Technical Briefs

Vibrations of Circular Cylindrical Shells With General Elastic Boundary Restraints

[+] Author and Article Information
W. L. Li

Department of Mechanical Engineering,
Wayne State University,
5050 Anthony Wayne Drive,
Detroit, MI 48202
e-mail: wli@wayne.edu

Contributed by the Design Engineering Division of ASME for publication in the Journal of Vibration and Acoustics. Manuscript received March 10, 2010; final manuscript received June 26, 2012; published online February 25, 2013. Assoc. Editor: Weidong Zhu.

J. Vib. Acoust 135(2), 024501 (Feb 25, 2013) (6 pages) Paper No: VIB-10-1083; doi: 10.1115/1.4023048 History: Received March 10, 2010; Revised June 26, 2012

Vibration of a circular cylindrical shell with elastic boundary restraints is of interest to both researchers and structural engineers. This class of problems, however, is far less attempted in the literature than its counterparts for beams and plates. In this paper, a general solution method is presented for the vibration analysis of cylindrical shells with elastic boundary supports. This method universally applies to shells with a wide variety of boundary conditions including all 136 classical (homogeneous) boundary conditions which represent the special cases when the stiffnesses for the restraining springs are set as either zero or infinity. The Rayleigh–Ritz procedure based on the Donnell–Mushtari theory is utilized to find the displacement solutions in the form of the modified Fourier series expansions. Numerical examples are given to demonstrate the accuracy and reliability of the current solution method. The modal characteristics of elastically restrained shells are discussed against different supporting stiffnesses and configurations.

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Grahic Jump Location
Fig. 1

A shell with general elastic supports at ends

Grahic Jump Location
Fig. 2

Effect on the fundamental frequency of the stiffnesses of the elastic supports




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