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Tytuł artykułu

Free vibration analysis of point supported rectangular plates using quadrature element method

Autorzy
Treść / Zawartość
Identyfikatory
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this study, the hybrid approach of the Quadrature Element Method (QEM) has been employed to generate solutions for point supported isotropic plates. The Hybrid QEM technique consists of a collocation method with the Galerkin finite element technique to combine the high accurate and rapid converging of Differential Quadrature Method (DQM) for effi- cient solution of differential equations. To present the validity of the solutions, the results have been compared with other known solutions for point supported rectangular plates. In addition, different solutions are carried out for different type boundary conditions, different locations and number of point supports. Results for the first vibration modes of plates are also tested using a commercial finite element code, and it is shown that they are in good agreement with literature.
Rocznik
Strony
1041--1053
Opis fizyczny
Bibliogr. 41 poz., rys., tab.
Twórcy
autor
  • Afyon Kocatepe University, Technical Education Faculty, Afyon, Turkey
autor
  • Osmangazi University, Department of Mechanical Engineering, Eskisehir, Turkey
Bibliografia
  • 1. Bapat A.V., Suryanarayan S., 1989, Flexibility function approach to vibration analysis of rectangular plates with arbitrary multiple point supports on the edges, Journal of Sound and Vibration, 128, 209-233
  • 2. Bellman R., Casti J., 1971, Differential quadrature and long-term integration, Journal of Mathematical Analysis and Applications, 34, 235-238
  • 3. Chen C.-N., 2004, DQEM and DQFDM irregular elements for analyses of 2-D heat conduction in orthotropic media, Applied Mathematical Modeling, 28, 7, 617-638
  • 4. Chen W.L., Striz A.G., Bert C.W., 2000, High-accuracy plane stress and plate elements in the quadrature element method, International Journal of Solids and Structures, 37, 627-647
  • 5. Cheung Y.K., Zhou D., 1999, Free vibration of rectangular composite plates with point-supports using static beam functions, Composite Structures, 44, 2, 145-154
  • 6. Cheung Y.K., Zhou D., 2000, Free vibration of thick, layered rectangular plates with point supports by finite layer method, International Journal of Solids and Structures, 37, 10, 1483-1499
  • 7. Cox H.L., Boxer J., 1960, Vibration of rectangular plates point-supported at the corners, Aeronautical Quarterly, 11, 41-50
  • 8. Damle S.K., Feeser L.J., 1972, Vibration of four point supported plates by a finite element method, Journal of the Aeronautical Society of India, 24, 375-377
  • 9. Fan S.C., Cheung Y.K., 1984, Flexural free vibrations of rectangular plates with complex support conditions, Journal of Sound and Vibration, 93, 81-94
  • 10. Franciosi C., Tomasiello S., 2004, A modified quadrature element method to perform static analysis of structures, International Journal of Mechanical Sciences, 46, 6, 945-959
  • 11. Gorman D.J., 1991, Analytical and experimental study of vibrating rectangular plates on rigid point supports, AIAA Journal, 29, 8, 38-44
  • 12. Gu H.Z., Wang X.W., 1997, On the free vibration analysis of circular plates with stepped thickness over a concentric region by the quadrature element method, Journal of Sound and Vibration, 202, 452-459
  • 13. Gutierrez R.H., Laura P.A.A., 1995, Analysis of vibrating, thin, rectangular plates with point-supports by the method of differential quadrature, Ocean Engineering, 22, 101-103
  • 14. Han J.B., Liew K.M., 1996, The differential quadrature element method (DQEM) for axisymmetric bending of thick circular plates, Proceedings of the 3rd Asian-Pacific Conference on Computational Mechanics, 2363-2368
  • 15. Huang M.H., Thambiratnam D.P., 2001a, Analysis of plate resting on elastic supports and elastic foundation by finite strip method, Computers and Structures, 79, 29-30, 2547-2557
  • 16. Huang M.H., Thambiratnam D.P., 2001b, Free vibration analysis of rectangular plates on elastic intermediate supports, Journal of Sound and Vibration, 240, 3 567-580
  • 17. Kato Y., Honma T., 1998, The Rayleigh-Ritz solution to estimate vibration characteristics of building floors, Journal of Sound and Vibration, 211, 2, 195-206
