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2019 | 138 | 2 | 141-166
Article title

Nonlinear Thermally Induced Dynamic Analysis of Non-Homogenous Rectangular Plate with Varying Thickness Using Three-Dimensional Differential Transform Method

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EN
Abstracts
EN
The practical importance of thermally induced varying thickness plates has recently become an area of increase interest for engineers due to its wide applications. The temperature effect alters the modulus of elasticity of the plate causing an irrational behavior of the plate. This present study presents the application of three-dimensional differential transform method (3D-DTM) to nonlinear thermally induced dynamic analysis of non-homogenous rectangular plate with varying thickness under external excitation. Three-dimensional differential transform is used to obtain the analytical solution to the governing differential equation and the solution is used for the parametric studies. It is shown that, taper constant increases with increase in maximum deflection, thermal constant increases with decreases in maximum deflection, increases in aspect ratio leads to decreases in maximum deflection, increase in natural frequency results to increases in maximum deflection and non-homogeneity constant increases with increase in maximum deflection. Findings of the research is expected to add value to existing knowledge of classical plate theory.
Discipline
Year
Volume
138
Issue
2
Pages
141-166
Physical description
Contributors
  • Department of Mechanical Engineering, University of Lagos, Akoka, Lagos State, Nigeria
author
  • Department of Civil and Environmental Engineering, University of Lagos, Akoka, Lagos State, Nigeria
author
  • Department of Mechanical Engineering, University of Lagos, Akoka, Lagos State, Nigeria
author
  • Faculty of Military Science, Stellenbosch University, Private Bag X2, Saldanha 7395, South Africa
References
  • [1] K. Gupta, Non-linear Thermally induced vibrations of Non-homogenous rectangular plate of linearly varying thickness in the presence of external force. International Journal of Acoustics and Vibration, 22(4) (2017) 462-466.
  • [2] R.K. Jain and S.R. Soni. Free vibration of rectangular plates of parabolically varying thickness. Indian journal of Pure applied Mathematics, 4, (1977) 267-277.
  • [3] T. Irie and G. Yamada. Thermally Inducecd vibration of circular plate. Bullentin of the JSME 21(162) (1978) 162-165.
  • [4] P. A. Laura, R.O. Grossi and G.I. Carneiro, Transverse vibration of rectaangular plates with thickness varying in the two direction andwith edges elastically restrained against rotation. Journal of sound and vibration 63(4) (1979) 499-505.
  • [5] J.S. Tomar and A.K. Gupta, Thermal effect on frequency of an Orthotropic rectangular plate of linearly varying thickness. Journal of Sound and vibration, 90(3) (1983) 325-331.
  • [6] J.S. Tomar and A.k. Gupta, Effect of thermal gradient on frequency of an Orthotropic rectangular plate whose thickness varies intwo-direction. Journal of Sound and Vibration, 98(2) (1985) 257-262.
  • [7] Singh and V. Saxena, Transverse vibration of a rectangular plate with bidirectional thickness variation. Journal of Sound and Vibration 198(1) (1996) 51-65.
  • [8] A.K. Gupta, T. Johri and R.P. Vats, Thermal effect on vibration of non-homogenous Orthotropic rectangular plates having bi-direction parabolically varying thickness. In Proceedings of the International Conference on World Congress on Enginerring and Computer Science, (2007) 784-787.
  • [9] A. Khanna and A. Singhal, An analytical approach on thermally induced vibrations of non-homogenous tapered plate. Journal of Mathematics, (2013), 6-10. http://dx.doi.org/10.1155/2013/721868
  • [10] J.S. Chang, J.H. Wang and T.T Tsai, Thermally induced vibration of laminated plate by finite element method. Computers and structures, 42(1) (1992) 117-128.
  • [11] S. Natarajan and G. Manickam, Bending and vibration of functionally graded material sandwich plates using an accurate theory. Finite elments in analysis and design, 57 (2012) 32-42.
  • [12] M. Hemmatnezhad, R. Ansari and G.H. Rahimi, Large-amplitude free vibration of functional graded beams by means of finite element formulation. Applied Mathematics Modelling, 37 (2013) 18-19.
  • [13] S. Pandey and S. Pradyumna, A finite elment formulation for thermally induced vibration of functionally graded material Sandwich plates and shell panel. Composite Structure, 160 (2017) 877-886.
  • [14] A. Gupta and P. Singhal, Effect of non-homogeneity on thermally induced vibration of Orthotropic Visco-elastic rectangular plate of linearly varying thickness. Applied Mathematics Scientific Research, 1 (2010) 326-333.
  • [15] R. Kawamura, Y. Tanigawa, S. Kusuki, H. Hamamura, Thermo-elasticity equation for thermally induced flexural vibration problem for in-homogenous plates and thermo elastic dynamical responses to a sinusoidal varying surface temperature. Journal of Engineering Mathematics, 61(2) (2008) 143-160.
  • [16] U.S. Gupta, R. Lai and S. Sharma, Vibration analysis of non-homogenous circular plate of nonlinear thickness variation by differential Quadrature method. Journal of sound and vibration, 298(4-5) (2006) 892-906.
  • [17] M.M. Rashidi, A. Shooshtan and O. Anwar. Homotopy Perturbation study of nonlinear vibration of Von Karman rectangular plates. Computers and Structures 106-107 (2012) 46-55. https://doi.org/10.1016/j.compstruc.2012.04.004
  • [18] Marinca, N. Herisanu ans I. Nemes, Optimal Homotopy Asymptotic method with application to thin flow. Central European Journal of Physics, 6(3) (2008) 648-653.
  • [19] M.M Rashidi, E. Erfani, O.A. Berg and S.K. Ghosh, Modofied Differential Transform method simulation of hydromagnetic Multi physical flow phenomena from a rotating disk. World Journal of Mechanics, 1 (2011) 217-230.
  • [20] J. S. Shabnam, A. Reza and K. F. Rahmat. Free vibration analysis of variable thickness thin plates by two-dimensional differential transform method. Acta Mechanica, 224(8) (2013) 1643-1658.
  • [21] L. Fryba, Vibration of solids and structures under moving loads, Czechoslovak, Prague: Noordhoff International Publishing, 1972.
  • [22] J.K. Zhou, Differential transsformation and its application for electric circuits. Huazhong Uni. Press. China, (1986).
  • [23] K. Chen and S. H. HO, Application of differential transform method to eigen value problems. Applied maths and Computation, 79 (1996) 172-188.
  • [24] F. Ayaz, Soutions of the system of differential equations by differential transform method. Applied Mathematics and Computation, 147(2) (2004) 547-567. DOI: 10.1016/S0096-3003(02)00794-4
  • [25] Y. Zhang. Large deflectionof clamped circular plate and accuracy of its approximate analytical solutions. SCIENCE CHINA Physics, Mechanics & Astronomy, 59(2), 624602-11. (2016). doi:10.1007/s11433-015-5751-y
  • [26] A.K. Gupta, J. Tripti, and P.P, Vats. Thermal effcet on vibration of non-homogenous orthotropic rectangular plate having bi-directional parabolically varying thickness. Proceeding of World Congress on Engineering and Computer Science. WCECS 2007, October 24-26, 2007, San Francisco, USA.
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article
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YADDA identifier
bwmeta1.element.psjd-d8343991-493d-4e9f-9874-88191a9f8ce8
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