Document Type: Research Paper

Authors

Department of Mechanical Engineering, Qom University of Technology, Qom, 1519-37195, Iran

Abstract

In the present work, study of the vibration of a functionally graded (FG) cylindrical shell made up of stainless steel, zirconia, and nickel is presented. Free vibration analysis is presented for FG cylindrical shells with simply supported-simply supported and clamped–clamped boundary condition based on temperature independent material properties. The equations of motion are derived by Hamilton’s principle. Material properties assume to be graded in the thickness direction according to a simple power law distribution in terms of the volume fraction of the constituents. Effects of boundary conditions and volume fractions (power law exponent) on the natural frequencies of the FG cylindrical shell are studied. Frequency characteristics of the FG shell are found to be similar to those of isotropic cylindrical shells. Furthermore, natural frequencies of these shells are observed to be dependent on the constituent volume fractions and boundary conditions. Strain displacement relations from Love's and first-order shear deformation theories are employed. Galerkin method is used to derive the governing equations for clamped boundary conditions. Further, analytical results are validated with those reported in the literature and excellent agreement is observed. Finally, in order to investigate the effects of the temperature gradient, functionally graded materials cylindrical shell with high temperature specified on the inner surface and outer surface at ambient temperature,1D heat conduction equation along the thickness of the shell is applied and the results are reported.

