Free Vibration and Buckling of Rectangular Plates under Nonuniform In-Plane Edge Shear Loads
A method for determining the stress distribution of a rectangular plate subjected to two pairs of arbitrarily distributed in-plane edge shear loads is proposed, and the free vibration and buckling of such a rectangular plate are investigated in this work. The method utilizes two stress functions to synthesize the stress-resultant field of the plate with each of the stress functions satisfying the biharmonic compatibility equation. The sum of stress-resultant fields due to these two stress functions satisfies the boundary conditions at the edges of the plate, from which these two stress functions are determined. Then, the free vibration and buckling of the rectangular plate are investigated by the Galerkin method. Numerical results obtained by this work are compared with those appeared in the literature, and good agreements are observed.
[1] A. W. Leissa, Vibration of Plates, NASA SP-160, 1969.
[2] N. Tahan, M. N. Pavlovic, and M. D. Kotsovos, “Single Fourier series solutions for rectangular plates under in-plane forces, with particular reference to the basic problem of collinear compression. Part 1: Closed-form solution and convergence study,” Thin-Walled Structures, vol. 15, pp. 291-303, 1993.
[3] N. Tahan, M. N. Pavlovic, and M. D. Kotsovos, “Single Fourier series solutions for rectangular plates under in-plane forces, with particular reference to the basic problem of collinear compression. Part 1: Stress distribution,” Thin-Walled Structures, vol. 17, pp. 1-26, 1993.
[4] J. H. Kang, and A.W. Leissa, “Exact solutions for the buckling of rectangular plates having linearly varying in-plane loading on two opposite simply supported edges,” International Journal of Solids and Structures, vol. 42, pp. 4220-4238, 2005.
[5] O. Civalek, A. Korkmaz, and C. Demir, “Discrete singular convolution approach for buckling analysis of rectangular Kirchhoff plates subjected to compressive loads on two-opposite edges,” Advances in Engineering Software, vol. 41, pp. 557-560, 2010.
[6] A.V. Lopatin, and E. V. Morozov, “Buckling of the SSCF rectangular orthotropic plate subjected to linearly varying in-plane loading,” Composite Structures, vol. 93, pp. 1900-1909, 2011.
[7] X. Wang, L. Gan, and Y. Zhang, “Differential quadrature analysis of the buckling of thin rectangular plates with cosine-distributed compressive loads on two opposite sides,” Advances in Engineering Software, vol. 39, pp. 497-504, 2008.
[8] P. Jana, and K. Bhaskar, “Stability analysis of simply-supported rectangular plates under non-uniform uniaxial compression using rigorous and approximate plane stress solutions,” Thin-Walled Structures, vol. 44, pp. 507-516, 2006.
[9] S. K. Panda, and L. S. Ramachandra, “Buckling of rectangular plates with various boundary conditions loaded by non-uniform in-plane loads,” International Journal of Mechanical Sciences, vol. 52, pp. 819-828, 2010.
[10] Y. Tang, and X. Wang, “Buckling of symmetrically laminated rectangular plates under parabolic edge compressions,” International Journal of Mechanical Sciences, vol. 53, pp. 91-97, 2011.
[11] Y. G. Liu, and M. N. Pavlovic, “A generalized analytical approach to the buckling of simply-supported rectangular plates under arbitrary loads,” Engineering Structures, vol. 30, pp. 1346-1359, 2008.
[12] G. Ikhenazen, M. Saidani, and A. Chelghoum, “Finite element analysis of linear plates buckling under in-plane patch loading,” Journal of Constructional Steel Research, vol. 66, pp. 11112-1117, 2010.
[13] X. Wang, L. Gan and Y. Wang, “A differential quadrature analysis of vibration and buckling of an SS-C-SS-C rectangular plate loaded by linearly varying in-plane stresses,” Journal of Sound and Vibration, vol. 298, pp. 420-431, 2006.
[14] A. K. L. Srivastava, P. K. Datta, and A. H. Sheikh, “Buckling and vibration of stiffened plates subjected to partial edge loading,” International Journal of Mechanical Sciences, vol. 45, pp. 73-93, 2003.
[15] S. M. Dickinson, “Lateral vibrations of rectangular plates subjected to in-plane forces,” Journal of Sound and Vibration, vol. 16, pp. 465-472, 1971.
[16] J. P. Singh, and S. S. Dey, “Transverse vibration of rectangular plates subjected to in-plane forces by a difference based variational approach,” International Journal of Mechanical Sciences, vol. 32, pp. 591-599, 1990.
[17] M. Azhari, S. Hoshdar, and M. A. Bradford, “On the use of bubble functions in the local buckling analysis of plate structures by the spline finite strip method,” International Journal for Numerical Methods in Engineering, vol. 48, pp. 583-593, 2000.
[18] K. M .Liew, J. Wang, T. Y. Ng, and M. J. Tan, “Free vibration and buckling analyses of shear-deformable plates based on FSDT meshfree method,” Journal of Sound and Vibration, vol. 276, pp. 997-1017, 2004.
[19] T. Q. Bui, M. N. Nguyen, and C. Zhang, “Buckling analysis of Reissner-Mindlin plates subjected to in-plane edge loads using a shear-locking-free and meshfree method,” Engineering Analysis with Boundary Elements, vol. 35, pp. 1038-1053, 2011.
[1] A. W. Leissa, Vibration of Plates, NASA SP-160, 1969.
