Structural Engineering and Mechanics

  • 제73권3호
  • /
  • Pages.319-330
  • /
  • 2020
  • /
  • 1225-4568(pISSN)
  • /
  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Effect of different viscoelastic models on free vibrations of thick cylindrical shells through FSDT under various boundary conditions

  • Daemi, Hossein (Faculty of Mechanical and Mechatronics Engineering, Shahrood University of Technology) ;
  • Eipakchi, Hamidreza (Faculty of Mechanical and Mechatronics Engineering, Shahrood University of Technology)
  • 투고 : 2018.12.30
  • 심사 : 2019.10.11
  • 발행 : 2020.02.10
⟨ 이전 논문 다음 논문 ⟩

초록

This paper investigates the free vibrations of cylindrical shells made of time-dependent materials for different viscoelastic models under various boundary conditions. During the extraction of equations, the displacement field is estimated through the first-order shear deformation theory taking into account the transverse normal strain effect. The constitutive equations follow Hooke's Law, and the kinematic relations are linear. The assumption of axisymmetric is included in the problem. The governing equations of thick viscoelastic cylindrical shell are determined for Maxwell, Kelvin-Voigt and the first and second types of Zener's models based on Hamilton's principle. The motion equations involve four coupled partial differential equations and an analytical method based on the elementary theory of differential equations is used for its solution. Relying on the results, the natural frequencies and mode shapes of viscoelastic shells are identified. Conducting a parametric study, we examine the effects of geometric and mechanical properties and boundary conditions, as well as the effect of transverse normal strain on natural frequencies. The results in this paper are compared against the results obtained from the finite elements analysis. The results suggest that solutions achieved from the two methods are ideally consistent in a special range.

