DOI QR코드

DOI QR Code

Free vibration analysis of circular cylindrical shell on elastic foundation using the Rayleigh-Ritz method

  • Yang, Jinsong (School of Traffic and Transportation Engineering, Central South University) ;
  • Cao, Jianbin (School of Mechatronic Engineering, Jiangsu Normal University) ;
  • Xie, Jingsong (School of Traffic and Transportation Engineering, Central South University) ;
  • Zhao, Haixiao (School of Physics and Electronic Engineering, Jiangsu Normal University)
  • 투고 : 2021.04.04
  • 심사 : 2021.07.16
  • 발행 : 2021.10.10

초록

A general approach is presented for the free vibration analysis of circular cylindrical shell resting on elastic foundation and subjected to classical boundary conditions of any type. The Winkler/Pasternak model is utilized to simulate the elastic foundation imposed on the cylindrical shell, and then it is easily to derive the potential energy of the elastic foundation. Based on the Flugge shell theory, explicit expressions for the mass and stiffness matrices are obtained. By taking the characteristic beam modal functions as the admissible functions, the Rayleigh-Ritz method is employed to derive the frequency equations of circular cylindrical shell with all the classical boundary conditions and resting on elastic foundation. Once the frequency equation has been determined, the frequencies can be calculated numerically. The excellent accuracy and validity of the present approach are demonstrated by numerical examples and comparisons with the results available in the literature. Finally, some further numerical results are given to illustrate the comprehensive effect of geometric properties and foundation coefficients on the frequencies of circular cylindrical shell in contact with elastic foundation.

키워드

과제정보

The research described in this paper was financially supported by the Natural Science Basic Research Program of Shaanxi (No. 2020JQ-630) and Graduate Student Practice Innovation Program of Jiangsu (No. SJCX20_0909).

