EFFECT OF TWO - PARAMETER FOUNDATION ON FREE TRANSVERSE VIBRATION OF NON- HOMOGENEOUS ORTHOTROPIC RECTANGULAR PLATE OF LINEARLY VARYING THICKNESS

Year 2014, , 32 - 51, 01.06.2014

U.s. Gupta Seema Sharma Prag Singhal

https://doi.org/10.24107/ijeas.251220

Cited By: 1

Abstract

Differential Quadrature Method (DQM) is employed to obtain natural frequencies and mode shapes of nonhomogeneous rectangular orthotropic plates of linearly varying thickness resting on two -parameter foundation (Pasternak). The analysis is based on classical plate theory. Numerical results are presented for various values of plate parameters for different boundary conditions. Convergence studies have been made to ensure accuracy of the results. A comparison of our results with those available in the literature shows the versatility and accuracy of DQM

Keywords

DQM, varying thickness, non-homogeneity, two-parameter foundation

References

• Leissa, A. W., Vibration of Plates: Washington: office of Technology Utilization. SP, NASA, 1965.
• Leissa, A. W., Recent research in plane vibrations, Complicating effects. Shock and Vibration Digest, 9 (1), 21-35, 1977.
• Leissa, A. W., Recent research in plane vibrations, 1973-1976, Complicating effects. Shock and Vibration Digest, 10 (12), 21-35, 1978.
• Leissa, A. W., Plate vibration research, 1976-1980, (9),11-22, 1981a.
• Leissa, A. W., Plate vibration research, 13 (10), 19-36, 1981b.
• Leissa, A. W., Recent studies in plate vibrations: part Ι, Classical theory. The Shock and Vibration Digest, 19 (2), 10-24, 1987a
• Leissa, A. W., Recent studies in plate vibrations: part ΙΙ, Complicating effects. The Shock and Vibration Digest, 19 (3), 10-24, 1987b.
• Rao, G. V., Rao, B. P. and Raju, L. S., Vibrations of inhomogeneous thin plates using a high- precision triangular element. Journal of Sound and Vibration, 34(3), 444 – 445, 1974.
• Tomar, J. S., Gupta, D. C. and Jain, N. C., Free vibrations of an isotropic non-homogenous infinite plate of linearly varying thickness. Meccanica, Journal of Italian Association of Theoretical and Applied Mechanics AIMETA, 18, 30-33, 1983
• Gutierrez, R. H. and Laura, P. A. A., Vibrations of rectangular plates with Linearly varying thickness and non-uniform boundary conditions. Journal of Sound and Vibration, 178 (4), 563-566, 1994
• Lal, R., Gupta, U. S. and Reena, Quintic splines in the study of transverse vibrations of non- uniform orthotropic rectangular plates. Journal of Sound and Vibration, 207(1), 1-13, 1997.
• Lal, R., Gupta, U.S and Goel, C., Chebyshev polynomials in the study of transverse Vibration of non-uniform rectangular plates. The Shock and Vibration Digest, 33 (2), 103-112, 2001.
• Gupta, U. S., Lal, R. and Sharma, S., Vibration analysis of non-homogeneous circular plate of non-linear thickness variation by differential quadrature method. Journal of Sound and Vibration, 298 (4-5), 892-906, 2006.
• Lal, R. and Dhanpati, Transverse vibrations of non-homogeneous orthotropic rectangular plates of variable thickness: A spline technique. Journal of Sound and Vibration, 306 (1-2), 203-214, 2007.
• Sharma, S., Gupta, U. S and Singhal, P., Vibration analysis of non- homogeneous Orthotropic rectangular plate of variable thickness resting on Winkler foundation, Journal of Applied Sciences and Engineering, 15 (3), 291-300, 2012.
• Gupta, U. S., Sharma, S. and Singhal, P. (2012). Numerical simulation vibration of nonhomogeneous plates of variable thickness. International Journal of Engineering and Applied Sciences, 4(4), 26 - 40, 2012.
• Selvadurai, A. P. S., Elastic Analysis of Soil-Foundation Interaction. Elsevier, NY, 1979.
