Document Type : Research Article


Faculty of Materials and Manufacturing Technologies, Malek Ashtar University of Technology, Tehran, Iran.


In this research, by improving the accuracy of existing high-order theories, a new corrected high-order composite cylindrical shell theory with twelve displacement components has been developed. In this theory, the effect of terms related to the trapezoidal shape of the shell cross-section (1+z/R) in the results of the shell stress has been accurately calculated. After adding the strain energy such as the initial stresses and the strain energy such as the prevention of the rotation of the rigid body to the shell energy functional, based on Hamilton's principle, the equilibrium equations of the cylindrical shell with two ends have been derived. By using these equations, eigenvalue analysis (free vibrations) have been performed. Validation of the results of the present research was done by comparing with the theoretical and experimental results of other researchers and the results of the ABAQUS software, and a good match has been achieved.


Main Subjects

  • Sheinman, S. Greif, “Dynamic analysis of laminated shells of revolution”, Journal of Composite Materials, Vol. 18, pp. 200-215, 1984.
  • A. Jafari, S.M.R. Khalili, R. Azarafza, “Transient dynamic response of composite circular cylindrical shells under radial impulse load and axial compressive loads”, Thin-Walled Structures, Vol. 43, pp. 1763–1786, 2005.
  • رضا آذرافزا، " بهینه‌سازی وزنی و دینامیکی پوسته‌های استوانه‌ای کامپوزیتی چند‌لایه " ، رساله دکتری، دانشگاه صنعتی خواجه نصیرالدین طوسی، تهران، ایران، 1384.
  • M.R. Khalili, R. Azarafza, A. Davar, “Transient dynamic response of initially stressed composite circular cylindrical shells under radial impulse load”, Composite Structures, Vol. 89, pp. 275–284, 2009.
  • Setoodeh, M. Enferadi, “Effect of structural damping on dynamic response of laminated cylindrical shell subjected to low velocity impact”, 17th Annual (International) Conference on Mechanical Engineering, Tehran Universiy, Tehran, Iran, Paper code: ISME-2009-1722, May 19-21 2009.
  • Rahmani, S.M.R. Khalili, K. Malekzadeh, “Free vibration response of composite sandwich cylindrical shell with flexible core”, Composite Structures, Vol. 92, pp. 1269-1281, 2010.
  • ارژنگ پی آ.، انصاری خلخالی ر.، درویزه م.، تحلیل ارتعاشات پوسته ی استوانه ای FGM با روش MLPG . مهندسی مکانیک مدرس، ج ۱۳ (۳) ص93 – 101، 1392.
  • زارعی م.، رحیمی غ.، تحلیل ارتعاشات آزاد پوسته های استوانه‌ای کامپوزیتی مشبک دوار، مهندسی مکانیک مدرس، ج ۱۶ (۹)، ص ۱7۵-۱8۵، 1395.
  • موسوی س. ع.، الهامی م. ر.، رحیمی م.، تحلیل دینامیکی و ارتعاشی پوسته استوانه‌ای کامپوزیتی با لایه‌های پیزوالکتریک، نشریه علمی مکانیک هوافضا، جلد 16 ،شماره 2 ، ص 15-25، 1399.
  • Zhao, M. Hooman, M. Yarigarravesh, M. Algarni, M.J.C. Opulencia, F. Alsaikhan, A.T. Jalil, A. Mohamed, K.M. AboRas, M.L. Rahman, and M.S. Sarjadi, “Vibration analysis of size dependent micro FML cylindrical shell reinforced by CNTs based on modified couple stress theory”, Arabian Journal of Chemistry, 15(10), p.104115. 2022.
  • W. Leissa, J. Chang, “Elastic deformation of thick, laminated composite shallow shells”, Composite Structures, Vol. 35, pp. 153-170, 1996.
  • Sanders, An improved first approximation theory of thin shells”, NASA TR-R24, 1959.
  • W. Leissa, “Vibration of shells, NASA SP-288, US Government Printing office”, Washington D.C., Reprinted by the Acoustical Society of America 1993, 1973.
  • Amabili, “A comparison of shell theories for large-amplitude vibrations of circular cylindrical shells: Lagrangian approach”, Journal of Sound and Vibration, Vol. 264, pp. 1091–1125, 2003.
  • K. Garg, R.K. Khare, T. Kant, Higher-order closed-form solutions for free vibration of laminated composite and sandwich shells”, Journal of Sandwich Structures and Materials, Vol. 8, pp. 205-235, 2006.
  • S. Lee, K.D. Lee, “On the dynamic response of laminated circular cylindrical shells under impulse loads”, Computers & Structures, Vol. 63, No. 1, pp. 149-157, 1997.
  • Meirovitch, Fundamentals of vibrations, McGraw-Hill, 2001.
  • A. Larson, “A novel method for characterizing the impact response of functionally graded plate”, Ph.D. Dissertation, Air Force Institute of Technology, Air University, Department of the Air Force, Ohio, USA, Sptember 2008.
  • Mori, K. Tanaka, “Average stress in matrix and average elastic energy of materials with misfitting inclusions”, Acta Metallurgica, Vol. 21, pp. 571-574, 1973.
  • H. Chi, Y.L. Chung, “Mechanical behavior of functionally graded material plates under transverse load—Part I: Analysis”, International Journal of Solids and Structures, Vol. 43, pp. 3657–3674, 2006.

A.E. Armenakas, D.C. Gazis, G. Herrmann, “Free vibrations of Circular Cylindrical Shells ”, Pergamon Press, Oxford, 1969.