How to cite this paper
Torabi, K & Afshari, H. (2017). Vibration analysis of a cantilevered trapezoidal moderately thick plate with variable thickness.Engineering Solid Mechanics, 5(1), 71-92.
Refrences
Bert, C. W., & Malik, M. (1996a). The differential quadrature method for irregular domains and application to plate vibration. International Journal of Mechanical Sciences, 38(6), 589-606.
Bert, C. W., & Malik, M. (1996b). Differential quadrature method in computational mechanics: a review. Applied Mechanics Reviews, 49(1), 1-28.
Chen, S. S., Xu, C. J., Tong, G. S., & Wei, X. (2015). Free vibration of moderately thick functionally graded plates by a meshless local natural neighbor interpolation method. Engineering Analysis with Boundary Elements, 61, 114–126.
Chopra, I., & Durvasula, S. (1971). Vibration of simply supported trapezoidal plates. I. symmetric trapezoids. Journal of Sound and Vibration, 19, 379-392.
Chopra, I., & Durvasula, S. (1972). Vibration of simply supported trapezoidal plates. II. un-symmetric trapezoids. Journal of Sound and Vibration, 20, 125-134.
Dehghany, M., & Farajpour, A. (2014). Free vibration of simply supported rectangular plates on Pasternak foundation: An exact and three-dimensional solution. Engineering Solid Mechanics, 2(1), 29-42.
Dehghan, M., Nejad, M., & Moosaie, A. (2016). An effective combination of finite element and differential quadrature method for analyzing of plates partially resting on elastic foundation. Engineering Solid Mechanics, 4(4), 201-218.
Eftekhari, S. A., & Jafari, A. A. (2013). Modified mixed Ritz-DQ formulation for free vibration of thick rectangular and skew plates with general boundary conditions. Applied Mathematical Modelling, 37(12), 7398-7426.
Huang, C. S., Leissa, A. W., & Chang, M. J. (2005). Vibrations of skewed cantilevered triangular, trapezoidal and parallelogram Mindlin plates with considering corner stress singularities. International Journal for Numerical Methods in Engineering, 62(13), 1789-1806.
Gupta, U., Sharma, S., & Singhal, P. (2016). DQM modeling of rectangular plate resting on two parameter foundation. Engineering Solid Mechanics, 4(1), 33-44.
Kaneko, T. (1975). On Timoshenko's correction for shear in vibrating beams.Journal of Physics D: Applied Physics, 8(16), 1927.
Liew, K. M., Xiang, Y., Kitipornchai, S., & Wang, C. M. (1998). Vibration of Mindlin plates: programming the p-version Ritz method. Elsevier.
Maruyama, K., Ichinomiya, O., & Narita, Y. (1983). Experimental study of the free vibration of clamped trapezoidal plates. Journal of Sound and Vibration, 88(4), 523-534.
Mindlin, R. D. (1951). Influence of rotary inertia and shear on flexural motions of isotropic elastic plates. Journal of Applied Mechanics-T ASME, 18, 31–38.
Naghsh, A., & Azhari, M. (2015). Non-linear free vibration analysis of points supported laminated composite skew plate. International Journal of Non-linear Mechanics, 76, 64-76.
Orris, R. M., & Petyt, M. (1973). A finite element study of the vibration of trapezoidal plates. Journal of Sound and Vibration, 27, 325-344.
Petrolito, J. (2014). Vibration and stability analysis of thick orthotropic plates using hybrid-Trefftz elements. Applied Mathematical Modelling, 38(24), 5858-5869.
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.
Shu, C., Wu, W. X., Ding, H., & Wang, C. M. (2007). Free vibration analysis of plates using least-square-based finite difference method. Computer Methods in Applied Mechanics and Engineering, 196(7), 1330-1343.
Shufrin, I., Rabinovitch, O., & Eisenberger, M. (2010). A semi-analytical approach for the geometrically nonlinear analysis of trapezoidal plates. International Journal of Mechanical Sciences, 52(12), 1588-1596.
Srinivasan, R.S., & Babu, B.J.C. (1983). Free vibration of cantilever quadrilal plates. Journal of the Acoustical Society of America, 73, 851-855.
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.
Torabi, K. & Afshari, H. (2016). Generalized differential quadrature method for vibration analysis of cantilever trapezoidal FG thick plate. Journal of Solid Mechanics, 8(1), 184-203.
Wang, X., Wang, Y., & Yuan, Z. (2013). Accurate vibration analysis of skew plates by the new version of the differential quadrature method. Applied Mathematical Modelling, 38(3), 926-937.
Xia, P., Long, S. Y., Cui, H. X., & Li, G. Y. (2009). The static and free vibration analysis of a nonhomogeneous moderately thick plate using the meshless local radial point interpolation method. Engineering Analysis with Boundary Elements, 33(6), 770-777.
Zamani, M., Fallah, A., & Aghdam, M. M. (2012). Free vibration analysis of moderately thick trapezoidal symmetrically laminated plates with various combinations of boundary conditions. European Journal of Mechanics-A/Solid, 36, 204–212.
Zhao, X., Lee, Y. Y., & Liew, K. M. (2009). Free vibration analysis of functionally graded plates using the element-free kp-Ritz method. Journal of sound and Vibration, 319(3), 918-939.
