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Year 2011, Volume: 3 Issue: 3, 60 - 71, 01.09.2011

M. Rafiee A. Nezamabadi S. Mareishi

Abstract

References

  • [1] Ng, T.Y., Lam, K.Y., Liew, K.M., 2000. Effect of FGM materials on the parametric resonance of plate structures. Comput. Methods Appl. Mech. Eng. 190, 953–962.
  • [2] Yang, J., Kitipornchai, S., Liew, K.M., 2003. Large amplitude vibration of thermoelectromechanically stressed FGM laminated plates. Comput. Methods Appl. Mech. Eng. 192, 3861–3885.
  • [3] Della Croce, L., Venini, P., 2004. Finite elements for functionally graded ReissnerMindlin plates. Comput. Methods Appl. Mech. Eng. 193, 705–725.
  • [4] Liew, K.M., He, X.Q., Kitipornchai, S., 2004. Finite element method for the feedback control of FGM shells in the frequency domain via piezoelectric sensors and actuators. Comput. Methods Appl. Mech. Eng. 193, 257–273.
  • [5] Wu, C.P., Tsai, Y.H., 2004. Asymptotic DQ solutions of functionally graded annular spherical shells. Eur. J. Mech. A – Solids 23, 283–299.
  • [6] Elishakoff, I., Gentilini, C., Viola, E., 2005a. Forced vibrations of functionally graded plates in the three-dimensional setting. AIAA J. 43, 2000–2007.
  • [7] Elishakoff, I., Gentilini, C., Viola, E., 2005b. Three-dimensional analysis of an all around clamped plate made of functionally graded materials. Acta Mech. 180, 21–36.
  • [8] Patel, B.P., Gupta, S.S., Loknath, M.S., Kadu, C.P., 2005. Free vibration analysis of functionally graded elliptical cylindrical shells using higher-order theory. Compos. Struct. 69, 259–270.
  • [9] Pelletier, J.L., Vel, S.S., 2006. An exact solution for the steady-state thermoelastic response of functionally graded orthotropic cylindrical shells. Int. J. Solids Struct. 43, 1131– 1158.
  • [10] Zenkour, A.M., 2006. Generalized shear deformation theory for bending analysis of functionally graded plates. Appl. Math. Model. 30, 67–84.
  • [11] Arciniega, R.A., Reddy, J.N., 2007. Large deformation analysis of functionally graded shells. Int. J. Solids Struct. 44, 2036–2052.
  • [12] Nie, G.J., Zhong, Z., 2007. Semi-analytical solution for three dimensional vibration of functionally graded circular plates. Comput. Methods Appl. Mech. Eng. 196, 4901–4910.
  • [13] Roque, C.M.C., Ferreira, A.J.M., Jorge, R.M.N., 2007. A radial basis function for the free vibration analysis of functionally graded plates using refined theory. J. Sound Vib. 300, 1048–1070.
  • [14] Najafizadeh, M.M., Isvandzibaei, M.R.: Vibration of functionally graded cylindrical shells based on higher order shear deformation plate theory with ring support. Acta Mech. 191, 75–91 (2007)
  • [15] Yang, J., Shen, H.S., 2007. Free vibration and parametric resonance of shear deformable functionally graded cylindrical panels. J. Sound Vib. 261, 871–893.
  • [16] He XQ, Liew KM, Ng TY, Sirvashanker S. A FEM model for the active control of curved FGM shells using piezoelectric sensor/actuator layers. International Journal for Numerical Methods in Engineering 2002;54:853–70.
  • [17] Liew KM, Kitipornchai S, Zhang XZ, Lim CW. Analysis of the thermal stress behavior of functionally graded hollow circular cylinders. International Journal of Solids and Structures 2003;40:2355–80.
  • [18] Jabbari M, Sohrabpour S, Eslami MR. General solution for mechanical and thermal stresses in a functionally graded hollow cylinder due to nonaxisym- metric steady-state loads. Journal of Applied Mechanics 2003;70:111–18.
  • [19] Jocob LP, Vel SS. An exact solution for the steady-state thermoelastic response of functionally graded orthotropic cylindrical shells. International Journal of Solids and Structures 2006;43:1131–58.
  • [20] Hosseini Kordkheili SA, Naghdabadi R. Geometrically non-linear thermo- elastic analysis of functionally graded shells using finite element method. International Journal for Numerical Methods in Engineering 2007 964–86.
  • [21] Arciniega RA, Reddy JN. Large deformation analysis of functionally graded shells. International Journal of Solids and Structures 2007;44:2036–52.
  • [22] Woo J, Merguid SA, Stranata JC, Liew KM. Thermomechanical postbuckling analysis of moderately thick functionally graded plates and shallow shells. International Journal of Mechanical Sciences 2005;47:1147–71.
  • [23] Bahtui A, Eslami MR. Generalized coupled thermoelasticity of functionally graded cylindrical shells. International Journal for Numerical Methods in Engineering 2007;69:676–97.
  • [24] Loy CT, Lam KY, Reddy JN. Vibration of functionally graded shells. Interna- tional Journal of Mechanical Sciences 1999;41:309–24.
  • [25] Zhang, X.M., Liu, G.R., Lam, K.Y. 2001: Vibration analysis of thin cylindrical shells using wave propagation approach. J. Sound Vib. 239, 397–403.
  • [26] Arshad, S. H., Naeem, M. N., and Sultana, N. Frequency analysis of functionally graded material cylindrical shells with various volume fraction laws. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 221, 1483–1495 (2007)
  • [27] Touloukian YS. Thermophysical properties of high temperature solid materials. New York: Mac- millian, 1967.
  • [28] Love AEH. A treatise on the mathematical theory of elasticity. 4th Ed. Cambridge: Cambridge University Press, 1952.
  • [29] Bhimaraddi A. A higher order theory for free vibration analysis of circular cylindrical shells. International Journal of Solids and Structures 1984;20:623±30.
  • [30] Zhang, X.M., Liu, G.R., Lam, K.Y.: Vibration analysis of cylindrical shells using the wave propagation approach. J. Sound Vib. 239, 397–401 (2001).