키워드

참고문헌

  1. Apuzzo, A., Barretta, R., Faghidian, S.A., Luciano, R., and de Sciarra, F. M. (2018), "Free vibrations of elastic beams by modified nonlocal strain gradient theory", J. Eng. Sci., 133, 99-108. https://doi.org/10.1016/j.ijengsci.2018.09.002.
  2. Barretta, R., Faghidian, S.A., Luciano, R., Medaglia, C.M., and Penna, R. (2018), "Free vibrations of FG elastic Timoshenko nano-beams by strain gradient and stress-driven nonlocal models", Compos Part B. Eng., 154, 20-32. https://doi.org/10.1016/j.compositesb.2018.07.036.
  3. Barretta, R., Faghidian, S.A., and Luciano, R. (2018), "Longitudinal vibrations of nano-rods by stress-driven integral elasticity", Mech. Adv. Mater. Struct., 26(15), 1307-1315. https://doi.org/10.1080/15376494.2018.1432806.
  4. Bhimaraddi, A. (1984), "A higher order theory for free vibration analysis of circular cylindrical shells", J. Solids Struct., 20(7), 623-630. https://doi.org/10.1016/0020-7683(84)90019-2.
  5. Boresi, A.P, Chong, K. and Lee, J.D. (2010), Elasticity in Engineering Mechanics, John Wiley and Sons, New Jersey, U.S.A.
  6. Barati, M.R. (2017), "Vibration analysis of FG nanoplates with nanovoids on viscoelastic substrate under hygro-thermo-mechanical loading using nonlocal strain gradient theory", Struct. Eng. Mech., 64(6), 683-693. https://doi.org/10.12989/sem.2017.64.6.683.
  7. Buchanan, G.R. and Yii, C.B.Y. (2002), "Effect of symmetrical boundary conditions on the vibration of thick hollow cylinders", Appl. Acoustics, 63, 547-566. https://doi.org/10.1016/S0003-682X(01)00048-2.
  8. Cammalleri, M. and Costanza, A. (2016), "A closed-form solution for natural frequencies of thin-walled cylinders with clamped edges", J. Mech. Sci., 110, 116-126. https://doi.org/10.1016/j.ijmecsci.2016.03.005.
  9. Canadija, M., Barretta, R., and de Sciarra, F. M. (2016), "On functionally graded Timoshenko nonisothermal nanobeams", Compos. Struct., 135, 286-296. https://doi.org/10.1016/j.compstruct.2015.09.030.
  10. Cox, R.H. (1968), "Wave propagation through a newtonian fluid contained within a thick-walled, viscoelastic tube", Biophys. J., 8, 691-709. https://doi.org/10.1016/S0006-3495(68)86515-4.
  11. El-Kaabazi, N. and Kennedy, D. (2012), "Calculation of natural frequencies and vibration modes of variable thickness cylindrical shells using the Wittrick-Williams algorithm", Comput. Struct., 104, 4-12. https://doi.org/10.1016/j.compstruc.2012.03.011.
  12. Eratl, N., Argeso, H., Calim, F.F., Temel, B., Mehmet H. Omurtag, M.H. (2014), "Dynamic analysis of linear viscoelastic cylindrical and conical helicoidal rods using the mixed FEM", J. Sound Vib., 333, 3671-3690. https://doi.org/10.1016/j.jsv.2014.03.017.
  13. Jithin, A.J., Jung, D.W., Lakshmi, R.R., and Sanal Kumar, V.R. (2018), "Mechanical characterization of a thick-walled viscoelastic hollow cylinder under multiaxial stress conditions", Mater. Sci. Forum, 917, 329-336. https://doi.org/10.4028/www.scientific.net/MSF.917.329.
  14. Hamidzadeh, H.R. and Sawaya, N.N. (1995), "Free vibration of thick multilayer cylinders", Shock Vib., 2(5), 393-401. https://doi.org/10.3233/SAV-1995-2505.
  15. Khadem Moshir, S., Eipakchi, H.R., and Sohani, F. (2017), "Free vibration behavior of viscoelastic annular plates using first order shear deformation theory", Struct. Eng. Mech.,,62(5), 607-618. https://doi.org/10.12989/sem.2017.62.5.607.
  16. Lee, H. and Kwak, M.K. (2015), "Free vibration analysis of a circular cylindrical shell using the Rayleigh-Ritz method and comparison of different shell theories", J. Sound Vib., 353, 344-377. https://doi.org/10.1016/j.jsv.2015.05.028.
  17. Mirsky, I. and Hermann, G. (1958), "Axially motions of thick cylindrical shells", Appl. Mech., 25, 97-102. https://doi.org/10.1115/1.4011695
  18. Moghtaderi, S.H., Faghidian, S.A., and Shodja, M.H. (2018), "Analytical determination of shear correction factor for Timoshenko beam model", Steel Compos. Struct., 29(4), 483-491. https://doi.org/10.12989/scs.2018.29.4.483.
  19. Mohammadi, F. and Sedaghati, R. (2012), "Linear and nonlinear vibration analysis of sandwich cylindrical shell with constrained viscoelastic core layer", J. Mech. Sci., 54(1), 156-171. https://doi.org/10.1016/j.ijmecsci.2011.10.006.
  20. Mokhtari, M., Permoon, M.R. and Haddadpour, H. (2018), "Dynamic analysis of isotropic sandwich cylindrical shell with fractional viscoelastic core using Rayleigh-Ritz method", Compos. Struct., 186, 165-174. https://doi.org/10.1016/j.compstruct.2017.10.039.
  21. Pellicano, F. (2007), "Vibrations of circular cylindrical shells: theory and experiments", J. Sound Vib., 303,154-170. https://doi.org/10.1016/j.jsv.2007.01.022.
  22. Poloei, E., Zamanian, M., and Hosseini, S.A.A. (2017) "Nonlinear vibration analysis of an electrostatically excited micro cantilever beam coated by viscoelastic layer with the aim of finding the modified configuration", Struct. Eng. Mech., 61 (2), 193-207. https://doi.org/10.12989/sem.2017.61.2.193.
  23. Rao, S.S. (2007), Vibration of Continuous Systems, John Wiley and Sons, U.S.A.
  24. Romano, G., Barretta, A., and Barretta, R. (2012), "On torsion and shear of Saint-Venant beams", European J. Mech. A/Solids, 35, 47-60. https://doi.org/10.1016/j.euromechsol.2012.01.007.
  25. Skrzypek, J.J. and Ganczarski, A.W. (2015), Mechanics of Anisotropic Materials, Springer, Heidelberg, Germany.
  26. Soedel, W. (1982), "On the vibration of shells with Timoshenko-Mindlin type shear deflections and rotatory inertia", J. Sound Vib., 83(1), 67-79. https://doi.org/10.1016/S0022-460X(82)80076-X.
  27. Suzuki, K., Konno, M. and Takahashi, S. (1981), "Axisymmetric vibrations of a cylindrical shell with varying thickness", Bullet. Japan Soc. Mech. Eng., 24(198), 2112-2132. https://doi.org/10.1299/jsme1958.24.2122.
  28. Suzuki, K. and Leissa, A.W. (1986), "Exact solutions for the free vibrations of open cylindrical shells with circumferentially varying curvature and thickness", J. Sound Vib., 107(1), 1-15. https://doi.org/10.1016/0022-460X(86)90278-6.
  29. Vlachoutsis, S. (1992), "Shear correction factors for plates and shells", Numeric. Methods Eng., 33, 1537-1552. https://doi.org/10.1002/nme.1620330712.
  30. Wong, S.K. and Bush, W.B. (1993), "Axisymmetric vibrations of a clamped cylindrical shell using matched asymptotic expansions", J. Sound Vib., 160(3), 523-531. https://doi.org/10.1006/jsvi.1993.1042.
  31. Yang, C., Jin, G., Liu, Z., Wang, X. and Miao, X. (2015), "Vibration and damping analysis of thick sandwich cylindrical shells with a viscoelastic core under arbitrary boundary conditions", J. Mech. Sci., 92, 162-177. https://doi.org/10.1016/j.ijmecsci.2014.12.003.
  32. Zhang, W., Fang, Z., Yang, X.D. and Liang, F. (2018), "A series solution for free vibration of moderately thick cylindrical shell with general boundary conditions", Eng. Struct., 165, 422-440. https://doi.org/10.1016/j.engstruct.2018.03.049.
  33. Zhang, W., Cui, W., Xiao, Z. and Xu, X. (2010), "The quasi-static analysis for the viscoelastic hollow circular cylinder using the symplectic system method", J. Eng. Sci., 48, 727-741. https://doi.org/10.1016/j.ijengsci.2010.03.003.
  34. Zhao, J., Choe, K., Zhang,Y., Wang, A., Lin, C. and Wang, Q. (2018), "A closed form solution for free vibration of orthotropic circular cylindrical shells with general boundary conditions", Compos Part B. Eng., 159, 447-460. https://doi.org/10.1016/j.compositesb.2018.09.106.