DOI QR코드

DOI QR Code

Complex modes in damped sandwich beams using beam and elasticity theories

  • Ahmad, Naveed (Department of Engineering Science and Mechanics, Virginia Tech) ;
  • Kapania, Rakesh K. (Department of Aerospace and Ocean Engineering, Virginia Tech)
  • 투고 : 2014.08.27
  • 심사 : 2014.09.30
  • 발행 : 2015.01.25

초록

We investigated complex damped modes in beams in the presence of a viscoelastic layer sandwiched between two elastic layers. The problem was solved using two approaches, (1) Rayleigh beam theory and analyzed using the Ritz method, and (2) by using 2D plane stress elasticity based finite-element method. The damping in the layers was modeled using the complex modulus. Simply-supported, cantilever, and viscously supported boundary conditions were considered in this study. Simple trigonometric functions were used as admissible functions in the Ritz method. The key idea behind sandwich structure is to increase damping in a beam as affected by the presence of a highly-damped core layer vibrating mainly in shear. Different assumptions are utilized in the literature, to model shear deformation in the core layer. In this manuscript, we used FEM without any kinematic assumptions for the transverse shear in both the core and elastic layers. Moreover, numerical examples were studied, where the base and constraining layers were also damped. The loss factor was calculated by modal strain energy method, and by solving a complex eigenvalue problem. The efficiency of the modal strain energy method was tested for different loss factors in the core layer. Complex mode shapes of the beam were also examined in the study, and a comparison was made between viscoelastically and viscously damped structures. The numerical results were compared with those available in the literature, and the results were found to be satisfactory.