Vibration Characteristics of Functionally Gradient Shells with an Exponential Law Distribution Using Wave Propagation Approach Rested on Two Parameters Foundations

Year 2011, Volume: 3 Issue: 3, 60 - 71, 01.09.2011

M. Rafiee A. Nezamabadi S. Mareishi

Abstract

The aim of this paper is to deal with the dynamic behaviour and vibration characteristics of thin functionally graded circular cylindrical shells. Material properties in the shell thickness direction are graded in accordance with the exponential law. Expressions for the strain-displacement and curvature-displacement relationships are taken from Love’s thin shell theory. The Rayleigh-Ritz approach is used to derive the shell eigenfrequency equation. Axial modal dependence is assumed in the characteristic beam functions. Natural frequencies of the shells are observed to be dependent on the constituent volume fractions. The results are compared with those available in the literature for the validity of the present methodology

Keywords

Elastic Shell functionally gradient material exponential law

References

  • [1] Ng, T.Y., Lam, K.Y., Liew, K.M., 2000. Effect of FGM materials on the parametric resonance of plate structures. Comput. Methods Appl. Mech. Eng. 190, 953–962.
  • [2] Yang, J., Kitipornchai, S., Liew, K.M., 2003. Large amplitude vibration of thermoelectromechanically stressed FGM laminated plates. Comput. Methods Appl. Mech. Eng. 192, 3861–3885.
  • [3] Della Croce, L., Venini, P., 2004. Finite elements for functionally graded ReissnerMindlin plates. Comput. Methods Appl. Mech. Eng. 193, 705–725.
  • [4] Liew, K.M., He, X.Q., Kitipornchai, S., 2004. Finite element method for the feedback control of FGM shells in the frequency domain via piezoelectric sensors and actuators. Comput. Methods Appl. Mech. Eng. 193, 257–273.
  • [5] Wu, C.P., Tsai, Y.H., 2004. Asymptotic DQ solutions of functionally graded annular spherical shells. Eur. J. Mech. A – Solids 23, 283–299.
  • [6] Elishakoff, I., Gentilini, C., Viola, E., 2005a. Forced vibrations of functionally graded plates in the three-dimensional setting. AIAA J. 43, 2000–2007.
  • [7] Elishakoff, I., Gentilini, C., Viola, E., 2005b. Three-dimensional analysis of an all around clamped plate made of functionally graded materials. Acta Mech. 180, 21–36.
  • [8] Patel, B.P., Gupta, S.S., Loknath, M.S., Kadu, C.P., 2005. Free vibration analysis of functionally graded elliptical cylindrical shells using higher-order theory. Compos. Struct. 69, 259–270.
  • [9] Pelletier, J.L., Vel, S.S., 2006. An exact solution for the steady-state thermoelastic response of functionally graded orthotropic cylindrical shells. Int. J. Solids Struct. 43, 1131– 1158.
  • [10] Zenkour, A.M., 2006. Generalized shear deformation theory for bending analysis of functionally graded plates. Appl. Math. Model. 30, 67–84.
  • [11] Arciniega, R.A., Reddy, J.N., 2007. Large deformation analysis of functionally graded shells. Int. J. Solids Struct. 44, 2036–2052.
  • [12] Nie, G.J., Zhong, Z., 2007. Semi-analytical solution for three dimensional vibration of functionally graded circular plates. Comput. Methods Appl. Mech. Eng. 196, 4901–4910.
