Vibration Analysis of Functionally Graded Spinning Cylindrical Shells Using Higher Order Shear Deformation Theory
الموضوعات :
1 - Department of Mechanical Engineering, Islamic Azad University, Khomeinishahr Branch
الکلمات المفتاحية: Vibration, Functionally graded material, Spinning cylindrical shell, Higher order shear deformation theory,
ملخص المقالة :
In this paper the vibration of a spinning cylindrical shell made of functional graded material is investigated. After a brief introduction of FG materials, by employing higher order theory for shell deformation, constitutive relationships are derived. Next, governing differential equation of spinning cylindrical shell is obtained through utilizing energy method and Hamilton’s principle. Making use of the principle of minimum potential energy, the characteristic equation of natural frequencies is derived. After verification of the results, the effect of changing different parameters such as material grade, geometry of shell and spinning velocity on the natural frequency are examined.
[1] Yamanouchi M., Koizumi M., Hirai T., Shiota I., 1990, in: Proceedings of the First International Symposium on Functionally Gradient Materials, Japan.
[2] Koizumi M., 1993, The concept of FGM, Ceramic Transactions, Functionally Gradient Materials 34: 3-10.
[3] Anon, 1996, FGM components: PM meets the challenge, Metal Powder Report 51: 28-32.
[4] Sata N., 1993, Characteristic of SiC-TiB composites as the surface layer of SiC-TiB-Cu functionally gradient material produced by self-propagating high-temperature synthesis, Ceramic Transactions, Functionally Gradient Materials 34: 109-116.
[5] Yamaoka H., Yuki M., Tahara K., Irisawa T., Watanabe R., Kawasaki A., 1993, Fabrication of functionally gradient material by slurry stacking and sintering process, Ceramic Transactions, Functionally Gradient Materials 34: 165-172.
[6] Rabin B.H., Heaps R.J., 1993, Powder processing of NI- Al2O3 FGM, Ceramic Transactions, Functionally Gradient Materials 34: 173-180.
[7] Fukui Y., 1991, Fundamental investigation of functionally gradient material manufacturing system using centrifugal force, International Journal of Japan Society of Mechanical Engineers Series III 34: 144-148.
[8] Wetherhold R.C., Seelman S., Wang J.Z., 1996, Use of functionally graded materials to eliminate or control thermal deformation, Composites Science and Technology 56: 1099-1104.
[9] Obata Y., Noda N., 1994, Steady thermal stresses in a hollow circular cylinder and a hollow sphere of a functionally gradient material, Journal of Thermal Stresses 17: 471-87.
[10] Arnold R.N., Warburton G.B., 1949, Flexural vibrations of the walls of thin cylindrical shells having freely supported ends, in: Proceedings of the Royal Society London A 197: 238-56.
[11] Ludwig A., Krieg R., 1981, An analytical quasi-exact method for calculating eigenvibrations of thin circular cylindrical shells, Journal of Sound and Vibration 74: 155-74.
[12] Chung H., 1981, Free vibration analysis of circular cylindrical shells, Journal of Sound and Vibration 74: 331-350.
[13] Soedel W., 1980, A new frequency formula for closed circular cylindrical shells for a large variety of boundary conditions, Journal of Sound and Vibration 70: 309-317.
[14] Forsberg K., 1964, Influence of boundary conditions on modal characteristics of cylindrical shells, AIAA Journal 2: 182-189.
[15] Bhimaraddi A., 1984, A higher order theory for free vibration analysis of circular cylindrical shells, International Journal of Solids and Structures 20: 623-630.
[16] Soldatos K.P., Hajigeoriou V.P., 1990, Three-dimensional solution of the free vibration problem of homogeneous isotropic cylindrical shells and panels, Journal of Sound and Vibration 137: 369-384.
[17] Soldatos K.P., 1984, A comparison of some shell theories used for the dynamic analysis of cross-ply laminated circular cylindrical panels, Journal of Sound and Vibration 97: 305-319.
[18] Lam K.Y., Loy C.T., 1995, Effects of boundary conditions on frequencies characteristics for a multi-layered cylindrical shell, Journal of Sound and Vibration 188: 363-384.
[19] Loy C.T., Lam K.Y., 1997, Vibration of cylindrical shells with ring support, International Journal of Mechanical Sciences 39: 455-471.
[20] Loy C.T., Lam K.Y., Shu C., 1997, Analysis of cylindrical shells using generalized differential quadrature, Shock and Vibration 4: 193-98.
[21] Loy C.T., Lam K.Y., Reddy J.N., 1999, Vibration of functionally graded cylindrical shells, International Journal of Mechanical Sciences 41: 316-323.
[22] Zhao X, Liew K.M., Ng T.Y., 2002, Vibration of rotating cross ply laminated circular cylindrical shells with stringer and ring stiffeners, International Journal of Solids and Structures 39(2): 529-545.
[23] Reddy J.N., 2004, Mechanics of Laminated Composite Plates and Shells, USA.