[2] N. Tahan, M. N. Pavlovic, and M. D. Kotsovos, “Single Fourier series solutions for rectangular plates under in-plane forces, with particular reference to the basic problem of collinear compression. Part 1: Closed-form solution and convergence study,” Thin-Walled Structures, vol. 15, pp. 291-303, 1993.
[3] N. Tahan, M. N. Pavlovic, and M. D. Kotsovos, “Single Fourier series solutions for rectangular plates under in-plane forces, with particular reference to the basic problem of collinear compression. Part 1: Stress distribution,” Thin-Walled Structures, vol. 17, pp. 1-26, 1993.
[4] J. H. Kang, and A.W. Leissa, “Exact solutions for the buckling of rectangular plates having linearly varying in-plane loading on two opposite simply supported edges,” International Journal of Solids and Structures, vol. 42, pp. 4220-4238, 2005.
[5] O. Civalek, A. Korkmaz, and C. Demir, “Discrete singular convolution approach for buckling analysis of rectangular Kirchhoff plates subjected to compressive loads on two-opposite edges,” Advances in Engineering Software, vol. 41, pp. 557-560, 2010.
[6] A.V. Lopatin, and E. V. Morozov, “Buckling of the SSCF rectangular orthotropic plate subjected to linearly varying in-plane loading,” Composite Structures, vol. 93, pp. 1900-1909, 2011.
[7] X. Wang, L. Gan, and Y. Zhang, “Differential quadrature analysis of the buckling of thin rectangular plates with cosine-distributed compressive loads on two opposite sides,” Advances in Engineering Software, vol. 39, pp. 497-504, 2008.
[8] P. Jana, and K. Bhaskar, “Stability analysis of simply-supported rectangular plates under non-uniform uniaxial compression using rigorous and approximate plane stress solutions,” Thin-Walled Structures, vol. 44, pp. 507-516, 2006.
[9] S. K. Panda, and L. S. Ramachandra, “Buckling of rectangular plates with various boundary conditions loaded by non-uniform in-plane loads,” International Journal of Mechanical Sciences, vol. 52, pp. 819-828, 2010.
[10] Y. Tang, and X. Wang, “Buckling of symmetrically laminated rectangular plates under parabolic edge compressions,” International Journal of Mechanical Sciences, vol. 53, pp. 91-97, 2011.
[11] Y. G. Liu, and M. N. Pavlovic, “A generalized analytical approach to the buckling of simply-supported rectangular plates under arbitrary loads,” Engineering Structures, vol. 30, pp. 1346-1359, 2008.
[12] G. Ikhenazen, M. Saidani, and A. Chelghoum, “Finite element analysis of linear plates buckling under in-plane patch loading,” Journal of Constructional Steel Research, vol. 66, pp. 11112-1117, 2010.
[13] X. Wang, L. Gan and Y. Wang, “A differential quadrature analysis of vibration and buckling of an SS-C-SS-C rectangular plate loaded by linearly varying in-plane stresses,” Journal of Sound and Vibration, vol. 298, pp. 420-431, 2006.
[14] A. K. L. Srivastava, P. K. Datta, and A. H. Sheikh, “Buckling and vibration of stiffened plates subjected to partial edge loading,” International Journal of Mechanical Sciences, vol. 45, pp. 73-93, 2003.
[15] S. M. Dickinson, “Lateral vibrations of rectangular plates subjected to in-plane forces,” Journal of Sound and Vibration, vol. 16, pp. 465-472, 1971.
[16] J. P. Singh, and S. S. Dey, “Transverse vibration of rectangular plates subjected to in-plane forces by a difference based variational approach,” International Journal of Mechanical Sciences, vol. 32, pp. 591-599, 1990.
[17] M. Azhari, S. Hoshdar, and M. A. Bradford, “On the use of bubble functions in the local buckling analysis of plate structures by the spline finite strip method,” International Journal for Numerical Methods in Engineering, vol. 48, pp. 583-593, 2000.
[18] K. M .Liew, J. Wang, T. Y. Ng, and M. J. Tan, “Free vibration and buckling analyses of shear-deformable plates based on FSDT meshfree method,” Journal of Sound and Vibration, vol. 276, pp. 997-1017, 2004.
[19] T. Q. Bui, M. N. Nguyen, and C. Zhang, “Buckling analysis of Reissner-Mindlin plates subjected to in-plane edge loads using a shear-locking-free and meshfree method,” Engineering Analysis with Boundary Elements, vol. 35, pp. 1038-1053, 2011.
@article{"International Journal of Mechanical, Industrial and Aerospace Sciences:79003", author = "T. H. Young and Y. J. Tsai", title = "Free Vibration and Buckling of Rectangular Plates under Nonuniform In-Plane Edge Shear Loads", abstract = "A method for determining the stress distribution of a rectangular plate subjected to two pairs of arbitrarily distributed in-plane edge shear loads is proposed, and the free vibration and buckling of such a rectangular plate are investigated in this work. The method utilizes two stress functions to synthesize the stress-resultant field of the plate with each of the stress functions satisfying the biharmonic compatibility equation. The sum of stress-resultant fields due to these two stress functions satisfies the boundary conditions at the edges of the plate, from which these two stress functions are determined. Then, the free vibration and buckling of the rectangular plate are investigated by the Galerkin method. Numerical results obtained by this work are compared with those appeared in the literature, and good agreements are observed.
", keywords = "Stress analysis, free vibration, plate buckling, nonuniform in-plane edge shear.", volume = "13", number = "7", pages = "506-13", }
