The Journal of the Acoustical Society of Korea (한국음향학회지)

The Acoustical Society of Korea (한국음향학회)
권호 표지
DOI QR코드

DOI QR Code

Application of Spectral Element Method for the Vibration Analysis of Passive Constrained Layer Damping Beams

수동감쇠 적층보의 진동해석을 위한 스펙트럴요소법의 적용

  • 송지훈 (서울대학교 조선해양공학과) ;
  • 홍석윤 (서울대학교 조선해양공학과)
  • Published : 2009.01.31
Download PDF
⟨ Previous Next ⟩

Abstract

This paper introduces a spectrally formulated element method (SEM) for the beams treated with passive constrained layer damping (PCLD). The viscoelastic core of the beams has a complex modulus that varies with frequency. The SEM is formulated in the frequency domain using dynamic shape functions based on the exact displacement solutions from progressive wave methods, which implicitly account for the frequency-dependent complex modulus of the viscoelastic core. The frequency response function and dynamic responses obtained by the SEM and the conventional finite element method (CFEM) are compared to evaluate the validity and accuracy of the present spectral PCLD beam element model. The spectral PCLD beam element model is found to provide very reliable results when compared with the conventional finite element model.

본 논문에서는 수동감쇠 적층보에 대한 스펙트럴요소법을 유도하였다. 수동감쇠 적층보의 중심층인 점탄성층은 주파수에 따라 값이 변하는 복소 계수를 가지고 있다. 그래서 점탄성층의 주파수 종속적인 복소 계수를 계산하기 위하여, 스펙트럴요소법을 주파수축 상에서 파동해로부터 얻은 엄밀해를 기반으로 하는 동적형상함수를 사용하여 유도하였다. 유도된 수동감쇠 적층보에 대한 스펙트럴요소의 신뢰성과 정밀도를 검증하기 위하여 스펙트럴요소법과 유한요소법을 사용하여 구한 주파수응답함수와 동적응답을 비교하였다. 비교 결과 수동감쇠 적층보에 대한 스펙트럴요소가 유한요소에 비해서 보다 신뢰성 있는 결과를 제공하는 것을 알 수 있었다.

Keywords

References

  1. E. M. Kerwin, "Damping of Flexural Waves by a Constrined Viscoelastic Layer," Journal of Acoustical Society of America 31(7), 952-962, 1959 https://doi.org/10.1121/1.1907821
  2. R. A. DiTaranto, "Theory of Vibratory Bending for Elastic and Viscoelastic Layered Finite Length Beams," Journal of Applied Mechanics 87, 881-887, 1965
  3. D. J. Mead and S. Markus, "The Forced Vibration of a Three-Layer Damped Sandwich Beam with Arbitrary Boundary Conditions," Journal of Sound and Vibration 10(2), 163-175, 1969 https://doi.org/10.1016/0022-460X(69)90193-X
  4. M. J. Yan and E. H. Dowell, "Governing Equations for Vibrating Constrained -Layer Damping Sandwich Plates and Beams," Journal of Applied Mechanics 39, 1041-1046, 1972 https://doi.org/10.1115/1.3422825
  5. Y. P. Lu and B. E. Douglas, "On the Forced Vibrations of Three-Layer Damped Sandwich Beams," Journal of Sound and Vibration 32(4), 513-516, 1974 https://doi.org/10.1016/S0022-460X(74)80145-8
  6. Y. V. K. S. Rao and B. C. Nakara, "Vibrations of Un-symmetrical Sandwich Beams and Plates with Viscoelastic Cores," Journal of Sound and Vibration 34(3), 309-326, 1974 https://doi.org/10.1016/S0022-460X(74)80315-9
  7. J. M. Bai and C. T. Sun, "A Refined Theory of Flexural Vibration for Viscoelastic Damped Sandwich Beams," Pro-ceedings of Damping, pp.1-16, San Francisco, CA, 1993
  8. S. A. Nayfeh and A. H. Slocum, "Flexural Vibration of a Viscoelastic Sandwich Beam in its Plane of Lamination," Proceedings of DETC, DETC/VIB-4071, Sacramento, California, 1997
  9. J. F. Doyle, Wave Propagation in Structures : An FFT Based Spectral Analysis Methodology (Springer-Verlag, New York, 1989)
  10. G. Gopalakrishnan, M. Martin and J. F. Doyle, "A matrix methodology for spectral analysis of wave propagation in multiple connected Timoshenkobeams," Journal of Sound and Vibration 158(4), 11-24, 1992 https://doi.org/10.1016/0022-460X(92)90660-P
  11. S. Gopalakrishnan and J. F. Doyle, "Wave Propagation in Connected Wave Guides of Varying Cross-Section," Journal of Sound and Vibration 175(3), 347-363, 1994 https://doi.org/10.1006/jsvi.1994.1333|
  12. J. R. Banerjee and F. W. Williams, "Exact Bernoulli-Euler Dynamic Stiffness Matrix for a Range of Tappered Beams," International Journal for Numerical Methods in Engineering 21, 2289-2302, 1985 https://doi.org/10.1002/nme.1620211212
  13. J. R. Banerjee and F. W. Williams, "Coupled Bending-Torsional Dynamic Stiffness Matrix for Timoshenko Beam Element," Computers and Structures 42(3), 301-310, 1992 https://doi.org/10.1016/0045-7949(92)90026-V
  14. J. R. Banerjee, S. Guo and W. P. Howson, "Exact Dynamic Stiffness Matrix of a Bending-Torsional Coupled Beam Including Warping," Computers and Structures 59(4), 613-621, 1996 https://doi.org/10.1016/0045-7949(95)00307-X
  15. J. R. Banerjee, "Free Vibration of Axially Loaded Composite Timoshenko Beams Using the Dynamic Stiffness Matrix Method," Computers and Structures 69, 197-208, 1998 https://doi.org/10.1016/S0045-7949(98)00114-X
  16. A. T. T. Leung and W. E. Zhou, "Dynamic Stiffness Analysis of Laminated Composite Plates," Thin-Walled Structures 25(2), 109-133, 1996 https://doi.org/10.1016/0263-8231(95)00047-X
  17. G. Wang and N. M. Wereley, "Frequency Response of Beam with Passively Damping Layers and Piezo-Actuators," Pro-ceedings of SPIE conference, 44-60, San Diego, CA, 1998
  18. L. Meirovitch, Analytical Methods in Vibrations (Macmillan, New York, 1967)
  19. D. J. McTavish and P. C. Hughesm "Modeling of Linear Vis-coelastic Space Structures," Journal of Vibration and Acoustics 115, 103-110, 1993 https://doi.org/10.1115/1.2930302
  20. G. A. Lesietre and U. Lee, "A Finite Element for Beams Having Segment Active Constrained Layers with Frequency-Dependent Viscoelastic Materials Properties," Smart Structures and Materials 5, 615-627, 1996 https://doi.org/10.1088/0964-1726/5/5/010