• Kerr, A. D., Elastic and viscoelastic foundation models. ASME Journal of Applied Mechanics, 31, 491-498, 1964.
• Hetenyi, M., Beams and plates on elastic foundation and related problems. Applied Mechanics Reviews, 19, 95-102, 1966.
• Yingshi, Z., Vibration of stepped rectangular thin plates on Winkler foundation. Applied Mathematics and Mechanics, 20(5), 568-578, 1972.
• Raju, K. K. and Rao, G. V., Effect of elastic foundation on the mode shapes in stability and vibration problems of simply supported rectangular plates. Journal of Sound and Vibration, 139(1), 170-173, 1990.
• Turvey, G. J., Uniformly loaded, simply supported, antisymmetrically laminated, rectangular plate on a Winkler-Pasternak foundation. International Journal of and Structures, 13, 437-444, 1977.
• Kerr, A. D., Elastic and viscoelastic foundation models. ASME Journal of Applied Mechanic, 31, 491-498, 1964.
• Katiskadelis, J. T. and Kallivokas, L. F., Clamped plates on Pasternak-type elastic foundation by the boundary element method. Journal of Applied Mechanics Division, ASME, 53, 909-917, 1986.
• Wang, C. W., Wang, C. and Ang, K. K., Vibration of initially stressed Reddy Plates on a Winkler-Pasternak foundation. Journal of Sound and Vibration, 204(2), 203-212, 1997.
• Wang, J. G., Wang , X. X . and Haung, M. K., Fundamental solutions and Boundary integral equations for Reissner’s plates on two parameter foundations. International Journal of Solids and Structures, 29, 1233-1239, 1992.
• Xiang, Y., Wang, C. M. and Kitipornchai, S., Exact vibration solution for initially stressed Mindlin plates on Pasternak foundations. International Journal of Mech. Science, 36 (4), 311-316, 1994.
• Shen, H. S., Postbuckling of orthotropic plates on two-parameter elastic foundation, Journal of Engineering Mechanics, 121, 50-56, 1995.
• Teo, T. M. and Liew, K. M., Differential cubature method for analysis of shear deformable rectangular plates on Pasternak foundation. International Journal of Mechanical Sciences, 44, 1179-1194, 2002.
• Omurtag, M. H. and Kadioglu, F., Free vibration analysis of orthotropic plates resting on Pasternak foundation by mixed finite element formulation. Computers and Structures, 67 (4), 253-265, 1998.
• Malekzadeh, P. and Karami, G., Vibration of non-uniform thick plates on elastic foundation by differential quadrature method. Engineering Structures, 26, 1473-1482, 2004.
• Leung, A. V. T. and Zhu, B., Transverse vibration of Mindlin plates on two- parameter foundation by analytical trapezoidal p-elements. Journal of Engineering Mechanics, 131(11), 1140-1145, 2005.
• Lal, R. and Dhanpati., Effect of non-homogeneity on vibration of orthotropic rectangular plates of varying thickness resting on Pasternak Foundation. ASME Journal of Vibration and Acoustics, 131, 1-9, 2009.
• Biancolini, M. E., Brutti, C. and Reccia, L., Approximate solution for free vibration of thin orthotropic rectangular plates. Journal of Sound and Vibration, 228, 321-344, 2005.
• Lekhnitskii, S. G., Anisotropic plates. Translated by S.W. Tsai and T. Cheron, Gorden and Breach, New York, 1968.
• Panc, V., Theories of Elastic Plates. Noordhoff International Publishing, Leydon, the Netherlands, 1975.
• Shu, C., Differential quadrature and its application in Engineering. Springer-Verlag, Great-Briatain, 2000.
• Shu, C., Differential quadrature and its application in Engineering. Springer-Verlag, Great-Briatain, 2000.
• Jain, R. K. and Soni, S. R., Free vibration of rectangular plates of parabolically varying thickness. Indian Journal of Pure and Applied Mathematics, 4 (3), 267-277, 1973.