  • [13] Roque, C.M.C., Ferreira, A.J.M., Jorge, R.M.N., 2007. A radial basis function for the free vibration analysis of functionally graded plates using refined theory. J. Sound Vib. 300, 1048–1070.
  • [14] Najafizadeh, M.M., Isvandzibaei, M.R.: Vibration of functionally graded cylindrical shells based on higher order shear deformation plate theory with ring support. Acta Mech. 191, 75–91 (2007)
  • [15] Yang, J., Shen, H.S., 2007. Free vibration and parametric resonance of shear deformable functionally graded cylindrical panels. J. Sound Vib. 261, 871–893.
  • [16] He XQ, Liew KM, Ng TY, Sirvashanker S. A FEM model for the active control of curved FGM shells using piezoelectric sensor/actuator layers. International Journal for Numerical Methods in Engineering 2002;54:853–70.
  • [17] Liew KM, Kitipornchai S, Zhang XZ, Lim CW. Analysis of the thermal stress behavior of functionally graded hollow circular cylinders. International Journal of Solids and Structures 2003;40:2355–80.
  • [18] Jabbari M, Sohrabpour S, Eslami MR. General solution for mechanical and thermal stresses in a functionally graded hollow cylinder due to nonaxisym- metric steady-state loads. Journal of Applied Mechanics 2003;70:111–18.
  • [19] Jocob LP, Vel SS. An exact solution for the steady-state thermoelastic response of functionally graded orthotropic cylindrical shells. International Journal of Solids and Structures 2006;43:1131–58.
  • [20] Hosseini Kordkheili SA, Naghdabadi R. Geometrically non-linear thermo- elastic analysis of functionally graded shells using finite element method. International Journal for Numerical Methods in Engineering 2007 964–86.
  • [21] Arciniega RA, Reddy JN. Large deformation analysis of functionally graded shells. International Journal of Solids and Structures 2007;44:2036–52.
  • [22] Woo J, Merguid SA, Stranata JC, Liew KM. Thermomechanical postbuckling analysis of moderately thick functionally graded plates and shallow shells. International Journal of Mechanical Sciences 2005;47:1147–71.
  • [23] Bahtui A, Eslami MR. Generalized coupled thermoelasticity of functionally graded cylindrical shells. International Journal for Numerical Methods in Engineering 2007;69:676–97.
  • [24] Loy CT, Lam KY, Reddy JN. Vibration of functionally graded shells. Interna- tional Journal of Mechanical Sciences 1999;41:309–24.
  • [25] Zhang, X.M., Liu, G.R., Lam, K.Y. 2001: Vibration analysis of thin cylindrical shells using wave propagation approach. J. Sound Vib. 239, 397–403.
  • [26] Arshad, S. H., Naeem, M. N., and Sultana, N. Frequency analysis of functionally graded material cylindrical shells with various volume fraction laws. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 221, 1483–1495 (2007)
  • [27] Touloukian YS. Thermophysical properties of high temperature solid materials. New York: Mac- millian, 1967.
  • [28] Love AEH. A treatise on the mathematical theory of elasticity. 4th Ed. Cambridge: Cambridge University Press, 1952.
  • [29] Bhimaraddi A. A higher order theory for free vibration analysis of circular cylindrical shells. International Journal of Solids and Structures 1984;20:623±30.
  • [30] Zhang, X.M., Liu, G.R., Lam, K.Y.: Vibration analysis of cylindrical shells using the wave propagation approach. J. Sound Vib. 239, 397–401 (2001).
There are 30 citations in total.