참고문헌

  1. Amabili, M. and Paidoussis, M.P. (2003), "Review of studies on geometrically nonlinear vibrations and dynamics of circular cylindrical shells and panels, with and without fluid structure interaction", Appl. Mech. Rev., 56, 349-381. https://doi.org/10.1115/1.1565084.
  2. Bakhtiari-Nejad, F. and Bideleh, S.M.M. (2012), "Nonlinear free vibration analysis of prestressed circular cylindrical shells on the Winkler/Pasternak foundation", Thin Wall. Struct., 53, 26-39. https://doi.org/10.1016/j.tws.2011.12.015.
  3. Blevins, R.D. (1987), Formulas for Natural Frequency and Mode Shape, Robert E. Krieger Publishing Co., Florida, USA.
  4. Chen, G., Huo, H., Zhan, S. and Yang, D. (2021), "Analytical stochastic responses of thin cylindrical shells under various stationary excitations", Int. J. Mech. Sci., 190, 106048. https://doi.org/10.1016/j.ijmecsci.2020.106048.
  5. Dinh, G.N., Vu, N.C.H. and Vu, L.H. (2021), "A new structure study: Vibrational analyses of FGM convex-concave shells subjected to electro-thermal-mechanical loads surrounded by Pasternak foundation", Eur. J. Mech. A-Solid, 86, 104168. https://doi.org/10.1016/j.euromechsol.2020.104168.
  6. Farshidianfar, A., Farshidianfar, M.H., Crocker, M.J. and Smith, W.O. (2011), "Vibration analysis of long cylindrical shells using acoustical excitation", J. Sound Vib., 330, 3381-3399. https://doi.org/10.1016/j.jsv.2011.02.002.
  7. Habtemariam, A.K., Koenke, C. and Zabel, V. (2021), "Generalized beam theory formulation for thin-walled pipes with circular axis", Thin Wall. Struct., 159, 107243. https://doi.org/10.1016/j.tws.2020.107243.
  8. Hoang, V.N.V., Minh, V.T., Ninh, D.G., Nguyen, C.T. and Huy, V.L. (2020), "Effects of non-uniform elastic foundation on the nonlinear vibration of nanocomposite plates in thermal environment using Selvadurai methodology", Compos. Struct., 253, 112812. https://doi.org/10.1016/j.compstruct.2020.112812.
  9. Hoang, V.N.V., Ninh, D.G., Truong, D.V., Bao, H.V. and Huy, V.L. (2021), "Behaviors of dynamics and stability standard of graphene nanoplatelet reinforced polymer corrugated plates resting on the nonlinear elastic foundations", Compos. Struct., 260, 113253. https://doi.org/10.1016/j.compstruct.2020.113253.
  10. Kwak, M.K., Heo, S. and Jeong, M. (2009), "Dynamic modeling and active vibration controller design for a cylindrical shell equipped with piezoelectric sensors and actuators", J. Sound Vib., 321, 510-524. https://doi.org/10.1016/j.jsv.2008.09.051.
  11. Kwak, M.K., Koo, J. and Bae, C. (2011), "Free vibration analysis of a hung clamped-free cylindrical shell partially submerged in fluid", J. Sound Vib., 27, 283-296. https://doi.org/10.1016/j.jfluidstructs.2010.11.005.
  12. 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.
  13. Lee, K.L., Chang, K.H. and Pan, W.F. (2016), "Failure life estimation of sharp-notched circular tubes with different notch depths under cyclic bending", Struct. Eng. Mech., 60(3), 387-404. https://doi.org/10.12989/sem.2016.60.3.387.
  14. Leissa, A.W. (1993), Vibration of Shells, NASA SP-288, Government Printing Office, Washington, DC, USA.
  15. Li, W., Hao Y. and Zhang, W. (2021), "Resonance response of clamped functionally graded cylindrical shells with initial imperfection in thermal environments". Compos. Struct., 259, 113245. https://doi.org/10.1016/j.compstruct.2020.113245.
  16. Liu, J.X., Li, T.Y., Liu, T.G. and Yan, J. (2005), "Vibration characteristic analysis of buried pipes using the wave propagation approach", Appl. Acoust., 66, 353-364. https://doi.org/10.1016/j.apacoust.2004.06.010.
  17. Malekzadeh, P., Farid, M., Zahedinejad, P. and Karami, G. (2008), "Three-dimensional free vibration analysis of thick cylindrical shells resting on two-parameter elastic supports", J. Sound Vib., 313, 655-675. https://doi.org/10.1016/j.jsv.2007.12.004.
  18. Moshkelgosha, E., Askari, E., Jeong, K.H. and Shaflee, A.A. (2017), "Fluid-structure coupling of concentric double FGM shells with different lengths", Struct. Eng. Mech., 16(2), 231-244. https://doi.org/10.12989/sem.2017.61.2.231.
  19. Muttaqie, T., Do, Q.T., Prabowo, A.R., Cho, S.R. and Sohn, J.M. (2019), "Numerical studies of the failure modes of ring-stiffened cylinders under hydrostatic pressure", Struct. Eng. Mech., 70(4), 431-443. https://doi.org/10.12989/sem.2019.70.4.431.
