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Free Vibration Analysis of Mindlin Plates Resting on Pasternak Foundation Using Coupled Displacement Method

Treść / Zawartość
Identyfikatory
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The authors developed a simple and efficient method, called the Coupled Displacement method, to study the linear free vibration behavior of the moderately thick rectangular plates in which a single-term trigonometric/algebraic admissible displacement, such as total rotations, are assumed for one of the variables (in both X,Y directions), and the other displacement field, such as transverse displacement, is derived by making use of the coupling equations. The coupled displacement method makes the energy formulation to contain half the number of unknown independent coefficients in the case of a moderately thick plate, contrary to the conventional Rayleigh-Ritz method. The smaller number of undetermined coefficients significantly simplifies the vibration problem. The closed form expression in the form of fundamental frequency parameter is derived for all edges of simply supported moderately thick rectangular plate resting on Pasternak foundation. The results obtained by the present coupled displacement method are compared with existing open literature values wherever possible for various plate boundary conditions such as all edges simply supported, clamped and two opposite edges simply supported and clamped and the agreement found is good.
Rocznik
Strony
107--128
Opis fizyczny
Bibliogr. 26 poz., rys., tab.
Twórcy
autor
  • Jawaharlal Nehru Technological University Kakinada, AP India-533003
autor
  • Jawaharlal Nehru Technological University Kakinada, AP India-533003
Bibliografia
  • [1] A.Karasin. Vibration of rectangular plates on elastic foundations by finite grid solution. International Journal of Mathematical and Computational Methods, 1:140–145, 2016.
  • [2] A.J.M. Ferreira, C.M.C. Roque, A.M.A. Neves, R.M.N. Jorge, and C.M.M. Soares. Analysis of plates on Pasternak foundations by radial basis functions. Journal of Computational Mechanics, 46(6):791–803, 2010. doi: 10.1007/s00466-010-0518-9.
  • [3] H. Matsunaga. Vibration and stability of thick plates on elastic foundations. Journal of Engineering Mechanics, 126(1):27–34, 2000. doi: 10.1061/(ASCE)0733-9399(2000)126:1(27).
  • [4] D. Zhou, Y.K. Cheung, S.H. Lo, and F.T.K. Au. Three dimensional vibration analysis of rectangular thick plates on Pasternak foundation. International Journal for Numerical Methods in Engineering, 59(10):1313–1334, 2004. doi: 10.1002/nme.915.
  • [5] E. Bahmyari, M.M. Banatehrani, M. Ahmadi, and M. Bahmyari. The Vibration analysis of thin plates resting on Pasternak foundations by element free Galerkin method. Shock and Vibration, 20(2):309–326, 2013. doi: 10.3233/SAV-2012-00746.
  • [6] G.V. Rao. M.K. Saheb, and R.G. Janardhan. Large-amplitude free vibrations of uniform Timoshenko beams: A novel formulation. AIAA Journal, 45(11):2810–2812, 2007. doi:10.2514/1.27718.
  • [7] H. Liu, F. Liu, X. Jing, Z.Wang, and L. Xia. Three Dimensional vibration analysis of rectangular thick plates on Pasternak foundation with arbitrary boundary conditions. Shock and Vibration,2017:1–10,2017. doi: 10.1155/2017/3425298.
  • [8] J. Rouzegar and R.A. Sharifpoor. Flexure of thick plates resting on elastic foundation using two-variable refined plate theory. Archive of Mechanical Engineering, 62(2):181–203, 2015. doi: 10.1515/meceng-2015-0011.
  • [9] K.K. Bhaskar and K.M. Saheb. Large amplitude free vibrations of Timoshenko beams at higher modes using coupled displacement method. Journal of Physics: Conference Series, 662(1), 2015. Article number 012019. doi: 10.1088/1742-6596/662/1/012019.
  • [10] K. Rajesh and K.M. Saheb. Linear free vibration analysis of rectangular Mindlin plates using coupled displacement method. Mathematical Models in Engineering, 2(1):41–47, 2016.
  • [11] K. Rajesh and K.M. Saheb. Free vibrations of uniformTimoshenko beams on Pasternak foundation using coupled displacement method. Archive of Mechanical Engineering, 64(3):359–373, 2017. doi: 10.1515/meceng-2017-0022.
