Generalized Differential Quadrature Method for Vibration Analysis of Cantilever Trapezoidal FG Thick Plate

Subject Areas : Engineering

K Torabi ¹ , H Afshari ²

1 - Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan, Kashan, Iran
2 - Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan, Kashan, Iran

Received: 2016-01-09 Accepted : 2016-03-05 Published : 2016-03-30

Keywords:

References:

[1] Chopra I., Durvasula S., 1971, Vibration of simply supported trapezoidal plates I. symmetric trapezoids, Journal of Sound and Vibration 19: 379-392.
[2] Chopra I., Durvasula S., 1972, Vibration of simply supported trapezoidal plates II. un-symmetric trapezoids, Journal of Sound and Vibration 20: 125-134.
[3] Orris R.M., Petyt M., 1973, A finite element study of the vibration of trapezoidal plates, Journal of Sound and Vibration 27: 325-344.
[4] Srinivasan R.S., Babu B.J.C., 1983, Free vibration of cantilever quadrilal plates, Journal of the Acoustical Society of America 73: 851-855.
[5] Maruyama K., Ichinomiya O., Narita Y., 1983, Experimental study of the free vibration of clamped trapezoidal plates, Journal of Sound and Vibration 88: 523-534.
[6] Bert C.W., Malik M., 1996, Differential quadrature method for irregular domains and application to plate vibration, International Journal of Mechanical Sciences 38: 589-606.
[7] Xing Y., Liu B., 2009, High-accuracy differential quadrature finite element method and its application to free vibrations of thin plate with curvilinear domain, International Journal for Numerical Methods in Engineering 80: 1718-1742.
[8] 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: 1588-1596.
[9] Zhou L., Zheng W.X., 2008, Vibration of skew plates by the MLS-Ritz method, International Journal of Mechanical Sciences 50: 1133-1141.
[10] 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/Solids 36: 204-212.
[11] Hosseini-Hashemi Sh., Fadaee M., Atashipour S.R., 2011, A new exact analytical approach for free vibration of Reissner–Mindlin functionally graded rectangular plates, International Journal of Mechanical Sciences 53: 11-22.
[12] Shaban M., Alipour M.M., 2011, Semi-analytical solution for free vibration of thick functionally graded plates rested on elastic foundation with elastically restrained edge, Acta Mechanica Solida Sinica 24: 340-354.
[13] Hasani Baferani A., Saidi A.R., Ehteshami H., 2011, Accurate solution for free vibration analysis of functionally graded thick rectangular plates resting on elastic foundation, Composite Structure 93: 1842-1853.
[14] Zhu P., Liew K.M., 2011, Free vibration analysis of moderately thick functionally graded plates by local Kriging meshless method, Composite Structure 93: 2925-2944.
[15] Hosseini-Hashemi Sh., Salehipour H., Atashipour S.R, Sburlati R., 2013, On the exact in-plane and out-of-plane free vibration analysis of thick functionally graded rectangular plates: Explicit 3-D elasticity solutions, Composites Part B 46: 108-115.
[16] Jin G., Su Z., Shi Sh., Ye T., Gao S., 2014, Three-dimensional exact solution for the free vibration of arbitrarily thick functionally graded rectangular plates with general boundary conditions, Composite Structure 108: 565-577.
[17] 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: 770-777.
[18] Huang M., Ma X.O., Sakiyama T., Matuda M., Morita C., 2005, Free vibration analysis of plates using least-square-based on finite difference method, Journal of Sound and Vibration 288: 931-955.
[19] Nguyen-Xuan H., Liu G.R., Thai-Hoang C., 2010, An edge-based smoothed finite element method (ES-FEM) with stabilized discrete shear gap technique for analysis of Reissner-Minslin, Computer Methods in Applied Mechanics and Engineering 199: 471-489.
[20] Leung A.Y.T., Zhu B., 2005, Transverse vibration of Mindlin Plates on two-parameter foundations by analytical trapezoidal p-elements, Journal of Engineering Mechanics 131: 1140-1145.
[21] 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: 1789-1806.
[22] Abrate S., 2006, Free vibration, buckling, and static deflections of functionally graded plates, Composites Science and Technology 66: 2383-2394.
[23] 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: 918- 939.
[24] 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: 7398-7426.
[25] Petrolito J., 2014, Vibration and stability analysis of thick orthotropic plates using hybrid-Trefftz elements, Applied Mathematical Modelling 38:5858-5869.
[26] Mindlin R.D., 1951, Influence of rotary inertia and shear on flexural motions of isotropic elastic plates, Journal of Applied Mechanics 18: 31-38.
[27] Liew K.M., Wang C.M., Xiang Y., Kitipornchai S., 1998, Vibration of Mindlin Plates, Elsevier.
[28] Kaneko T., 1975, On Timoshenko’s correction for shear in vibrating beams, Journal of Physics D: Applied Physics 8: 1928-1937.
[29] Bert C.W., Malik M., 1996, Differential quadrature method in computational mechanics: A review, Applied Mechanics Reviews 49: 1-28.