  20. Ninh, D.G., Minh, V.T., Nguyen, V.T., Nguyen, C.H. and Dinh, V.P. (2021), "Novel numerical approach for free vibration of nanocomposite joined conical-cylindrical-conical shells", AIAA J., 59(1), 366-378. https://doi.org/10.2514/1.j059518.
  21. Ninh, D.G., Tien, N.D. and Hoang, V.N.V. (2019), "Analyses of nonlinear dynamics of imperfect nanocomposite circular cylindrical shells with swirling annular and internal fluid flow using higher order shear deformation shell theory", Eng. Struct., 198, 109502. https://doi.org/10.1016/j.engstruct.2019.109502.
  22. Ninh, D.G., Tien, N.D., Hoang, V.N.V. and Bich, D.H. (2020), "Vibration of cylindrical shells made of three layers W-Cu composite containing heavy water using Flugge-Lur'e-Bryrne theory", Thin Wall. Struct., 146, 106414. https://doi.org/10.1016/j.tws.2019.106414.
  23. Paliwal, D.N. and Pandey, R.K. (1998), "The free vibration of a cylindrical shell on an elastic foundation", J. Vib. Acoust., 120, 63-71. https://doi.org/10.1115/1.2893828.
  24. Pradhan, S.C., Loy, C.T., Lam, K.Y. and Reddy, J.N. (2000), "Vibration characteristics of functionally graded cylindrical shells under various boundary conditions", Appl. Acoust., 61, 111-129. https://doi.org/10.1016/s0003-682x(99)00063-8.
  25. Quta, M.S. (2004), Vibration of Laminated Shells and Plates, Elsevier, San Diego, USA.
  26. Reddy, J.N. (2003), Mechanics of Laminated Composite Plates and Shells: Theory and Analysis, CRC Press, Florida, USA.
  27. Sakhr, J. and Chronik, B.A. (2021), "Harmonic standing-wave excitations of simply-supported thick-walled hollow elastic circular cylinders: exact 3D linear elastodynamic response", Adv. Appl. Math. Mech., 13(1), 18-57. https://doi.org/10.4208/aamm.OA-2019-0203.
  28. Shah, A.G., Mahmood, T., Naeem, M.N. and Arshad, S.H. (2011), "Vibration characteristics of fluid-filled cylindrical shells based on elastic foundations", Acta Mech., 216, 17-28. https://doi.org/10.1007/s00707-010-0346-1.
  29. Tien, N.D., Hoang, V.N.V., Ninh, D.G., Huy, V.L. and Hung, N.C. (2020), "Nonlinear dynamics and chaos of a nanocomposite plate subjected to electro-thermo-mechanical loads using Flugge-Lur'e-Bryrne theory", J. Vib. Control, 27(9-10), 1184-1197. https://doi.org/10.1177/1077546320938185.
  30. Tj, H.G., Mikami, T., Kanie, S. and Sato, M. (2006), "Free vibration characteristics of cylindrical shells partially buried in elastic foundations", J. Sound Vib., 290, 785-793. https://doi.org/10.1016/j.jsv.2005.04.014.
  31. Yaylaci, M. (2016), "The investigation crack problem through numerical analysis", Struct. Eng. Mech., 57(6), 1143-1156. https://doi.org/10.12989/sem.2016.57.6.1143.
  32. Yaylaci, M. and Birinci, A. (2013), "The receding contact problem of two elastic layers supported by two elastic quarter planes", Struct. Eng. Mech., 48(2), 241-255. https://doi.org/10.12989/sem.2013.48.2.241.
  33. Yaylaci, M., Adiyaman, G., Oner, E. and Birinci, A. (2020), "Examination of analytical and finite element solutions regarding contact of a functionally graded layer", Struct. Eng. Mech., 76(3), 325-336. https://doi.org/10.12989/sem.2020.76.3.325.
  34. Yaylaci, M., Adiyaman, G., Oner, E. and Birinci, A. (2021a), "Investigation of continuous and discontinuous contact cases in the contact mechanics of graded materials using analytical method and FEM", Comput. Concrete, 27(3), 199-210. https://doi.org/10.12989/cac.2021.27.3.199.
  35. Yaylaci, M., Eyuboglu, A., Adiyaman, G., Uzun, Y.E., Oner, E. and Birinci, A. (2021b), "Assessment of different solution methods for receding contact problems in functionally graded layered mediums", Mech. Mater., 154, 103730. https://doi.org/10.1016/j.mechmat.2020.103730.
  36. Yaylaci, M., Terzi, C. and Avcar, M. (2019), "Numerical analysis of the receding contact problem of two bonded layers resting on an elastic half plane", Struct. Eng. Mech., 72(6), 775-783. https://doi.org/10.12989/sem.2019.72.6.775.
  37. Yaylaci, M., Yayli, M., Uzun, Y.E., Olmez, H. and Birinci, A. (2021c), "Analyzing the contact problem of a functionally graded layer resting on an elastic half plane with theory of elasticity, finite element method and multilayer perceptron", Struct. Eng. Mech., 78(5), 585-597. https://doi.org/10.12989/sem.2021.78.5.585.
  38. Ye, T., Jin, G., Shi, S. and Ma, X. (2014), "Three-dimensional free vibration analysis of thick cylindrical shells with general end conditions and resting on elastic foundations", Int. J. Mech. Sci., 84, 120-137. https://doi.org/10.1016/j.ijmecsci.2014.04.017.