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Shock and Vibration
Volume 2016, Article ID 9748135, 14 pages
Research Article

Comparison Study on the Exact Dynamic Stiffness Method for Free Vibration of Thin and Moderately Thick Circular Cylindrical Shells

1School of Naval Architecture and Civil Engineering, Jiangsu University of Science and Technology, Zhangjiagang 215600, China
2Department of Civil Engineering, Tsinghua University, Beijing 100084, China

Received 3 September 2016; Revised 21 November 2016; Accepted 24 November 2016

Academic Editor: Marcello Vanali

Copyright © 2016 Xudong Chen and Kangsheng Ye. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Comparison study on free vibration of circular cylindrical shells between thin and moderately thick shell theories when using the exact dynamic stiffness method (DSM) formulation is presented. Firstly, both the thin and moderately thick dynamic stiffness formulations are examined. Based on the strain and kinetic energy, the vibration governing equations are expressed in the Hamilton form for both thin and moderately thick circular cylindrical shells. The dynamic stiffness is assembled in a similar way as that in classic skeletal theory. With the employment of the Wittrick-Williams algorithm, natural frequencies of circular cylindrical shells can be obtained. A FORTRAN code is written and used to compute the modal characteristics. Numerical examples are presented, verifying the proposed computational framework. Since the DSM is an exact approach, the advantages of high accuracy, no-missing frequencies, and good adaptability to various geometries and boundary conditions are demonstrated. Comprehensive parametric studies on the thickness to radius ratio () and the length to radius ratio () are performed. Applicable ranges of are found for both thin and moderately thick DSM formulations, and influences of on frequencies are also investigated. The following conclusions are reached: frequencies of moderately thick shells can be considered as alternatives to those of thin shells with high accuracy where   is small and is large, without any observation of shear locking.