  • 18. Kerstens J.G.M., 1979, Vibration of a rectangular plate supported at an arbitrary number of points, Journal of Sound and Vibration, 65, 493-504
  • 19. Kim C.S., Dickinson S.M., 1987, Flexural vibration of rectangular plates with point supports, Journal of Sound and Vibration, 117, 249-261
  • 20. Kitipornchai S., Xiang Y., Liew K.M., 1994, Vibration of analysis of corner supported Mindlin plates of arbitrary shape using the Lagrange multiplier method, Journal of Sound and Vibration, 173, 457-470
  • 21. Kocaturk T., Sezer S., Demir C., 2004, Determination of the steady state response of viscoelastically point-supported rectangular specially orthotropic plates with added concentrated masses, Journal of Sound and Vibration, 278, 4-5, 789-806
  • 22. Lee L.T., Lee D.C., 1997, Free vibration of rectangular plates on elastic point supports with the application of a new type of admissible function, Computer and Structures, 65, 2, 149-156
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  • 25. Liew K.M., Lam K.Y., 1994, Effects of arbitrarily distributed elastic point constraints on vibrational behavior of rectangular plates, Journal of Sound and Vibration, 174, 1, 23-36
  • 26. Liew K.M., Xiang Y., Kitipornchai S., 1994, Vibration of Mindlin plates on point supports using constraint functions, Journal of Engineering Mechanics, 120, 499-513
  • 27. Liu F.-L., Liew K.M., 1998, Static analysis of Reissner-Mindlin plates by differential quadrature element method, ASME Journal of Applied Mechanics, 65, 705-710
  • 28. Liu F.-L., Liew K.M., 1999a, Differential quadrature element method: a new approach for free vibration analysis of polar Mindlin plates having discontinuities, Computer Methods in Applied Mechanics and Engineering, 179, 3-4, 407-423
  • 29. Liu F.-L., Liew K.M., 1999b, Differential quadrature element method for static analysis of Reissner-Mindlin polar plates, International Journal of Solids and Structures, 36, 5101-5123
  • 30. Liu F.-L., 2000, Rectangular thick plates on Winkler foundation: differential quadrature element solutions, International Journal of Solids and Structures, 37, 12, 1743-1763
  • 31. Mizusawa T., Kajita T., 1987, Vibration of skew plates resting on point supports, Journal of Sound and Vibration, 115, 243-251
  • 32. Narita Y., Hodgkinson J.M., 2005, Layerwise optimisation for maximizing the fundamental frequencies of point-supported rectangular laminated composite plates, Composite Structures, 69, 2, 127-135
  • 33. Quan J.R., Chang C.T., 1989, New insights in solving distributed system equations by the quadrature method. I – Analysis, Computers and Chemical Engineering, 13, 7, 779-788
  • 34. Rui L., Bo W., Gang L., Bin T., 2016, Hamiltonian system-based analytic modeling of the free rectangular thin plates’ free vibration, Applied Mathematical Modelling, 40, 2, 984-992
  • 35. Rui L., Bo W., Gang L., Jiahui D., Xiaoting A., 2015, Analytic free vibration solutions of rectangular thin plates point-supported at a corner, International Journal of Mechanical Sciences, 96-97, 199-205
  • 36. Saadatpour M.M., Azhari M., Bradford M.A., 2000, Vibration analysis of simply supported plates of general shape with internal point and line supports using the Galerkin method, Engineering Structures, 22, 9, 1180-1188
  • 37. Striz A.G., Chen W., Bert C.W., 1994, Static analysis of structures by the quadrature element method (QEM), International Journal of Solids and Structures, 31, 20, 2807-2818
  • 38. Venkateswara R.G., Raju I.S., Murty G.K., 1073, Vibration of rectangular plates with mixed boundary conditions, Journal of Sound and Vibration, 30, 257-260
  • 39. Wang X.W., Gu H.Z., 1997, Static analysis of frame structure by the differential quadrature element method, International Journal of Numerical Methods in Engineering, 40, 759-772
  • 40. Zhao Y.B., Wei G.W., Xiang Y., 2002, Plate vibration under irregular internal supports, International Journal of Solids and Structures, 39, 5, 361-1383
  • 41. Zhou D., 2002, Vibrations of point-supported rectangular plates with variable thickness using a set of static tapered beam functions, International Journal of Mechanical Sciences, 44, 1, 149-164
Uwagi
Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017)
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-26c91b8c-1fff-440e-ae33-f86d1bb96606
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