  • [12] K. Özgan and A.T. Daloglu. Free vibration analysis of thick plates resting on winkler elastic foundation. Challenge Journal of Structural Mechanics, 1(2):78–83, 2015. doi: 10.20528/cjsmec. 2015.06.015.
  • [13] K. Özgan and A.T. Daloglu. Free vibration analysis of thick plates on elastic foundations using modified Vlasov model with higher order finite elements. Indian Journal of Engineering & Materials Sciences, 19:279–291, 2012.
  • [14] K. Özgan and A.T. Daloglu. Application of modified Vlasov model to free vibration analysis of thick plates resting on elastic foundations. Shock and Vibration, 16(5):439–454, 2009. doi: 10.3233/SAV-2009-0479.
  • [15] M. Dehghany and A. Farajpour. Free vibration of simply supported rectangular plates on Pasternak foundation: An exact and three-dimensional solution. Engineering Solid Mechanics, 2(1):29–42, 2014.
  • [16] M.H. Omurtag, A. Özütok, A.Y. Aköz, and Y. Özçelikörs. Free vibration analysis of Kirchhoff plates resting on elastic foundation by mixed finite element formulation based on Gateaux differential. International Journal for Numerical Methods in Engineering, 40(2): 295–317, 1997. doi: 10.1002/(SICI)1097-0207(19970130)40:2<295::AID-NME66>3.0.CO;2-2.
  • [17] R.D. Mindlin. Influence of rotatory inertia and shear on flexural motions of isotropic elastic plates. Journal of Applied Mechanics, 18:1031–1036, 1951.
  • [18] M. Zaman, M.O. Faruque, A. Agrawal, and J. Laguros. Free vibration analysis of rectangular plates resting on two-parameter elastic medium. Transactions on the Built Environment, 20:583–592, 1996.
  • [19] P.H. Wen. The fundamental solution of Mindlin plates resting on an elastic foundation in the Laplace domain and its applications. International Journal of Solids and Structures, 45(3–4):1032–1050, 2008. doi: 10.1016/j.ijsolstr.2007.09.020.
  • [20] R. Buczkowski, M. Taczała, and M. Kleiber. A 16-node locking-free Mindlin plate resting on two parameter elastic foundation – static and eigenvalue analysis. Computers Assisted Methods in Engineering and Science, 22(2):99–114, 2015.
  • [21] K.M. Saheb and K. Krishnabhaskar. Large amplitude free vibration of simply supported and clamped moderately thick square plates using coupled displacement method. Journal of Vibration Engineering and Technologies, 4(2):153–159, 2016.
  • [22] K.M. Saheb, G.V. Rao, and G.R. Janardhana. Evaluation of large amplitude free vibration behavior of uniform Timoshenko beams using coupled displacement method. Advances in Vibration Engineering, 9(1):15–23, 2010.
  • [23] Y.H. Wang, L.G. Tham, Y.K. Cheung. Beams and plates on elastic foundation: a review. Progress in Structural Engineering and Materials, 7(4):174–182, 2005. doi: 10.1002/pse.202.
  • [24] Y. Xiang, S. Kitipornchai, and K.M. Liew. Buckling and vibration of thick laminates on Pasternak foundations. Journal of Engineering Mechanics, 122(1):54–63, 1996. doi: 10.1061/(ASCE)0733-9399(1996)122:1(54).
  • [25] Y. Xiang, C.M.Wang, and S. Kitipornchai. Exact vibration solution for initially stressed Mindlin plates on Pasternak foundations. International Journal of Mechanical Sciences, 36(4):311–316,1994. doi: 10.1016/0020-7403(94)90037-X.
  • [26] Y. Zhong and J.H. Yin. Free vibration analysis of plate on foundation with completely free boundary by finite integral transformation method. Mechanics Research Communications, 35(4):268–275, 2008. doi: 10.1016/j.mechrescom.2008.01.004.
Uwagi
EN
1. The authors would like to thank the authorities of University College of Engineering, Jawaharlal Nehru Technological University Kakinada (JNTUK), for sponsoring and publishing the research paper under TEQIP-III
PL
2. Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-9272bdf5-2d35-49ab-b0b3-a03921d0cd2a
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