Third Order Formulation for Vibrating Non-Homogeneous Cylindrical Shells in Elastic Medium

Subject Areas : Engineering

M Gheisari ¹ (Faculty of Engineering, Khomein Branch, Islamic Azad University)
H Molatefi ² (Railway Engineering School, Iran University of Science and Technology, Narmak)
S.S Ahmadi ³ (Department of Mechanical Engineering, Iran University of Science and Technology, Arak Branch)

Received: 2011-10-28 Accepted : 2011-12-08 Published : 2011-12-30

Keywords: Vibration, Elastic medium, Non-homogeneous cylindrical shell, Third order shear deformation theory, Donnell shell theory,

Abstract :

Third order shear deformation theory of cylindrical shells is employed to investigate the vibration characteristics of non-homogeneous cylindrical shells surrounded by an elastic medium. The kinematic relations are obtained using the strain-displacement relations of Donnell shell theory. The shell properties are considered to be dependent on both position and thermal environment. A suitable function through the thickness direction is assumed for the non-homogeneity property. The Winkler-Pasternak elastic foundation is used to model the elastic medium. Analytical solutions are presented for cylindrical shells with simply supported boundary conditions. From the numerical studies, it is revealed that, the natural frequencies are affected significantly by the elastic foundation coefficients and environmental temperature conditions.

References:

[1] Paliwal D.N., Bhalla V., 1993, Large deflection analysis of cylindrical shells on a pasternak foundation, International Journal of Pressure Vessels and Piping 53(2): 261-271.

[2] Ng T.Y., Lam K.Y., 1999, Effects of elastic foundation on the dynamic stability of cylindrical shells, Structural Engineering and Mechanics 8(2):193-205.

[3] Hong T., Teng J.G., Luo Y.F., 1999, Axisymmetric shells and plates on tensionless elastic foundations, International Journal of Solids and Structures 36(34): 5277-5300.

[4] Sheng G., Wang X., 2008, Thermal vibration, buckling and dynamic stability of functionally graded cylindrical shells embedded in an elastic medium, Journal of Reinforced Plastics and Composites 27: 117-134.

[5] Shen, H.-Sh., 2009, Postbuckling of shear deformable fgm cylindrical shells surrounded by an elastic medium, International Journal of Mechanical Sciences, 51, pp. 372-383.

[6] Shen H.-Sh., Yang J., Kitipornchai S., 2010, Postbuckling of internal pressure loaded FGM cylindrical shells surrounded by an elastic medium, European Journal of Mechanics A/Solids 29: 448-460.

[7] Sofiyev A.H., Avcar M., Ozyigit P., Adigozel S., 2009,The Free Vibration of non-homogeneous truncated conical shells on a winkler foundation, International Journal of Engineering and Applied Sciences 1(1):34-41.

[8] Reddy J.N., Chin C.D., 1998, Thermomechanical analysis of functionally graded cylinders and plates, Journal of Thermal Stresses 21: 593-629.

[9] Lee S.J., Reddy J.N., 2004, Vibration suppression of laminated shell structures investigated using higher order shear deformation theory, Smart Materials and Structures 13: 1176-1194.

[10] Paliwal D.N., Pandey R.K., Nath T., 1996, Free vibration of circular cylindrical shell on winkler and pasternak foundation, International Journal of Pressure Vessels and Piping 69: 79-89.

[11] Jenabi J., Khazaeinejad P., Najafizadeh M.M., 2011, Vibration characteristics of three-layer cylindrical shells with functionally graded middle layer on elastic foundation, National Conference on New Technologies in Mechanical Engineering, February 23-24, Islamic Azad University-Shiraz Branch, Shiraz, Iran.