How to cite this paper
Khare, S & Mittal, N. (2015). Free vibration analysis of thin circular and annular plate with general boundary conditions.Engineering Solid Mechanics, 3(4), 245-252.
Refrences
Bashmal, S., Bhat, R., & Rakheja, S. (2009). In-plane free vibration of circular annular disks. Journal of Sound and Vibration, 322(1), 216-226.
Bashmal, S., Bhat, R., & Rakheja, S. (2010). Frequency equations for the in-plane vibration of circular annular disks. Advances in Acoustics and Vibration, 2010.
Bhardwaj, H., Vimal, J., & Sharma, A. (2015). Study of free vibration analysis of laminated composite plates with triangular cutouts. Engineering Solid Mechanics, 3(1), 43-50.
Chakraverty, S., & Petyt, M. (1999). Free vibration analysis of elliptic and circular plates having rectangular orthotropy. Structural Engineering and Mechanics, 7(1), 53-67.
Chakraverty, S., Bhat, R. B., & Stiharu, I. (2000). Vibration of annular elliptic orthotropic plates using two dimensional orthogonal polynomials. Applied Mechanics and Engineering, 5(4), 843-866.
Chakraverty, S., Bhat, R. B., & Stiharu, I. (2001). Free vibration of annular elliptic plates using boundary characteristic orthogonal polynomials as shape functions in the Rayleigh–Ritz method. Journal of sound and vibration, 241(3), 524-539.
Chen, D. Y., & Ren, B. S. (1998). Finite element analysis of the lateral vibration of thin annular and circular plates with variable thickness. Journal of vibration and acoustics, 120(3), 747-752.
Farag, N. H., & Pan, J. (2003). Modal characteristics of in-plane vibration of circular plates clamped at the outer edge. The Journal of the Acoustical Society of America, 113(4), 1935-1946.
Kim, C. S. (2003). Natural frequencies of orthotropic, elliptical and circular plates. Journal of sound and vibration, 259(3), 733-745.
Komur, M. A., Sen, F., Ata?, A., & Arslan, N. (2010). Buckling analysis of laminated composite plates with an elliptical/circular cutout using FEM. Advances in Engineering Software, 41(2), 161-164.
Hassani, A., Hojjati, M. H., & Fathi, A. R. (2010). In-plane free vibrations of annular elliptic and circular elastic plates of non-uniform thickness under classical boundary conditions. International Review of Mechanical Engineering, 4(1), 112-119.
Liang, B., Zhang, S. F., & Chen, D. Y. (2007). Natural frequencies of circular annular plates with variable thickness by a new method. International journal of pressure vessels and piping, 84(5), 293-297.
Nia, M., Torabi, K., & Heidari-Rarani, M. (2014). Free vibration analysis of a composite beam with single delamination-An improved free and constrained model. Engineering Solid Mechanics, 2(4), 313-320.
Reddy, J. N. (2004). Mechanics of laminated composite plates and shells: theory and analysis. CRC press.
Samaei, A. T., Aliha, M. R. M., & Mirsayar, M. M. (2015). Frequency analysis of graphene sheet embedded in an elastic medium with consideration of small scale. Materials Physics and Mechanics, 22, 125-135.
Torabi, K., Afshari, H., & Heidari-Rarani, M. (2013). Free vibration analysis of a non-uniform cantilever Timoshenko beam with multiple concentrated masses using DQEM. Engineering Solid Mechanics, 1(1), 9-20.
Vera, S. A., Sanchez, M. D., Laura, P. A. A., & Vega, D. A. (1998). Transverse vibrations of circular, annular plates with several combinations of boundary conditions. Journal of Sound and Vibration, 213(4), 757-762.
Vera, S. A., Laura, P. A. A., & Vega, D. A. (1999). Transverse vibrations of a free-free circular annular plate. Journal of Sound and Vibration, 224(2), 379-383.
Vimal, J., Srivastava, R., Bhatt, A., & Sharma, A. (2014). Free vibration analysis of moderately thick functionally graded skew plates. Engineering Solid Mechanics, 2(3), 229-238.
Wang, C. Y. (2003). Vibration of an annular membrane attached to a free, rigid core. Journal of sound and vibration, 260(4), 776-782.
Wang, C. Y., & Wang, C. M. (2005). Examination of the fundamental frequencies of annular plates with small core. Journal of sound and vibration, 280(3), 1116-1124.
Wu, T. Y., Wang, Y. Y., & Liu, G. R. (2002). Free vibration analysis of circular plates using generalized differential quadrature rule. Computer Methods in Applied Mechanics and Engineering, 191(46), 5365-5380.
Yuan, J., & Dickinson, S. M. (1996). On the vibration of annular, circular and sectorial plates with cut-outs or on partial supports. Computers & structures, 58(6), 1261-1264.
Yadav, D., Sharma, A., & Shivhare, V. (2015). Free vibration analysis of isotropic plate with stiffeners using finite element method. Engineering Solid Mechanics, 3(3), 167-176.
