Application of the Adomian Modified Decomposition Method to Free Vibration Analysis of Thin Plates with Elastic Supports
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Abstract
The purpose of this study is to introduce an innovative method, the Adomian modified decomposition method, to solve the vibration problem of thin elastic plates. By applying the present method to vibration problem of thin plates, the fundamental and higher frequencies as well as their mode shapes can be obtained easily for common and complicated boundary conditions, including elastic supports. Other benefits of using this method can be realized in terms of rapid convergence, small computational expensiveness and stability in calculation. The significant effects such as effects of boundary conditions, aspect ratios and translational and rotational spring constants, which lead to considerable changes in frequency results and mode shapes, are investigated and discussed.
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Copyright @2021 Engineering Transactions
Faculty of Engineering and Technology
Mahanakorn University of Technology
References
G. Adomian, Solving frontier problems of physics: The decomposition method, Kluwer Academic Publishers, Dordrecht, 1994.
G. Adomian and R. Rach, “Modified decomposition solution of nonlinear partial differential equations”, Computer and mathematics with applications, vol. 23, pp. 17-23, 1992.
A. M. Wazwaz, “A reliable modification of Adomian decomposition method”, Applied mathematics and computation, vol. 102, pp. 77-86, 1999.
B. Jang, “Exact solutions to one dimensional non-homogeneous parabolic problems by the homogeneous Adomian decomposition method”, Applied mathematics and computation, vol. 189, pp. 969-979, 2007.
Q. Mao and S. Pietrzko, “Free vibration analysis of stepped beams by using Adomian decomposition method”, Applied mathematics and computation, vol. 217, pp. 3429-3441, 2010.
Q. Mao, “Free vibration analysis of multiple-stepped beams by using Adomian decomposition method,” Mathematical and computer modeling, vol. 54, pp.756-764, 2011.
H.Y. Lai, J.C. Hsu and C.K. Chen, “An innovative eigenvalue problem solver for free vibration of Euler-Bernoulli beam by using the Adomian decomposition method”, Computers and mathematics with application, vol. 56, pp. 3204-3220, 2008.
J.C. Hsu, H.Y. Lai and C.K. Chen, “Free vibration of non-uniform Euler-Bernoulli beams with general elastically end constraints using Adomian modified decomposition method,” Journal of Sound and vibration, vol. 318, pp. 965-981, 2008.
J.C. Hsu, H.Y. Lai and C.K. Chen., “An innovative eigenvalue problem solver for free vibration of uniform Timoshenko beams by the Adomian modified decomposition method”, Journal of Sound and vibration, vol. 325, pp. 451-470, 2009.
J.N. Reddy, Theory and analysis of elastic plates and shells, 2nd Ed., CRC Press, U.S.A, 2007.
V. Ungbhakorn, and N. Wattanasakulpong, “Bending analysis of symmetrically laminated rectangular plates with arbitrary edge supports by the extended Kantorovich method”, Thammasat Int. J. Science and technology, vol. 11, pp. 33-44, 2006.
V. Ungbhakorn and P. Singhatanadgid, “Buckling analysis of symmetrically laminated composite plates by the extended Kantorovich method”, Composite Structures, vol. 73, pp. 120-128, 2006.
H. Khov, W.L. Li, and R.F. Gibson, “An accurate solution method for static and dynamic deflections of orthotropic plates with general boundary conditions,” Composite structures, vol. 90, pp. 474-481, 2009.
A.W. Leissa, “The free vibration of rectangular plates”, Journal of Sound and vibration, vol. 31, pp. 257-293, 1973.
L. Dozio, “On the use of the trigonometric Ritz method for general vibration analysis of rectangular Kirchhoff plates”, Thin-walled structures, vol. 49, pp. 129-144, 2011.
P. Malekzadeh and S.A. Shahpari, “Free vibration analysis of variable thickness thin and moderately thick plates with elastically restrained edges by DQM”, Thin-walled structures, vol. 43, pp. 1037-1050, 2005.
W.L. Li and M. Daniels, “A fourier series method for the vibrations of elastically restrained plates arbitrarily loaded with springs and masses”, Journal Sound and vibration, vol. 252, pp. 768-781, 2002.