Zhou, L., & Zheng, W. X. (2008). Vibration of skew plates by the MLS-Ritz method. International Journal of Mechanical Sciences, 50(7), 1133-1141.
Bert, C. W., & Malik, M. (1996b). Differential quadrature method in computational mechanics: a review. Applied Mechanics Reviews, 49(1), 1-28.
Chen, S. S., Xu, C. J., Tong, G. S., & Wei, X. (2015). Free vibration of moderately thick functionally graded plates by a meshless local natural neighbor interpolation method. Engineering Analysis with Boundary Elements, 61, 114–126.
Chopra, I., & Durvasula, S. (1971). Vibration of simply supported trapezoidal plates. I. symmetric trapezoids. Journal of Sound and Vibration, 19, 379-392.
Chopra, I., & Durvasula, S. (1972). Vibration of simply supported trapezoidal plates. II. un-symmetric trapezoids. Journal of Sound and Vibration, 20, 125-134.
Dehghany, M., & Farajpour, A. (2014). Free vibration of simply supported rectangular plates on Pasternak foundation: An exact and three-dimensional solution. Engineering Solid Mechanics, 2(1), 29-42.
Dehghan, M., Nejad, M., & Moosaie, A. (2016). An effective combination of finite element and differential quadrature method for analyzing of plates partially resting on elastic foundation. Engineering Solid Mechanics, 4(4), 201-218.
Eftekhari, S. A., & Jafari, A. A. (2013). Modified mixed Ritz-DQ formulation for free vibration of thick rectangular and skew plates with general boundary conditions. Applied Mathematical Modelling, 37(12), 7398-7426.
Huang, C. S., Leissa, A. W., & Chang, M. J. (2005). Vibrations of skewed cantilevered triangular, trapezoidal and parallelogram Mindlin plates with considering corner stress singularities. International Journal for Numerical Methods in Engineering, 62(13), 1789-1806.
Gupta, U., Sharma, S., & Singhal, P. (2016). DQM modeling of rectangular plate resting on two parameter foundation. Engineering Solid Mechanics, 4(1), 33-44.
Kaneko, T. (1975). On Timoshenko's correction for shear in vibrating beams.Journal of Physics D: Applied Physics, 8(16), 1927.
Liew, K. M., Xiang, Y., Kitipornchai, S., & Wang, C. M. (1998). Vibration of Mindlin plates: programming the p-version Ritz method. Elsevier.
Maruyama, K., Ichinomiya, O., & Narita, Y. (1983). Experimental study of the free vibration of clamped trapezoidal plates. Journal of Sound and Vibration, 88(4), 523-534.
Mindlin, R. D. (1951). Influence of rotary inertia and shear on flexural motions of isotropic elastic plates. Journal of Applied Mechanics-T ASME, 18, 31–38.
Naghsh, A., & Azhari, M. (2015). Non-linear free vibration analysis of points supported laminated composite skew plate. International Journal of Non-linear Mechanics, 76, 64-76.
Orris, R. M., & Petyt, M. (1973). A finite element study of the vibration of trapezoidal plates. Journal of Sound and Vibration, 27, 325-344.
Petrolito, J. (2014). Vibration and stability analysis of thick orthotropic plates using hybrid-Trefftz elements. Applied Mathematical Modelling, 38(24), 5858-5869.
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.
Shu, C., Wu, W. X., Ding, H., & Wang, C. M. (2007). Free vibration analysis of plates using least-square-based finite difference method. Computer Methods in Applied Mechanics and Engineering, 196(7), 1330-1343.
Shufrin, I., Rabinovitch, O., & Eisenberger, M. (2010). A semi-analytical approach for the geometrically nonlinear analysis of trapezoidal plates. International Journal of Mechanical Sciences, 52(12), 1588-1596.
Srinivasan, R.S., & Babu, B.J.C. (1983). Free vibration of cantilever quadrilal plates. Journal of the Acoustical Society of America, 73, 851-855.
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.
Torabi, K. & Afshari, H. (2016). Generalized differential quadrature method for vibration analysis of cantilever trapezoidal FG thick plate. Journal of Solid Mechanics, 8(1), 184-203.
Wang, X., Wang, Y., & Yuan, Z. (2013). Accurate vibration analysis of skew plates by the new version of the differential quadrature method. Applied Mathematical Modelling, 38(3), 926-937.
Xia, P., Long, S. Y., Cui, H. X., & Li, G. Y. (2009). The static and free vibration analysis of a nonhomogeneous moderately thick plate using the meshless local radial point interpolation method. Engineering Analysis with Boundary Elements, 33(6), 770-777.
Zamani, M., Fallah, A., & Aghdam, M. M. (2012). Free vibration analysis of moderately thick trapezoidal symmetrically laminated plates with various combinations of boundary conditions. European Journal of Mechanics-A/Solid, 36, 204–212.
Zhao, X., Lee, Y. Y., & Liew, K. M. (2009). Free vibration analysis of functionally graded plates using the element-free kp-Ritz method. Journal of sound and Vibration, 319(3), 918-939.
Zhou, L., & Zheng, W. X. (2008). Vibration of skew plates by the MLS-Ritz method. International Journal of Mechanical Sciences, 50(7), 1133-1141.