  3. Theory of Viscoelasticity: An Introduction(2nd Edition) Christensen, R.M.
  4. Concepts and Applications of Finite Element Analysis(2nd Ed.) Cook, R. D.
  5. Trans. ASME, Journal of Applied Mechanics v.52 Dynamics of Viscoelastic Structure-A Time-Domain, Finite Element Formulation Golla, D. F.;Hughes, P. C.
  6. AIAA Journal v.3 Reduction of Stiffness and Mass Matrices Guyan, R. J.
  7. Vibrations with Control, Measurement and Stability Inman, D. J.
  8. Mechanics Research Communications v.16 no.4 Vibration Analysis of Viscoelastic Beams by Separation of Variables and Modal Analysis Inman, D. J.
  9. AIAA Journal v.3 Structural Eigenvalue Problem: Elimination of Unwanted Variabiles Irons, B.
  10. Trans. ASME, Journal of Engineering Materials and Technology v.119 Dynamics of Thick Viscoelastic Beams Johnson, A. R.;Tessler, A.;Dambach, M.
  11. Proc. JACC Computation of balancing Transformation Laub, A. J.
  12. Trans. ASME, Journal of Vibration and Acoustics v.117 Time Domain Modeling of Linear Viscoelasticity Using Anelastic Displacement Fields Lesieutre, G. A.;Bianchini, E.
  13. International Journal of Solids and Structures v.33 Finite Element Modeling of Frequency-Dependent and Temperature-Dependent Dynamic behavior of Viscoelastic Material in Simple Shear Lesieutre, G. A.;Govindswamy, K.
  14. AIAA Journal of Guidance Control and Dynamics v.13 Finite Element Modeling of Frequency-Dependent Material Properties Using Augmented Thermodynamic Fields Lesieutre, G. A.;Mingori, D. L.
  15. AIAA-92-2380-CP Finite Element Modeling of Linear Viscoelastic Structures: The GHM Method McTavish, D. J.;Hughes, P.C.
  16. Trans. ASME, Journal of Vibration and Acoustics v.115 Modeling of Linear Viscoelastic Space Structures McTavish, D. J.;Hughes, P.C.
  17. IEEE Trans. Automat. Contr. v.AC-26 Principal Component Analysis for Linear Systems: Controllability, Observability, and Model Reduction Moore, B. C.
  18. Vibration Damping Nashif, A.D.;Jones, D.;Henderson, J.P.
  19. The Journal of Sound and Vibration Model Rduction of Viscoelastic Finite Element Models Park, C. H.;Inman, D. J.;Lam, M. J.
  20. The Shock and Vibration Bulletin v.51 The Modal Strain Energy Finite Element Method and its Application to Damped Laminated Beams Rogers, L.C.;Johnson, C.D.;Keinholz, D. A.
  21. Trans. ASME, Journal of Dynamic Systems and Control v.115 Control-Oriented Order Reduction of Finite Element Model Yae, K. H.;Inman, D. J.
  22. Ph.D. dissertation. State University of New York at Buffalo Reduced Order Modeling and Analytical Model Modification for Structural Dynamics and Control Yae, K. H.