Structural Engineering and Mechanics

  • 제83권6호
  • /
  • Pages.757-770
  • /
  • 2022
  • /
  • 1225-4568(pISSN)
  • /
  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Vibration of a Circular plate on Pasternak foundation with variable modulus due to moving mass

  • 투고 : 2021.11.14
  • 심사 : 2022.07.24
  • 발행 : 2022.09.25
⟨ 이전 논문 다음 논문 ⟩

초록

In this paper, the vibration of a moderately thick plate to a moving mass is investigated. Pasternak foundation with a variable subgrade modulus is considered to tackle the shortcomings of Winkler model, and an analytical-numerical solution is proposed based on the eigenfunction expansion method. Parametric studies by using both CPT (Classical Plate Theory) and FSDT (First-Order Shear Deformation Plate Theory) are carried out, and, the differences between them are also highlighted. The obtained results reveal that utilizing FSDT without considering the rotary inertia leads to a smaller deflection in comparison with CPT pertaining to a thin plate, while it demonstrates a greater response for plates of higher thicknesses. Moreover, it is shown that CPT is unable to properly capture the variation of the plate thickness, thereby diminishing the accuracy as the thickness increases. The outcomes also indicate that the presence of a foundation contributes more to the dynamic response of thin plates in comparison to moderately thick plates. Furthermore, the findings suggest that the performance of the moving force approach for a moderately thick plate, in contrast to a thin plate, appears to be acceptable and it even provides a much better estimation in the presence of a foundation.

