Effect of Thermal Gradient on Vibration of Non-Homogeneous Square Plate with Exponentially Varying Thickness
Subject Areas : EngineeringA Khanna 1 , R Deep 2 , D Kumar 3
1 - Department of Mathematics, DAV College Sadhaura, Yamuna Nagar, Haryana
2 - Department of Mathematics, Maharishi Markandeshwar University- Mullana
3 - Department of Mathematics, Maharishi Markandeshwar University- Mullana
Keywords:
Abstract :
[1] Gupta A.K., Khanna A.., 2007, Vibration of visco-elastic rectangular plate with linearly thickness variations in both directions, Journal of Sound and Vibration 301 (3-5): 450-457.
[2] Gupta A.K., Singhal P., 2010, Thermal effect on free vibration of non-homogeneous orthotropic visco–elastic rectangular plate of parabolically varying thickness, Applied Mathematics 1 (6): 456-463.
[3] Khanna A., Sharma A.K., 2012, Mechanical vibration of visco-elastic plate with thickness variation, International Journal of Applied Mechanical Research 1 (2): 150-158.
[4] Khanna A., Bhatia M., 2011, Study of free vibrations of visco- elastic square plate of variable thickness with thermal effect, Innovative System Design and Engineering 2 (4): 85-90.
[5] Leissa A.W., 1969, Vibration of Plates, NASA, SP-160.
[6] Huang C.S., Leissa A.W., 2009, Vibration analysis of rectangular plates with side cracks via the Ritz method, Journal of Sound and Vibration 323 (3-5): 974-988.
[7] Singh B., Saxena V., 1996, Transverse vibration of rectangular plate with bi- directional thickness variation, Journal of Sound and Vibration 198(1): 51-65.
[8] Fauconneau G., Marangoni R.D., 1970, Effect of a thermal gradient on the natural frequencies of a rectangular plate, International Journal of Mechanical Sciences 12(2): 113-122.
[9] Wu L.H., Lu Y., 2011, Free vibration analysis of rectangular plates with internal columns and uniform elastic edge supports by pb-2 Ritz method, International Journal of Mechanical Sciences 53(7): 494-504.
[10] Lee H.P., Lim S.P., Chow T., 1987, Free vibration of composite rectangular plates with rectangular cutouts, Composite Structures 8 (1): 63-81.
[11] Kuttler J.R., Sigillit V.G., 1983, Vibrational frequencies of clamped plates of variable thickness, Journal of Sound and Vibration 86(2): 181-189.
[12] Daleh M., Keer A.D., 1996, Natural vibration analysis of clamped rectangular orthotropic plate, Journal of Sound and Vibration 189(3):399-406.
[13] 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.
[14] Lal Roshan., 2003, Transverse vibrations of orthotropic non-uniform rectangular plates with continuously varying density, Indian Journal of Pure and Applied Mathematics 34(4): 587-606.
[15] Malhotra S.K., Ganesan N., Veluswami M.A., 1988, Vibrations of orthotropic square plates having variable thickness (linear variation), Composites 19(6): 467-72.
[16] Alijani F., Amabili M., 2013, Theory and experiments for nonlinear vibrations of imperfect rectangular plates with free edges, Journal of Sound and Vibration 332(14): 3564-588.
[17] Johri T., Johri I., 2011, Study of exponential thermal effect on vibration of non-homogeneous orthotropic rectangular plate having bi- directional linear variation in thickness, Proceeding of the World Congress on Engineering, London .
[18] Sakata T., Hosokawa K., 1988, Vibrations of clamped orthotropic rectangular plates with C-C-C-C boundary conditions, Journal of Sound and Vibration 125(3): 429-39.
[19] Quintana M. V., Nallim L.G., 2013, A general Ritz formulation for the free vibration analysis of thick trapezoidal and triangular laminated plates resting on elastic supports, International Journal of Mechanical Sciences 69 (2013) :1-9.
[20] Sakiyama, T ., Huang M., 1998, Free vibration analysis of rectangular plates with variable thickness, Journal of Sound and Vibration 216(3): 379-397.
[21] Xing Y.F., Liu B., 2009, New exact solutions for free vibrations of thin orthotropic rectangular plates, Composite Structures 89(4): 567-574.