Details

Other ID JA65ZF78RC
Journal Section Articles
Authors

M. Rafiee This is me

A. Nezamabadi This is me

S. Mareishi This is me

Publication Date September 1, 2011
Published in Issue Year 2011 Volume: 3 Issue: 3

Cite

APA Rafiee, M., Nezamabadi, A., & Mareishi, S. (2011). Vibration Characteristics of Functionally Gradient Shells with an Exponential Law Distribution Using Wave Propagation Approach Rested on Two Parameters Foundations. International Journal of Engineering and Applied Sciences, 3(3), 60-71.
AMA Rafiee M, Nezamabadi A, Mareishi S. Vibration Characteristics of Functionally Gradient Shells with an Exponential Law Distribution Using Wave Propagation Approach Rested on Two Parameters Foundations. IJEAS. September 2011;3(3):60-71.
Chicago Rafiee, M., A. Nezamabadi, and S. Mareishi. “Vibration Characteristics of Functionally Gradient Shells With an Exponential Law Distribution Using Wave Propagation Approach Rested on Two Parameters Foundations”. International Journal of Engineering and Applied Sciences 3, no. 3 (September 2011): 60-71.
EndNote Rafiee M, Nezamabadi A, Mareishi S (September 1, 2011) Vibration Characteristics of Functionally Gradient Shells with an Exponential Law Distribution Using Wave Propagation Approach Rested on Two Parameters Foundations. International Journal of Engineering and Applied Sciences 3 3 60–71.
IEEE M. Rafiee, A. Nezamabadi, and S. Mareishi, “Vibration Characteristics of Functionally Gradient Shells with an Exponential Law Distribution Using Wave Propagation Approach Rested on Two Parameters Foundations”, IJEAS, vol. 3, no. 3, pp. 60–71, 2011.
ISNAD Rafiee, M. et al. “Vibration Characteristics of Functionally Gradient Shells With an Exponential Law Distribution Using Wave Propagation Approach Rested on Two Parameters Foundations”. International Journal of Engineering and Applied Sciences 3/3 (September 2011), 60-71.
JAMA Rafiee M, Nezamabadi A, Mareishi S. Vibration Characteristics of Functionally Gradient Shells with an Exponential Law Distribution Using Wave Propagation Approach Rested on Two Parameters Foundations. IJEAS. 2011;3:60–71.
MLA Rafiee, M. et al. “Vibration Characteristics of Functionally Gradient Shells With an Exponential Law Distribution Using Wave Propagation Approach Rested on Two Parameters Foundations”. International Journal of Engineering and Applied Sciences, vol. 3, no. 3, 2011, pp. 60-71.
Vancouver Rafiee M, Nezamabadi A, Mareishi S. Vibration Characteristics of Functionally Gradient Shells with an Exponential Law Distribution Using Wave Propagation Approach Rested on Two Parameters Foundations. IJEAS. 2011;3(3):60-71.

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