Free Vibration of Annular Plate Reinforced with Multi-walled Carbon Nanotubes Resting on an Elastic Foundation Using Refined Theory

Document Type: Persian

Authors

1 MSc. Student, Department of Mechanical Engineering, Arak Branch, Islamic Azad University, Arak, Iran

2 Assistant Professor, Department of Mechanical Engineering, Arak Branch, Islamic Azad University, Arak, Iran

Abstract

In this paper, an attempt is made for solution of free vibration analysis of annular plate reinforced with carbon nanotubes for Uniformly Distribution (UD), resting on an elastic foundation using a refined theory presented. In this theory, a parabolic distribution of shear stress and strain in the thickness direction and satisfies the boundary conditions of zero shear stress on the upper and lower crust cut without using a correction factor to be considered. The equations of motion are obtained using Hamilton's principle. And then these equations are solved by GDQ method .Factors affecting the frequency such large radius to small radius, the ratio of thickness to the radius of the annular plate, the length of the radius is obtained. To check the compatibility equations and solving method is used, a comparison between the present work has been done with papers

Keywords


[1] Brush D.O., Almorth B.O., Buckling of bars, plates and shells, McGraw-Hill, New York, 1975.

[2] Goltermann P.M., Buckling of short, thin-walled cylinders under combined loading, ASME Journal of Offshore Mechanics Arct Engineering, Vol. 113, 1991, pp. 306-311.

[3] Koiter W.T., Over de stabiliteit van het elastisch evenwicht, doctoral thesis, Delft University of Technology, The Netherlands, 1945.

[4] Winterstetter T.A., Schmidt H., Stability of circular shells under combined loading, Journal of Thin-walled Structures, Vol. 40, 2002, pp. 893-909.

[5] Vodenticharova T., Ansourian P., Buckling of circular cylindrical shells subjected to uniform lateral pressure, Journal of Engineering Structure, Vol. 18, 1996, pp. 604-614.

[6] Thai H.-T., Park M., Choi D.-H., A simple refined theory for bending, buckling, and vibration of thick plates resting on elastic foundation, International Journal of Mechanical Sciences, 2013.

[7] Thai H.-T., Choi D.-H., Analytical solutions of refined plate theory for bending, buckling and vibration analyses of thick plates, Applied Mathematical Modeling, 2013.

[8] Thai H.-T., Choi D.-H., Analytical solutions of refined plate theory for bending, buckling and vibration analyses of thick plates, Journal of Applied Mathematical Modelling, 2013.

[9] Thai H.-T., Kim S.-E., Analytical solution of a two variable refined plate theory for bending analysis of orthotropic Levy-type plates, International Journal of Mechanical Sciences, Vol. 54 , 2012, pp. 269–276.

[10] Thai H.-T., Choi D.-H., A refined plate theory for functionally graded plates resting on elastic foundation, Journal of Composites Science and Technology, Vol. 71, 2011, pp. 1850-1858.

[11] Kim S.-E., Thai H.-T., Lee J., A two variable refined plate theory for laminated composite plates, Journal of Composite Structures, Vol. 89, 2009, pp. 197–205.

[12] Kim S.-E., Thai H.-T., Lee J., Buckling analysis of plates using the two variable refined plate theory, Journal of Composite Structures, Vol. 47, 2009, pp. 455 -462.

[13] Thai H.-T., Kim S.-E., Free vibration of laminated composite plates using two variable refined plate theories, International Journal of Mechanical Sciences, Vol. 52, 2010, pp. 626-633.

[14] Benachour A., Daouadji Tahar H., Ait Atmane H., Tounsi A., Sid Ahmed M., A four variable refined plate theory for free vibrations of functionally gradedplates with arbitrary gradient, Journal of Composites: Part B, Vol. 42, 2011, pp. 1386-1394.

 

 

[15] Mechab I., Mechab B., Benaissa S., Static and dynamic analysis of functionally graded plates using Four-variable refined plate theory by the new function, Journal of Composites: Part B, Vol. 45, 2013, pp. 748–757.

[16] Huang. C.S., McGee O.G., Chang M.J., Vibration of cracked rectangular FGM Thick plate, Composite structure, 2011, pp.1747-1764.

[17] Wang Z.X., Shen H.S., Nonlinear analysis of sandwich plates with FGM face Sheets resting on elastic foundations, Composite Structures, 2011, pp. 2521-2532.

[18] Hosseini Hashemi S.H., Rokni Damavandi Taher H., Akhavan H., Vibration Analysis of radialy FGM sectorial plate of variable thichness on elastic foundation, Composite Structure, 2010, pp. 1734-1743.

[19] Zhao X., Lee Y.Y., Liew K.M., Free vibration  analysis of functionally Graded  plate using the element –free KP-RITZ method, Journal of sound and  vibration, Vol. 319, 2009, pp. 918-939.

[20] Chang T., Gao H., Size–dependent elastic properties of a Single–walled carbon nanotubes via a molecular model, Journal of mechanics And physics of solid, 2003, pp. 1059-1074.

[21] Jafari Mehrabadi S., Jalilian M., Zarouni E., Free vibration analysis of nanotube –reinforced composite truncated conical shell resting on elastic foundation, Journal Modares mechanic Engineering, Vol. 14, No. 12, 2014, pp. 122-132.

[22] Heshmati M., Yas M.H., Dynamic analysis of functionally graded multi-walled carbon nanotube-polystyrene nanocomposite beams subjected to multi-moving loads, Materials and Design, Vol. 49, 2013, pp. 894–904.

[23] Andrews R., Jacques D., Minot M., Rantell T., Fabrication of carbon multiwall nanotube/polymer composites by shear mixing, Macromol Mater Engineering, Vol. 287, 2002, pp. 395–403.

[24] Bisadi H., Es’haghi M., Rokni H., Ilkhani M., Benchmark solution for transverse vibration of annular Reddy plates,  International Journal of Mechanical Sciences, Vol. 56, 2012, pp. 35–49