Zhou, Z. H., Wong, K. W., Xu, X. S., & Leung, A. Y. T. (2011). Natural vibration of circular and annular thin plates by Hamiltonian approach. Journal of Sound and Vibration, 330(5), 1005-1017.
Bashmal, S., Bhat, R., & Rakheja, S. (2010). Frequency equations for the in-plane vibration of circular annular disks. Advances in Acoustics and Vibration, 2010.
Bhardwaj, H., Vimal, J., & Sharma, A. (2015). Study of free vibration analysis of laminated composite plates with triangular cutouts. Engineering Solid Mechanics, 3(1), 43-50.
Chakraverty, S., & Petyt, M. (1999). Free vibration analysis of elliptic and circular plates having rectangular orthotropy. Structural Engineering and Mechanics, 7(1), 53-67.
Chakraverty, S., Bhat, R. B., & Stiharu, I. (2000). Vibration of annular elliptic orthotropic plates using two dimensional orthogonal polynomials. Applied Mechanics and Engineering, 5(4), 843-866.
Chakraverty, S., Bhat, R. B., & Stiharu, I. (2001). Free vibration of annular elliptic plates using boundary characteristic orthogonal polynomials as shape functions in the Rayleigh–Ritz method. Journal of sound and vibration, 241(3), 524-539.
Chen, D. Y., & Ren, B. S. (1998). Finite element analysis of the lateral vibration of thin annular and circular plates with variable thickness. Journal of vibration and acoustics, 120(3), 747-752.
Farag, N. H., & Pan, J. (2003). Modal characteristics of in-plane vibration of circular plates clamped at the outer edge. The Journal of the Acoustical Society of America, 113(4), 1935-1946.
Kim, C. S. (2003). Natural frequencies of orthotropic, elliptical and circular plates. Journal of sound and vibration, 259(3), 733-745.
Komur, M. A., Sen, F., Ata?, A., & Arslan, N. (2010). Buckling analysis of laminated composite plates with an elliptical/circular cutout using FEM. Advances in Engineering Software, 41(2), 161-164.
Hassani, A., Hojjati, M. H., & Fathi, A. R. (2010). In-plane free vibrations of annular elliptic and circular elastic plates of non-uniform thickness under classical boundary conditions. International Review of Mechanical Engineering, 4(1), 112-119.
Liang, B., Zhang, S. F., & Chen, D. Y. (2007). Natural frequencies of circular annular plates with variable thickness by a new method. International journal of pressure vessels and piping, 84(5), 293-297.
Nia, M., Torabi, K., & Heidari-Rarani, M. (2014). Free vibration analysis of a composite beam with single delamination-An improved free and constrained model. Engineering Solid Mechanics, 2(4), 313-320.
Reddy, J. N. (2004). Mechanics of laminated composite plates and shells: theory and analysis. CRC press.
Samaei, A. T., Aliha, M. R. M., & Mirsayar, M. M. (2015). Frequency analysis of graphene sheet embedded in an elastic medium with consideration of small scale. Materials Physics and Mechanics, 22, 125-135.
Torabi, K., Afshari, H., & Heidari-Rarani, M. (2013). Free vibration analysis of a non-uniform cantilever Timoshenko beam with multiple concentrated masses using DQEM. Engineering Solid Mechanics, 1(1), 9-20.
Vera, S. A., Sanchez, M. D., Laura, P. A. A., & Vega, D. A. (1998). Transverse vibrations of circular, annular plates with several combinations of boundary conditions. Journal of Sound and Vibration, 213(4), 757-762.
Vera, S. A., Laura, P. A. A., & Vega, D. A. (1999). Transverse vibrations of a free-free circular annular plate. Journal of Sound and Vibration, 224(2), 379-383.
Vimal, J., Srivastava, R., Bhatt, A., & Sharma, A. (2014). Free vibration analysis of moderately thick functionally graded skew plates. Engineering Solid Mechanics, 2(3), 229-238.
Wang, C. Y. (2003). Vibration of an annular membrane attached to a free, rigid core. Journal of sound and vibration, 260(4), 776-782.
Wang, C. Y., & Wang, C. M. (2005). Examination of the fundamental frequencies of annular plates with small core. Journal of sound and vibration, 280(3), 1116-1124.
Wu, T. Y., Wang, Y. Y., & Liu, G. R. (2002). Free vibration analysis of circular plates using generalized differential quadrature rule. Computer Methods in Applied Mechanics and Engineering, 191(46), 5365-5380.
Yuan, J., & Dickinson, S. M. (1996). On the vibration of annular, circular and sectorial plates with cut-outs or on partial supports. Computers & structures, 58(6), 1261-1264.
Yadav, D., Sharma, A., & Shivhare, V. (2015). Free vibration analysis of isotropic plate with stiffeners using finite element method. Engineering Solid Mechanics, 3(3), 167-176.
Zhou, Z. H., Wong, K. W., Xu, X. S., & Leung, A. Y. T. (2011). Natural vibration of circular and annular thin plates by Hamiltonian approach. Journal of Sound and Vibration, 330(5), 1005-1017.