How to cite this paper
Gupta, U., Sharma, S & Singhal, P. (2016). DQM modeling of rectangular plate resting on two parameter foundation.Engineering Solid Mechanics, 4(1), 33-44.
Refrences
Bhattacharya, B. (1977). Free vibration of plates on Vlasov’s foundation. Journal of Sound and Vibration, 54(3), 464-467.
Biancolini,, M.E., Brutti, C., & Reccia, L. (2005). Approximate solution for free vibration of thin orthotropic rectangular plates. Journal of Sound and Vibration, 288, 321-344.
Bellman, R.K., Kashef, B.G. & Casti, J. (1972). Differential quadrature technique for the rapid solution of nonlinear partial differential equation. Journal of Computational Physics, 10, 40-52.
Chonan, S. (1980). Random vibration of initially stressed thick plate on an elastic foundation. Journal of Sound and Vibration, 71(1), 117-127.
Civalek, O. & Acar, M. H. (2007). Discrete singular convolution method for the analysis of Mindlin plates on elastic foundation. International Journal of Pressure Vessels and Piping, 84, 527-535.
Gupta, U.S. & Lal, R. (1978). Transverse vibrations of non-uniform rectangular plates on an elastic foundation. Journal of Sound and Vibration, 61, 127-133.
Gupta, U.S., Seema, S. & Singhal, P. (2012). Numerical simulation of vibrations of rectangular plates of variable thickness. International Journal of Engineering & Applied Sciences, 4(4), 26-40.
Gupta, U.S., Sharma, S. & Prag, S. (2014). Effect of two – parameter foundation on free transverse vibration of non-homogeneous orthotropic rectangular plate of linearly varying thickness. International Journal of Engineering & Applied Sciences, 6 (2), 32-51.
Hasheminejad, S. M., & Gheshlaghi, B. (2012). Three-dimensional elastodynamic solution for an arbitrary thick FGM rectangular plate resting on a two parameter viscoelastic foundation. Composite Structures, 94(9), 2746-2755.
Hetenyi, M. (1966). Beams and plates on elastic foundation and related problems. Applied Mechanics Reviews, 19, 95-102.
Kerr, AD. (1964). Elastic and viscoelastic foundation models. ASME Journal of Applied Mechanics, 31, 491-498.
Jain. R. K., Soni, S. R. (1973). Free vibration of rectangular plates of Parabolically varying thickness. Indian Journal of pure and Applied Mathematics, 4(3), 267-277.
Lal, R., Gupta, U.S. & Goel C. (2001). Chebyshev polynomials in the study of transverse vibrations of non- uniform rectangular orthotropic plates. The Shock and Vibration Digest, 33(2), 103-112.
Lal, R. & Dhanpati. (2007). Transverse vibration of non-homogeneous Orthotropic rectangular plates of variable thickness: A spline technique. Journal of Sound and Vibration, 306, 203-214.
Leissa, A.W. (1969). Vibration of plates. NASA SP-160, Government Printing Office, Washington
, DC.
Liew, K. M., Han, J.B., Xiao, Z. M. & Du, H. (1996). Differential quadrature method for Mindlin plates on Winkler foundation. International Journal of Mechanical Science, 38(4), 405-421.
Malekzadeh, P. & Karami, G. (2004). Vibration of non-uniform thick plates on elastic foundation by differential method. Engineering Structures, 26, 1473-1482.
Omurtag, M. H. & Kadioglu, F. (1998). Free vibration analysis of orthotropic plates resting on
Pasternak foundation by mixed finite element formulation. Computers and Structures, 67(4),
253-265.
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, 779-788.
Samaei, A. T., Aliha, M. R. M., & Mirsayar, M. M. (2015). Frequency analysis of a graphene sheet embedded in an elastic medium with consideration of small scale. Materials Physics and Mechanics, 22, 125-135.
Selvadurai, A. P. S. (1979). Elastic Analysis of Soil-Foundation Interaction. Elsevier, NY.
Sharma, S., Gupta, U.S. & Singhal, P. (2012). Vibration analysis of non-homogeneous orthotropic rectangular plates of variable thickness resting on Winkler foundation. Journal of Applied Science and Engineering, 15(3), 291-300.
Shen, H. S., Yang, J. & Zhang, L. (2001). Free and forced vibration of Reissner-Mindlin plates with free edges resting on elastic foundations. Journal of Sound and Vibration, 244 (2), 299-320.
Shu, C. (2000). Differential quadrature and its application in Engineering. Springer-Verlag, Great-
Briatain.
Sonzogni, S.R., Idelson, Laura, P. A. A. & Cortinez, V.H. (1990). Free vibration of rectangular plates of exponentially varying thickness and with a free edge. Journal of sound and vibration,
140(3), 513-522.
Vlasov, V. Z. & Leontev, U. N. (1966). Beams, Plates and Shells on Elastic Foundation. (Translated from Russian), Israel Program for Scientific Translation Jerusllem, Israel.
Wang, T. M. & Stephens, J. E. (1977). Natural frequencies of Timoshenko beams on Pasternak foundation. Journal of Sound and Vibration, 51(2), 149-155.