키워드

참고문헌

  1. Abdoos, H., Khaloo, A. and Foyouzat, M. (2020), "On the out-ofplane dynamic response of horizontally curved beams resting on elastic foundation traversed by a moving mass", J. Sound Vib., 479, 115397. https://doi.org/10.1016/j.jsv.2020.115397.
  2. Akin, J.E. and Mofid, M. (1989), "Numerical solution for response of beams with moving mass", J. Struct. Eng., 115, 120-131. https://doi.org/10.1061/(ASCE)0733-9445(1989)115:1(120).
  3. Alimoradzadeh, M. and Akbas, S. (2022), "Nonlinear dynamic behavior of functionally graded beams resting on nonlinear viscoelastic foundation under moving mass in thermal environment", Struct. Eng. Mech., 81, 705-714. https://doi.org/10.12989/sem.2022.81.6.705.
  4. Amiri, J.V., Nikkhoo, A., Davoodi, M.R. and Hassanabadi, M.E. (2013), "Vibration analysis of a Mindlin elastic plate under a moving mass excitation by eigenfunction expansion method", Thin Wall. Struct., 62, 53-64. https://doi.org/10.1016/j.tws.2012.07.014.
  5. Awodola, T. (2018), "Flexural motion under moving masses of prestressed simply supported plate resting on bi-parametric foundation", J. Theor. Appl. Mech., 48, 3-22. https://doi.org/10.1007/s42417-018-0031-6.
  6. Bajer, C.I. and Dyniewicz, B. (2012), Numerical Analysis of Vibrations of Structures under moving Inertial Load, Springer Science & Business Media.
  7. Brogan, W.L. (1991), Modern Control Theory, Pearson Education india.
  8. Cifuentes, A. and Lalapet, S. (1992), "A general method to determine the dynamic response of a plate to a moving mass", Comput. Struct., 42, 31-36. https://doi.org/10.1016/0045-7949(92)90533-6.
  9. De Faria, A. and Oguamanam, D. (2004), "Finite element analysis of the dynamic response of plates under traversing loads using adaptive meshes", Thin Wall. Struct., 42, 1481-1493. https://doi.org/10.1016/j.tws.2004.03.012.
  10. Foyouzat, M., Abdoos, H., Khaloo, A. and Mofid, M. (2022), "Inplane vibration analysis of horizontally curved beams resting on visco-elastic foundation subjected to a moving mass", Mech. Syst. Signal Pr., 172, 109013. https://doi.org/10.1016/j.ymssp.2022.109013.
  11. Foyouzat, M., Estekanchi, H. and Mofid, M. (2018), "An analytical-numerical solution to assess the dynamic response of viscoelastic plates to a moving mass", Appl. Math. Model., 54, 670-696. https://doi.org/10.1016/j.apm.2017.07.037.
  12. Foyouzat, M. and Mofid, M. (2019), "An analytical solution for bending of axisymmetric circular/annular plates resting on a variable elastic foundation", Eur. J. Mech.-A/Solid., 74, 462-470. https://doi.org/10.1016/j.euromechsol.2019.01.006.
  13. Foyouzat, M., Mofid, M. and Akin, J. (2016), "Free vibration of thin circular plates resting on an elastic foundation with a variable modulus", J. Eng. Mech., 142, 04016007. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001050.
  14. Ghafoori, E. and Asghari, M. (2010), "Dynamic analysis of laminated composite plates traversed by a moving mass based on a first-order theory", Compos. Struct., 92, 1865-1876. https://doi.org/10.1016/j.compstruct.2010.01.011.
  15. Hassanabadi, M.E., Attari, N.K., Nikkhoo, A. and Baranadan, M. (2015), "An optimum modal superposition approach in the computation of moving mass induced vibrations of a distributed parameter system", Proc. Inst. Mech. Eng., Part C: J. Mech. Eng. Sci., 229, 1015-1028. https://doi.org/10.1177/0954406214542968.
  16. Hosseini-Hashemi, S. and Khaniki, H.B. (2018), "Three dimensional dynamic response of functionally graded nanoplates under a moving load", Struct. Eng. Mech., 66, 249-262. https://doi.org/10.12989/sem.2018.66.2.249.
  17. Iwan, W. and Stahl, K. (1973), "The response of an elastic disk with a moving mass system", J. Appl. Mech., 40(2), 445-451. https://doi.org/10.1115/1.3423004.
  18. Javidi, R., Moghimi Zand, M. and Dastani, K. (2018), "Dynamics of Nonlinear rectangular plates subjected to an orbiting mass based on shear deformation plate theory", J. Comput. Appl. Mech., 49, 27-36. https://doi.org/10.22059/jcamech.2017.238716.169.
  19. Kanwal, R.P. (1998), Generalized Functions Theory and Technique: Theory and Technique, Springer Science & Business Media.
  20. Katsikadelis, J. and Kallivokas, L. (1986), "Clamped plates on Pasternak-type elastic foundation by the boundary element method", J. Appl. Mech., 53(4), 909-917. https://doi.org/10.1115/1.3171880.
  21. Kerr, A.D. (1964), "Elastic and viscoelastic foundation models", J. Appl. Mech., 31(3), 491-498 https://doi.org/10.1115/1.3629667.
  22. Kukla, S. and Szewczyk, M. (2007), "Frequency analysis of annular plates with elastic concentric supports by Green's function method", J. Sound Vib., 300, 387-393. https://doi.org/10.1016/j.jsv.2006.04.046.
  23. Liew, K.M., Xiang, Y., Kitipornchai, S. and Wang, C. (1998), Vibration of Mindlin Plates: Programming the p-Version Ritz Method, Elsevier.
  24. Luong-Van, H., Nguyen-Thoi, T., Liu, G. and Phung-Van, P. (2014), "A cell-based smoothed finite element method using three-node shear-locking free Mindlin plate element (CS-FEMMIN3) for dynamic response of laminated composite plates on viscoelastic foundation", Eng. Anal. Bound. Elem., 42, 8-19. https://doi.org/10.1016/j.enganabound.2013.11.008.