키워드

과제정보

연구 과제 주관 기관 : UET

참고문헌

  1. Abdoun, F., Azrar, L., Daya, E.M. and Potier-Ferry, M. (2009), "Forced harmonic response of viscoelastic structures by an asymptotic numerical method", Comput. Struct., 87(1), 91-100. https://doi.org/10.1016/j.compstruc.2008.08.006
  2. Adhikari, S. (2004), "Optimal complex modes and an index of damping non-proportionality", Mech. Syst. Signal Pr., 18(1), 1-27. https://doi.org/10.1016/S0888-3270(03)00048-7
  3. Barkanov, E.N. (1993), "Method of complex eigenvalues for studying the damping properties of sandwichtype structures", Mech. Comput. Mater., 29(1), 90-94. https://doi.org/10.1007/BF00656275
  4. Barkanov, E.N. (1994), "Natural vibrations of a system with hysteretic and viscous damping", Mech. Comput. Mater., 29(6), 613-616. https://doi.org/10.1007/BF00616328
  5. Bhimaraddi, A. (1995), "Sandwich beam theory and the analysis of constrained layer damping", J. Sound Vib., 179(4), 591-602. https://doi.org/10.1006/jsvi.1995.0039
  6. Bilasse, M., Daya, E.M. and Azrar, L. (2010), "Linear and nonlinear vibrations analysis of viscoelastic sandwich beams", J. Sound Vib., 329(23), 4950-4969. https://doi.org/10.1016/j.jsv.2010.06.012
  7. Daya, E.M. and Potier-Ferry, M. (2001), "A numerical method for nonlinear eigenvalue problems application to vibrations of viscoelastic structures", Comput. Struct., 79(5), 533-541. https://doi.org/10.1016/S0045-7949(00)00151-6
  8. Fasana, A. and Marchesiello, S. (2001), "Rayleigh-Ritz analysis of sandwich beams", J. Sound Vib., 241(4), 643-652. https://doi.org/10.1006/jsvi.2000.3311
  9. Hu, H., Belouettar, S., Potier-Ferry, M. and Daya, E.M. (2008), "Review and assessment of various theories for modeling sandwich composites", Comput. Struct., 84(3), 282-292. https://doi.org/10.1016/j.compstruct.2007.08.007
  10. Imaino, W. and Harrison, J.C. (1991), "A comment on constrained layer damping structures with low viscoelastic modulus", J. Sound Vib., 149(2), 354-359. https://doi.org/10.1016/0022-460X(91)90646-2
  11. Johnson, C.D. and Kienholz, D.A. (1982), "Finite element prediction of damping in structures with constrained viscoelastic layers", AIAA J., 20(9), 1284-1290. https://doi.org/10.2514/3.51190
  12. Koruk, H. and Sanliturk, K.Y. (2011), "Assessment of the complex eigenvalue and the modal strain energy methods for damping predictions", International Congress on Sound and Vibration, Rio de Janeiro, Brazil, July.
  13. Koruk, H. and Sanliturk, K.Y. (2012), "Assessment of modal strain energy method: advantages and limitations", ASME 11th Biennial Conference on Engineering Systems Design and Analysis, Nantes, France, July.
  14. Koruk, H. and Sanliturk, K.Y. (2013), "A novel definition for quantification of mode shape complexity", J. Sound Vib., 332(14), 3390-3403. https://doi.org/10.1016/j.jsv.2013.01.039
  15. Koruk, H. and Sanliturk, K.Y. (2014), "Optimization of damping treatments based on big bang-big crunch and modal strain energy methods", J. Sound Vib., 333(5), 1319-1330. https://doi.org/10.1016/j.jsv.2013.10.023
  16. Kosmatka, J.B. and Liguore, S.L. (1993), "Review of methods for analyzing constrained-layer damped structures", J. Aerosp. Eng., 6(3), 268-283. https://doi.org/10.1061/(ASCE)0893-1321(1993)6:3(268)
  17. Krenk, S. (2004), "Complex modes and frequencies in damped structural vibrations", J. Sound Vib., 270(4), 981-996. https://doi.org/10.1016/S0022-460X(03)00768-5
  18. Lampoh, K., Charpentier, I. and El Mostafa, D. (2014), "Eigenmode sensitivity of damped sandwich structures", Comptes Rendus Mecanique, 342(12), 700-705. https://doi.org/10.1016/j.crme.2014.08.001
  19. Lee, D.H. (2008), "Optimal placement of constrained-layer damping for reduction of interior noise", AIAA J., 46(1), 75-83. https://doi.org/10.2514/1.30648
  20. Mead, D.J. and Markus, S. (1969), "The forced vibration of a three-layer, damped sandwich beam with arbitrary boundary conditions", J. Sound Vib., 10(2), 163-175. https://doi.org/10.1016/0022-460X(69)90193-X
  21. Prater, Jr, G. and Singh, R. (1990), "Eigenproblem formulation, solution and interpretation for nonproportionally damped continuous beams", J. Sound Vib., 143(1), 125-142. https://doi.org/10.1016/0022-460X(90)90572-H
  22. Rao, Y.V.K.S. and Nakra, B.C. (1973), "Theory of vibratory bending of unsymmetrical sandwich plates", Arch. Mech., 25, 213-225.
  23. Rao, M.D. (2003), "Recent applications of viscoelastic damping for noise control in automobiles and commercial airplanes", J. Sound Vib., 262(3), 457-474. https://doi.org/10.1016/S0022-460X(03)00106-8
  24. Reddy, J.N. (2005), An Introduction to the Finite Element method, 3rd Edition, McGraw-Hill, New York, NY, USA.
  25. Rikards, R.B. and Barkanov, E.N. (1992), "Determination of the dynamic characteristics of vibrationabsorbing coatings by the finite-element method", Mech. Compos. Mater., 27(5), 529-535. https://doi.org/10.1007/BF00613477
  26. Rikards, R. (1993), "Finite element analysis of vibration and damping of laminated composites", Comput. Struct., 24(3), 193-204. https://doi.org/10.1016/0263-8223(93)90213-A
  27. Sanliturk, K.Y. and Koruk, H. (2013), "Development and validation of a composite finite element with damping capability", Comput. Struct., 97, 136-146. https://doi.org/10.1016/j.compstruct.2012.10.020
  28. Sainsbury, M.G. and Zhang, Q.J. (1999), "The Galerkin element method applied to the vibration of damped sandwich beams", Comput. Struct., 71(3), 239-256. https://doi.org/10.1016/S0045-7949(98)00242-9
  29. Singhvi, S. and Kapania, R.K. (1994), "Comparison of simple and Chebychev polynomials in Rayleigh-Ritz analysis", J. Eng. Mech., 120(10), 2126-2135. https://doi.org/10.1061/(ASCE)0733-9399(1994)120:10(2126)
  30. Soni, M.L. (1981), "Finite element analysis of viscoelastically damped sandwich structures", Shock Vib. Bull., 55(1), 97-109.
  31. Sun, C.T. and Lu, Y.P. (1995), Vibration Damping of Structural Elements, Prentice Hall Inc., New Jersey, NJ, USA.