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[1] M. Yamanouchi, M. Koizumi, T. Hirai, and I. Shiota. Proceedings of the First International Symposium on Functionally Gradient Materials, Japan, (1990).
[2] M. Koizumi, “The concept of FGM” ,Ceramic Transactions, Functionally Gradient Materials, Vol. 34, pp. 3-10,(1993).
[3] Anon, FGM components: PM meets the challenge. Metal Powder Report; Vol. 51, pp. 28-32 ,(1996).
[4] N. Sata, ”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, Vol. 34, pp. 109-116,(1993).
[5] H. Yamaoka, M. Yuki, K. Tahara, T. Irisawa, R. Watanabe, and A. Kawasaki. “Fabrication of Functionally Gradient Material by slurry stacking and sintering process”, Ceramic Transactions, Functionally Gradient Materials, Vol. 34, pp. 72-165, (1993).
[6] B. H. Rabin, and R. J. Heaps, “Powder processing of Ni/Al2O3 FGM”, Ceramic Transactions, Functionally Gradient Materials, Vol. 34, pp. 173-180, (1993).
[7] N. Noda, “Thermal stresses in functionally graded materials”, Journal of Thermal Stresses Vol. 22, pp. 477-512, (1999).
[8] T. Fuchiyama, and N. Noda, “Analysis of thermal stress in a plate of functionally gradient material”, Journal of Science and Engineering, Vol. 16, pp. 263-268, (1995).
[9] Y. Obata, and N. Noda,” Steady thermal stresses in a hollow circular cylinder and hollow sphere of a functionally gradient material”, Journal of Thermal Stresses, Vol. 17, pp. 471-487, (1994).
[10] J. N. Reddy, and C. D. Chin, “Thermo mechanical analysis of functionally graded cylinders and plates”, Journal of Thermal Stresses, Vol. 21, pp. 593-626, (1998).
[11] M. Jabbari, S. Sohrabpour, and M. R. Eslami,”Mechanical and thermal stresses in a functionally graded hollow cylinder due to radially symmetric load”, International Journal of Pressure Vessels and Piping, Vol. 79, pp. 493-497, (2002).
[12] H. Awaji, and R. Sivakumar, “Temperature and stress distribution in a hollow cylinder of functionally graded material; the case of temperature-independent material properties”, Journal of the American Ceramic Society, Vol. 84, pp. 1059-1065, (2001).
[13] S. Takezono, K. Tao, E. Inamura, and M. Inoue, “Thermal stress and deformation in functionally graded material shells of revolution under thermal loading due to fluid”, JSME International Journal Series, Vol. 39, pp. 573-581, (1996).
[14] G. R. Ye, W. Q. Chen, and J. B. Cai, “A uniformly heated functionally graded cylindrical shell with transverse isotropy”, Mechanics Research Communications, Vol. 28, pp. 535-542, (2001).
[15] K. M. Liew, S. Kitipornchai, X. Z. Zhang, and C. W. Lim, “Analysis of the thermal stress behavior of functionally graded hollow circular cylinders”, International Journal of Solids and Structures, Vol. 40, pp. 2355-2380, (2003).
[16] R. N. Arnold, and G. B. Warburton, “Flexural vibrations of the walls of thin cylindrical shells having freely supported ends”, Proceedings of the Royal Society London A, Vol. 197, pp. 238-256, (1949).
[17] A. Ludwig, and R. Krieg,”An analytical quasi-exact method for calculating Eigen vibrations of thin circular cylindrical shells”, Journal of Sound and Vibration, Vol. 74, pp. 155-174, (1981).
[18] H. Chung,”Free vibration analysis of circular cylindrical shells”, Journal of Sound and Vibration, Vol. 74, pp. 331-350, (1981).
[19] W. Soedel, ”A new frequency formula for closed circular cylindrical shells for a large variety of boundary conditions”, Journal of Sound and Vibration, Vol. 70, pp. 309-317, (1980).
[20] A. Bhimaraddi, “A higher order theory for free vibration analysis of circular cylindrical shells”, International Journal of Solids and Structures, Vol. 20, pp. 623-630, (1984).
[21] K. P. Soldatos, and V. P. Hajigeoriou, “Three-dimensional solution of the free vibration problem of homogeneous isotropic cylindrical shells and panels”, Journal of Sound and Vibration, Vol. 137, pp. 369-384, (1990).
[22] K. Y. Lam, and C. T. Loy, ”Effects of boundary conditions on frequencies characteristics for a multi-layered cylindrical shell”, Journal of Sound and Vibration, Vol. 188, pp. 363-384, (1995).
[23] C. T. Loy, K. Y. Lam, and C. Shu, ”Analysis of cylindrical shells using generalized differential quadrature”, Shock and Vibration, Vol. 4, pp. 193-198, (1997).
[24] MM. Najafizadeh, MR. Isvandzibaei, Vibration of functionally graded cylindrical shells based on higher order shear deformation plate theory with ring support. Acta Mechanica 2007; 191: 75-91.
[25] M. M. Najafizadeh, and M. R. Isvandzibaei, "Vibration of functionally graded cylindrical shells based on different shear deformation shell theories with ring support under various boundary conditions", Journal of Mechanical Science and Technology, Vol. 23, pp. 2072-2084, (2009).
[26] F. Tornabene, "Free vibration analysis of functionally graded conical, cylindrical shell and annular plate structures with a four-parameter power-law distribution", Comput. Methods Appl. Mech. Engrg., Vol. 198, pp. 2911-2935, (2009).
[27] P. Malekzadeh, and Y. Heydarpour, "Free vibration analysis of rotating functionally graded cylindrical shells in thermal environment", Composite Structures, Vol. 94, pp. 2971-2981, (2012).
[28] M. J. Ebrahimi, and M. M. Najafizadeh, "Free vibration of two-dimensional functionally graded circular cylindrical shells on elastic foundation", Modares Mechanical Engineering, Vol. 38, No. 1, pp. 308-324, (2013).
[29] R. Bahadori, and M. M. Najafizadeh "Free vibration analysis of two-dimensional functionally graded axisymmetric cylindrical shell on Winkler–Pasternak elastic foundation by First-order Shear Deformation Theory and using Navier-differential quadrature solution methods", Applied Mathematical Modelling, Vol. 39, pp. 4877-4894, (2015).
[30] G. G. Sheng and X. Wang, “Effects of Thermal Loading on the Buckling and Vibration of Ring-Stiffened Functionally Graded Shell”, J. Therm. Stresses, Vol. 30, pp. 1249-1267, (2007).
[31] K. Y. Lam, and W. Qian, “Vibrations of Thick Rotating Laminated Composite Cylindrical Shells”, J. Sound Vibr., Vol.
225, No. 3, pp. 483-501, (1999).
[32] R. Naj, M. Sabzikar Boroujerdy and M. R. Eslami, “Thermal and mechanical instability of functionally graded truncated conical shells”, Thin-Walled Structures, Vol. 46, pp. 65-78, (2008).
[33] H.-S. Shen, and N. Noda, “Postbuckling of FGM Cylindrical Shells under Combined Axial and Radial Mechanical Loads in Thermal Environments”, Int. J. Solids Struct., Vol. 42, pp. 4641-4662, (2005).
[34] M. S. Qatu, “Vibration of Laminated Shells and Plates”, Elsevier, The Netherlands, (2004).
[35] A. V. Lopatin, and E. V. Morozov, "Buckling of the composite sandwich cylindrical shell with clamped ends under uniform external pressure", Compos. Struct., Vol. 122, pp. 209-216, (2015).

[36] M. Talebitooti, “Vibration and critical speed of orthogonally stiffened rotating FG cylindrical shell under thermo-mechanical loads using differential quadrature method” J. Term. Stresses, Vol. 36, pp.160-188, (2013).

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