A unified approach for the vibration analysis of cylindrical shells with general boundary conditions
Cylindrical shells are widely used in engineering practice; in particular, one of the special applications is a tire, which can be modeled as a cylindrical shell on an elastic foundation (CSEF). To investigate influences of related parameters on the dynamic characteristics of the shell and help engineers to gain insights into the tire dynamics, a unified formulation for vibration analysis of the cylindrical shell with general boundaries has been developed; this unified formulation includes (i) formulations for CSEF governing equations based on the Donnell–Mushtari theory and Hamilton’s principle; (ii) a unified approach for the solutions of the characteristic equation; and (iii) a general treatment of the boundary conditions by adjusting the foundation spring coefficients. All nine sets of possible solutions of the characteristic equation are clarified and examined. Five case studies have been conducted to validate and verify the developed algorithm. The results based on the developed method generally have good agreement with those of the finite element method and experiment; missed solutions can be recovered.
Unable to display preview. Download preview PDF.
- 2.Liu, Z., Zhou, F., Oertel, C., et al.: Three-dimensional vibration of a ring with a noncircular cross-section on an elastic foundation. In: Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, p. 0954406217720823 (2017)Google Scholar
- 4.Li, X.: Analysis and comparative study of static and dynamic characteristics of orthotropic circular cylindrical shells. Ph.D. Dissertation. Huazhong University of Science and Technology, China (2004)Google Scholar
- 6.Duan, H.: Analysis of dynamic characteristics of thin circular cylindrical shells. Master Dissertation. Northeastern University, China (2012)Google Scholar
- 7.Leissa, A.W.: Vibration of Shells. Acoustical Society of America, New York (1993)Google Scholar
- 11.Wang, Y., Luo, Z.: Forced vibration response characteristics of thin cylindrical shell. J. Vib. Shock 34(7), 103–108 (2015)Google Scholar
- 13.Zuo, Y., Gong, Z.: Study on the excited vibration of a cylindrical shell. Trans. Chin. Soc. Agric. Mach. 29(1), 88–93 (1998)Google Scholar
- 19.Ma, X., Du, J., Yang, T., et al.: Analysis of influence of boundary conditions on cylindrical shell dynamics based on wave propagation approach. J. Vib. Eng. 22(6), 608–613 (2009)Google Scholar
- 22.Li, X.: Study on free vibration analysis of circular cylindrical shells using wave propagation. J. Sound Vib. 311(3), 667–682 (2008)Google Scholar
- 25.Alujević, N., Campillo-Davo, N., Kindt, P., et al.: A simplified tire model based on a rotating shell. In: Proceedings of the 4th International Tyre Colloquium, pp. 383–392 (2015)Google Scholar
- 30.Sewall, J.L., Naumann, E.C.: An experimental and analytical vibration study of thin cylindrical shells with and without longitudinal stiffeners. In: National Aeronautic and Space Administration; for Sale by the Clearinghouse for Federal Scientific and Technical Information, Springfield, Va (1968)Google Scholar
- 35.Li, X.: A new approach for free vibration analysis of thin circular cylindrical shell. J. Sound Vib. 296(1), 91–98 (2006)Google Scholar