Abstract
This chapter deals with the free vibration analysis of SORs using the FE method. A family of variable-thickness, curved, C(0), MR axisymmetric FEs that include shear deformation and rotatory inertia effects is presented. The accuracy, convergence and efficiency of these newly developed elements are explored through a series of free-vibration analyses of axisymmetric shell structures and the results are compared with those obtained by other analytical and numerical methods. An interesting feature of the chapter is a brief study of the vibrational behaviour of church bells and a hand bell.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Chladni EFF. Die Akustik. Breitkopf and Hartel; 1830.
Perrin R, Charnley T, Banu H, Rossing TD. Chladni’s Law and the modern English Church Bell. J Sound Vib 1985;102:11–9.
Kunieda H. Flexural axisymmetric free Vibrations of a spherical Dome: exact Results and approximate Solutions. J Sound Vib 1984;92:l–10.
Leissa AW, Narita Y. Natural Frequencies of simply supported circular Plates. J Sound Vib 1980;70:221–9.
Grafton PE, Strome DR. Analysis of axisymmetric Shells by the direct Stiffness Method. AIAA J 1963;1:2342–47.
Soni SR, Amo-Rao CL. Axisymmetric Vibrations of annular Plates of variable Thickness. J Sound Vib 1975;38:465–73.
Kirkhope J, Wilson GJ. Vibration of circular and annular plates using finite elements. Int J Numer Methods Eng 1972;4:181–93.
Harris GZ. The normal Modes of a circular and annular Plate of variable Thickness. J Mech Appl Math 1968;21:321–27.
Leissa AW. Vibrations of Plates [internal report]. NASA; 1969. Report No.: SP-160.
Irie T, Yamada G, Aomura S. Natural Frequencies of Mindlin circular Plates. J Appl Mech 1980;47:652–5.
Irie T, Yamada G, Takagi K. Natural Frequencies of thick annular Plates. J Appl Mech 1982;49:633–8.
Irie T, Yamada G, Aomura S. Free vibration of a Mindlin annular plate of varying Thickness. J Sound Vib 1979;66:187–97.
Hinton E. Numerical Methods and Software for dynamic Analysis of Plates and Shells. Swansea: Pineridge Press; 1987.
Heppler GR, Wahl L. Finite Element Analysis of free-free Shells of Revolution. J Sound Vib 1991;139:263–83.
Sen SK, Gould PL. Free Vibration of Shells of Revolution using FEM. J Eng Mech 1974;100:283–303.
Nelson DL. Analysis of Cooling Tower Dynamics. J Sound Vib 1981;79:501–18.
Carter RL, Robinson AR, Schnobrich WC. Free Vibrations of hyperboloidal Shells of Revolution. J Eng Mech 1969;93:1033–53.
Garnet H, Kempner J. Axisymmetric free Vibration of conical Shells. J Appl Mech 1964;31:458–466.
Irie T, Yamada G, Kaneko T. Free Vibration of conical Shell with variable Thickness. J Sound Vib 1982;82:83–94.
Luah MH, Fan SC. General free Vibration Analysis of Shells of Revolution using the Spline Finite Element Method. Comput Struct 1989;33:1153–62.
Srinivasan RS, Hosur V. Axisymmetric Vibration of thick conical Shells. J Sound Vib 1989;135:171–6.
Perrin R, Charnley T, Depont J. Normal Modes of the modern English Church Bell. J Sound Vib 1983;90:29–49.
Tavakoli MS, Singh R. Eigensolutions of joined/hermetic Shell Structures using the State Space Method. J Sound Vib 1989;100:97–123.
Bathe KJ. Finite Element Procedures in Engineering Analysis. Englewood Cliffs (NJ): Prentice-Hall; 1982.
Tavakoli MS, Singh R. Modal Analysis of a hermetic Can. J Sound Vib 1990;136:141–5.
Chapman L. A Finite Element Analysis of the Modes of Vibration of an English Church Bell [BSc project]. Swansea: Department of Civil Engineering, University of Wales; 1988. Report No.: CP/995/88/.
Bletzinger, KU, Reitinger, R. Shape Optimization of Shells. In: Proceedings of International Symposium on Natural Structures-Principles, Strategies and Models in Architecture and Nature, 1991 Oct 1-4, Stuttgart, Germany. Stuttgart: Universität Stuttgart; 1991.
Reitinger R. Personal Communication: Stuttgart: University of Stuttgart.
Charnley T. Personal Communication. Loughborough: University of Technology.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer-Verlag London
About this chapter
Cite this chapter
Hinton, E., Sienz, J., Özakça, M. (2003). Basic Finite Element Formulation for Vibrating Axisymmetric Shells. In: Analysis and Optimization of Prismatic and Axisymmetric Shell Structures. Springer, London. https://doi.org/10.1007/978-0-85729-424-1_7
Download citation
DOI: https://doi.org/10.1007/978-0-85729-424-1_7
Publisher Name: Springer, London
Print ISBN: 978-1-4471-1059-0
Online ISBN: 978-0-85729-424-1
eBook Packages: Springer Book Archive