Xiang, Y., Wang, C. M. & Kitipornchai, S. (1994). Exact vibration solution for initially stressed Mindlin plates on Pasternak foundations. International Journal of Mech. Science, 36(4), 311- 316.
Biancolini,, M.E., Brutti, C., & Reccia, L. (2005). Approximate solution for free vibration of thin orthotropic rectangular plates. Journal of Sound and Vibration, 288, 321-344.
Bellman, R.K., Kashef, B.G. & Casti, J. (1972). Differential quadrature technique for the rapid solution of nonlinear partial differential equation. Journal of Computational Physics, 10, 40-52.
Chonan, S. (1980). Random vibration of initially stressed thick plate on an elastic foundation. Journal of Sound and Vibration, 71(1), 117-127.
Civalek, O. & Acar, M. H. (2007). Discrete singular convolution method for the analysis of Mindlin plates on elastic foundation. International Journal of Pressure Vessels and Piping, 84, 527-535.
Gupta, U.S. & Lal, R. (1978). Transverse vibrations of non-uniform rectangular plates on an elastic foundation. Journal of Sound and Vibration, 61, 127-133.
Gupta, U.S., Seema, S. & Singhal, P. (2012). Numerical simulation of vibrations of rectangular plates of variable thickness. International Journal of Engineering & Applied Sciences, 4(4), 26-40.
Gupta, U.S., Sharma, S. & Prag, S. (2014). Effect of two – parameter foundation on free transverse vibration of non-homogeneous orthotropic rectangular plate of linearly varying thickness. International Journal of Engineering & Applied Sciences, 6 (2), 32-51.
Hasheminejad, S. M., & Gheshlaghi, B. (2012). Three-dimensional elastodynamic solution for an arbitrary thick FGM rectangular plate resting on a two parameter viscoelastic foundation. Composite Structures, 94(9), 2746-2755.
Hetenyi, M. (1966). Beams and plates on elastic foundation and related problems. Applied Mechanics Reviews, 19, 95-102.
Kerr, AD. (1964). Elastic and viscoelastic foundation models. ASME Journal of Applied Mechanics, 31, 491-498.
Jain. R. K., Soni, S. R. (1973). Free vibration of rectangular plates of Parabolically varying thickness. Indian Journal of pure and Applied Mathematics, 4(3), 267-277.
Lal, R., Gupta, U.S. & Goel C. (2001). Chebyshev polynomials in the study of transverse vibrations of non- uniform rectangular orthotropic plates. The Shock and Vibration Digest, 33(2), 103-112.
Lal, R. & Dhanpati. (2007). Transverse vibration of non-homogeneous Orthotropic rectangular plates of variable thickness: A spline technique. Journal of Sound and Vibration, 306, 203-214.
Leissa, A.W. (1969). Vibration of plates. NASA SP-160, Government Printing Office, Washington
, DC.
Liew, K. M., Han, J.B., Xiao, Z. M. & Du, H. (1996). Differential quadrature method for Mindlin plates on Winkler foundation. International Journal of Mechanical Science, 38(4), 405-421.
Malekzadeh, P. & Karami, G. (2004). Vibration of non-uniform thick plates on elastic foundation by differential method. Engineering Structures, 26, 1473-1482.
Omurtag, M. H. & Kadioglu, F. (1998). Free vibration analysis of orthotropic plates resting on
Pasternak foundation by mixed finite element formulation. Computers and Structures, 67(4),
253-265.
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, 779-788.
Samaei, A. T., Aliha, M. R. M., & Mirsayar, M. M. (2015). Frequency analysis of a graphene sheet embedded in an elastic medium with consideration of small scale. Materials Physics and Mechanics, 22, 125-135.
Selvadurai, A. P. S. (1979). Elastic Analysis of Soil-Foundation Interaction. Elsevier, NY.
Sharma, S., Gupta, U.S. & Singhal, P. (2012). Vibration analysis of non-homogeneous orthotropic rectangular plates of variable thickness resting on Winkler foundation. Journal of Applied Science and Engineering, 15(3), 291-300.
Shen, H. S., Yang, J. & Zhang, L. (2001). Free and forced vibration of Reissner-Mindlin plates with free edges resting on elastic foundations. Journal of Sound and Vibration, 244 (2), 299-320.
Shu, C. (2000). Differential quadrature and its application in Engineering. Springer-Verlag, Great-
Briatain.
Sonzogni, S.R., Idelson, Laura, P. A. A. & Cortinez, V.H. (1990). Free vibration of rectangular plates of exponentially varying thickness and with a free edge. Journal of sound and vibration,
140(3), 513-522.
Vlasov, V. Z. & Leontev, U. N. (1966). Beams, Plates and Shells on Elastic Foundation. (Translated from Russian), Israel Program for Scientific Translation Jerusllem, Israel.
Wang, T. M. & Stephens, J. E. (1977). Natural frequencies of Timoshenko beams on Pasternak foundation. Journal of Sound and Vibration, 51(2), 149-155.
Xiang, Y., Wang, C. M. & Kitipornchai, S. (1994). Exact vibration solution for initially stressed Mindlin plates on Pasternak foundations. International Journal of Mech. Science, 36(4), 311- 316.