Free vibration analysis of Mindlin plates partially resting on Pasternak foundation

International Journal of Mechanical Sciences

Volumn 75, Issue , 2013, Pages 1-7

  Jahromi, H N ^a   Aghdam, M M ^a   Fallah, A ^a,b  

^a AMIRKABIR UNIVERSITY OF TECHNOLOGY   (Iran)

^b SHARIF UNIVERSITY OF TECHNOLOGY   (Iran)

Author keywords

Free vibration analysis; Generalized differential quadrature method; Moderately thick plates; Partially elastic foundation; Pasternak foundation

Indexed keywords

FREE-VIBRATION ANALYSIS; GENERALIZED DIFFERENTIAL QUADRATURE METHODS; MODERATELY THICK PLATE; PARTIALLY ELASTIC FOUNDATIONS; PASTERNAK FOUNDATION;

BOUNDARY CONDITIONS; DIFFERENTIATION (CALCULUS); EIGENVALUES AND EIGENFUNCTIONS; GEOMETRY; MINDLIN PLATES; NATURAL FREQUENCIES; PARTIAL DIFFERENTIAL EQUATIONS; VIBRATION ANALYSIS;

ALGEBRA;

EID: 84884652554     PISSN: 00207403     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijmecsci.2013.06.001     Document Type: Article

References (24)

1. A.W. Leissa The free vibration of rectangular plates J Sound Vib 31 1973 257 293
2. K.M. Liew, Y. Xiang, and S. Kitipornchai Research on thick plate vibration: a literature survey J Sound Vib 180 1995 163 176
3. E. Reissner The effect of transverse shear deformation on the bending of elastic plates ASME J Appl Mech 12 1945 A68 A77
4. R.D. Mindlin An introduction to the theory of vibrations of elastic plates ASME J Appl Mech 73 1951 31 38
5. C.M. Wang, J.N. Reddy, and K.H. Lee Chapter 12 - Free vibration relationships Shear deformable beams and plates 2000 Elsevier Science Ltd Oxford 223 242
6. M. Simsek, and T. Kocatürk Free vibration analysis of beams by using a third-order shear deformation theory Sadhana 32 2007 167 179 (Pubitemid 47298131)
7. E. Viola, F. Tornabene, and N. Fantuzzi General higher-order shear deformation theories for the free vibration analysis of completely doubly-curved laminated shells and panels Compos Struct 95 2013 639 666
8. K.M. Liew, Y. Xiang, and S. Kitipornchai Transverse vibration of thick rectangular plates - I. Comprehensive sets of boundary conditions Comput Struct 49 1993 1 29
9. K.M. Liew, K.C. Hung, and M.K. Lim A continuum three-dimensional vibration analysis of thick rectangular plates Int J Solids Struct 30 1993 3357 3379
10. K.M. Liew, K.C. Hung, and M.K. Lim Vibration of mindlin plates using boundary characteristic orthogonal polynomials J Sound Vib 182 1995 77 90
11. H.S. Shen, J. Yang, and L. Zhang Free and forced vibration of Reissner-Mindlin plates with free edges resting on rlastic foundations J Sound Vib 244 2001 299 320 (Pubitemid 32594395)
12. P. Malekzadeh, G. Karami, and M. Farid A semi-analytical DQEM for free vibration analysis of thick plates with two opposite edges simply supported ComputMethods Appl Mech Eng 193 2004 4781 4796 (Pubitemid 39408001)
13. F.L. Liu, and K.M. Liew Vibration analysis of discontinuous Mindlin plates by differential quadrature element method J Vib Acoust 121 1999 204 208
14. E. Winkler, Die Lehre von der Elastizität und Festigkeit mit besonderer Rücksicht auf ihre Anwendung in der Technik: für polytechnische Schulen, Bauakademien, Ingenieure, Maschinenbauer, Architecten, etc, Dominicius; 1868.
15. P.L.Pasternak, On a new method of analysis of an elastic foundation by means of two foundation constants (in Russian), Gosudarstrennoe Izdatelstvo Literaturi po Stroitelstvu i Arkhitekture; 1954.
16. K.Y. Lam, C.M. Wang, and X.Q. He Canonical exact solutions for Levy-plates on two-parameter foundation using Green's functions Eng Struct 22 2000 364 378 (Pubitemid 30000080)
17. Y. Xiang, C.M. Wang, and S. Kitipornchai Exact vibration solution for initially stressed Mindlin plates on Pasternak foundations Int J Mech Sci 36 1994 311 316
18. M.H. Omurtag, A. Ozutok, A.Y. Akoz, and Y. Özcelikors Free vibration analysis of Kirchhoff plates resting on elastic foundation by mixed finite element formulation based on Gateaux differential Int J Numer Methods Eng 40 1997 295 317 (Pubitemid 127571812)
19. S. Motaghian, M. Mofid, and J.E. Akin On the free vibration response of rectangular plates, partially supported on elastic foundation Appl Math Modell 36 2012 4473 4482
20. Y. Xiang Vibration of rectangular Mindlin plates resting on non-homogenous elastic foundations Int J Mech Sci 45 2003 1229 1244
21. S. Nobakhti, and M.M. Aghdam Static analysis of rectangular thick plates resting on two-parameter elastic boundary strips Eur J Mech - A/Solids 30 2011 442 448
22. J.B. Han, and K.M. Liew Numerical differential quadrature method for Reissner/Mindlin plates on two-parameter foundations Int J Mech Sci 39 1997 977 989 (Pubitemid 127382128)
23. C. Shu, W. Chen, H. Xue, and H. Du Numerical study of grid fistribution effect on accuracy of DQ analysis of beams and plates by error estimation of derivative approximations Int J Numer Methods Eng 51 2001 159 179 (Pubitemid 32386805)
24. D. Zhou, Y.K. Cheung, S.H. Lo, and F.T.K. Au Three-dimensional vibration analysis of rectangular thick plates on Pasternak foundation Int J Numer Methods Eng 59 2004 1313 1334 (Pubitemid 38335659)