  25. Nikkhoo, A., Asili, S., Sadigh, S., Hajirasouliha, I. and Karegar, H. (2019), "A low computational cost method for vibration analysis of rectangular plates subjected to moving sprung masses", Adv. Comput. Des., 4, 307-326. https://doi.org/10.12989/acd.2019.4.3.307
  26. Nikkhoo, A., Hassanabadi, M.E., Azam, S.E. and Amiri, J. V. (2014), "Vibration of a thin rectangular plate subjected to series of moving inertial loads", Mech. Res. Commun., 55, 105-113. https://doi.org/10.1016/j.mechrescom.2013.10.009.
  27. Nikkhoo, A. and Rofooei, F.R. (2012), "Parametric study of the dynamic response of thin rectangular plates traversed by a moving mass", Acta Mechanica, 223, 15-27. https://doi.org/10.1007/s00707-011-0547-2.
  28. Pasternak, P. (1954), "On a new method of an elastic foundation by means of two foundation constants", Gosudarstvennoe Izdatelstvo Literaturi po Stroitelstuve i Arkhitekture.
  29. Rai, A.K. and Gupta, S.S. (2021), "Nonlinear vibrations of a polar-orthotropic thin circular plate subjected to circularly moving point load", Compos. Struct., 256, 112953. https://doi.org/10.1016/j.compstruct.2020.112953.
  30. Rao, S.S. (2007), Vibration of Continuous Systems, Wiley Online Library.
  31. Reissner, E. (1958), "A note on deflections of plates on a viscoelastic foundation", J. Appl. Mech., 25, 144-145. https://doi.org/10.1115/1.4011704.
  32. Seifoori, S., Mahdian Parrany, A. and Darvishinia, S. (2021), "Experimental studies on the dynamic response of thin rectangular plates subjected to moving mass", J. Vib. Control, 27, 685-697. https://doi.org/10.1177/1077546320933136.
  33. Shadnam, M., Mofid, M. and Akin, J. (2001), "On the dynamic response of rectangular plate, with moving mass", Thin Wall. Struct., 39, 797-806. https://doi.org/10.1016/S0263-8231(01)00025-8.
  34. Smith, I.M. (1970), "A finite element approach to elastic soil-structure interaction", Can. Geotech. J., 7, 95-105. https://doi.org/10.1139/t70-011.
  35. Song, Q., Shi, J. and Liu, Z. (2017), "Vibration analysis of functionally graded plate with a moving mass", Appl. Math. Model., 46, 141-160. https://doi.org/10.1016/j.apm.2017.01.073.
  36. Stanisic, M., Hardin, J. and Lou, Y. (1968), "On the response of the plate to a multi-masses moving system", Acta Mechanica, 5, 37-53. https://doi.org/10.1007/BF01624442.
  37. Szilard, R. (2004), "Theories and applications of plate analysis: classical, numerical and engineering methods", Appl. Mech. Rev. 57, 45. https://doi.org/10.1115/1.1849175
  38. Takabatake, H. (1998), "Dynamic analysis of rectangular plates with stepped thickness subjected to moving loads including additional mass", J. Sound Vib., 213, 829-842. https://doi.org/10.1006/jsvi.1998.1555.
  39. Uzal, E. and Sakman, L.E. (2010), "Dynamic response of a circular plate to a moving load", Acta Mechanica, 210, 351-359. https://doi.org/10.1007/s00707-009-0207-y.
  40. Von Nanni, J. (1971), "Das eulersche knickproblem unter berucksichtigung der querkrafte", Zeitschrift fur Angewandte Mathematik und Physik ZAMP, 22, 156-185. https://doi.org/10.1007/BF01624060.
  41. Vosoughi, A., Malekzadeh, P. and Razi, H. (2013), "Response of moderately thick laminated composite plates on elastic foundation subjected to moving load", Compos. Struct., 97, 286-295. https://doi.org/10.1016/j.compstruct.2012.10.017.
  42. Wang, C. (1994), "Natural frequencies formula for simply supported Mindlin plates", J. Vib. Acoust., 116(4), 536-540. https://doi.org/10.1115/1.2930460.
  43. Wang, C., Reddy, J.N. and Lee, K. (2000), Shear Deformable Beams and Plates: Relationships with Classical Solutions, Elsevier.
  44. Wang, C.Y. and Wang, C. (2013), Structural Vibration: Exact Solutions for Strings, Membranes, Beams, and Plates, CRC Press.
  45. Wang, R.T. and Kuo, N.Y. (1999), "Nonlinear vibration of Mindlin plate subjected to moving forces including the effect of weight of the plate", Struct. Eng. Mech., 8, 151-164. https://doi.org/10.12989/sem.1999.8.2.151.
  46. Wang, Y., Tham, L. and Cheung, Y. (2005), "Beams and plates on elastic foundations: a review", Prog. Struct. Eng. Mater., 7, 174-182. https://doi.org/10.1002/pse.202.
  47. Winkler, E. (1867), "Die Lehre vonder elastizitat und festigkeit", Do-minicus, Prague.
  48. Wu, J.S., Lee, M.L. and Lai, T.S. (1987), "The dynamic analysis of a flat plate under a moving load by the finite element method", Int. J. Numer. Meth. Eng., 24, 743-762. https://doi.org/10.1002/nme.1620240407.
  49. Xing, Y. and Liu, B. (2009), "Closed form solutions for free vibrations of rectangular Mindlin plates", Acta Mechanica Sinica, 25, 689-698. https://doi.org/10.1007/s10409-009-0253-7.
  50. Zaman, M., Taheri, M.R. and Alvappillai, A. (1991), "Dynamic response of a thick plate on viscoelastic foundation to moving loads", Int. J. Numer. Anal. Meth. Geomech., 15, 627-647. https://doi.org/10.1002/nag.1610150903.