Free Vibration of Thick Isotropic Plates Using Trigonometric Shear Deformation Theory
Subject Areas : Engineering
1 - Department of Applied Mechanics, Government Engineering College, Aurangabad-431005 (Maharashtra State)
2 - Department of Applied Mechanics, Government Engineering College, Aurangabad-431005 (Maharashtra State)
Keywords:
Abstract :
[1] Kirchhoff G.R., 1850, Uber das gleichgewicht und die bewegung einer elastischen scheibe, Journal of Reine Angew. Math.(Crelle) 40: 51-88.
[2] Kirchhoff G.R., 1850, Uber die schwingungen einer kriesformigen elastischen scheibe, Poggendorffs Annalen 81: 258-264.
[3] Reissner E., 1944, On the theory of bending of elastic plates, Journal of Mathematics and Physics 23: 184-191.
[4] Reissner E., 1945, The effect of transverse shear deformation on the bending of elastic plates, ASME Journal of Applied Mechanics 12: 69-77.
[5] Mindlin R.D., 1951, Influence of rotatory inertia and shear on flexural motions of isotropic, elastic plates, ASME Journal of Applied Mechanics 18: 31-38.
[6] Wang C.M., Lim G.T., Reddy J.N., Lee K.H., 2001, Relationships between bending solutions of Reissner and Mindlin plate theories, Engineering Structures 23 (7): 838-849.
[7] Librescu L., 1975, Elastostatic and Kinetics of Anisotropic and Heterogeneous Shell-Type Structures, Nooedhoff International, Leyden, The Netherlands.
[8] Donnell L.H., 1976, Beams, Plates and Shells, McGraw-Hill, New York.
[9] Lo K.H., Christensen R.M., Wu E.M., 1977, A high-order theory of plate deformation, Part-1: Homogeneous plates, ASME Journal of Applied Mechanics 44: 663-668.
[10] Lo K.H., Christensen R.M., Wu E.M., 1977, A high-order theory of plate deformation, Part-2: Laminated plates, ASME Journal of Applied Mechanics 44: 669-676.
[11] Levinson M., 1980, An accurate, simple theory of the statics and dynamics of elastic plates, Mechanics Research Communications 7: 343-350.
[12] Murty A.V.K., Vellaichamy S., 1988, Higher-order theory of homogeneous plate flexure, AIAA Journal 26: 719-725.
[13] Reddy J.N., 1984, A refined nonlinear theory of plates with transverse shear deformation, International Journal of Solids and Structures 20(9/10): 881-896.
[14] Reddy J.N., 1984, A simple higher order theory for laminated composite plates, ASME Journal of Applied Mechanics 51: 745-752.
[15] Reddy J.N., Phan N.D., 1985, Stability and vibration of isotropic, orthotropic and laminated plates according to higher order deformation theory, Journal of Sound and Vibration 98: 157-170.
[16] Srinivas S., Rao A.K., Joga Rao C.V., 1969, Flexure of simply supported thick homogenous and laminated rectangular plates, ZAMM: Zeitschrift fur Angewandte Mathematic und Mchanik 49(8): 449-458.
[17] Srinivas S., Joga Rao C.V., Rao A. K., 1970, An exact analysis for vibration of simply supported homogeneous and laminated thick rectangular plates, Journal of sound and vibration 12(2): 187-199.
[18] Noor A.K., Burton W.S., 1989, Assessment of shear deformation theories for multilayered composite plates, Applied Mechanics Reviews 42: 1-13.
[19] Reddy J.N., 1989, On the generalization of displacement-based laminate theories, Applied Mechanics Reviews 42:S213-S222.
[20] Reddy J.N., Robbins D.H.Jr., 1994, Theories and computational models for composite laminates, Applied Mechanics Reviews 47: 147-169.
[21] Liu D., Li X., 1996, An overall view of laminate theories based on displacement hypothesis, Journal of Composite Materials 30:1539-561.
[22] Liew K.M., Xiang Y., Kitipornchai S., 1995, Research on thick plate vibration, Journal of Sound and Vibration 180:163-176.
[23] Ghugal Y.M., Shimpi R.P., 2002, A review of refined shear deformation theories for isotropic and anisotropic laminated plates, Journal of Reinforced Plastics and Composites 21: 775-813.
[24] Kreja I., 2011, A literature review on computational models for laminated composite and sandwich panels, Central European Journal of Engineering 1(1): 59-80.
[25] Levy M., 1877, Memoire sur la theorie des plaques elastique planes, Journal des Mathematiques Pures et Appliquees 30: 219-306.
[26] Stein M., Jegly D.C., 1987, Effect of transverse shearing on cylindrical bending, vibration and buckling of laminated plates, AIAA Journal 25: 123-129.
[27] Shimpi R.P., Arya H., Naik N.K., 2003, A higher order displacement model for the plate analysis, Journal of Reinforced Plastics and Composites 22: 1667-1688.
[28] Shimpi R.P., Patel H.G., 2006, Free vibration of plate using two variable refined plate theory, Journal of Sound and Vibration 296:979-999.
[29] Ghugal Y.M., Pawar M.D., 2011, Buckling and vibration of plates by hyperbolic shear deformation theory, Journal of Aerospace Engineering and Technology 1(1):1-12.
[30] Ghugal Y.M., Pawar M.D., 2011, Flexural analysis of thick plates by hyperbolic shear deformation theory, Journal of Experimental and Applied Mechanics 2(1):1-21.
[31] Ghugal Y.M., Sayyad A.S., 2010, Free vibration of thick orthotropic plates using trigonometric shear deformation theory, Latin American Journal of Solids and Structures 8: 229-243.
[32] Ghugal Y.M., Sayyad A.S., 2010, A flexure of thick isotropic plate using trigonometric shear deformation theory, Journal of Solid Mechanics 2(1): 79-90.
[33] Ghugal Y.M., Kulkarni S.K., 2011, Thermal stress analysis of cross-ply laminated plates using refined shear deformation theory,Journal of Experimental and Applied Mechanics: An International Journal 2(1): 47-66.
[34] Timoshenko S.P., Goodier J.N., 1970, Theory of Elasticity, Third edition, McGraw Hill, New York.
[35] Manjunatha B.S., Kant T., 1993, Different numerical techniques for the estimation of multiaxial stresses in symmetric/unsymmetric composite and sandwich beams with refined theories, Journal of Reinforced Plastics and Composites 12: 2-37.
[36] Vinayak R.U., Prathap G., Naganarayana B.P., 1996, Beam elements based on a higher order theory — I: Formulation and analysis of performance, Computers and Structures 58: 775-789.
[37] Lamb Horace, 1917, On waves in an elastic plate, Proceedings of Royal Society London, Series A 93: 114-128.
