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

Author:

Chen Xudong1,Ye Kangsheng2ORCID

Affiliation:

1. School of Naval Architecture and Civil Engineering, Jiangsu University of Science and Technology, Zhangjiagang 215600, China

2. Department of Civil Engineering, Tsinghua University, Beijing 100084, China

Abstract

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 (h/r) and the length to radius ratio (L/r) are performed. Applicable ranges of h/r are found for both thin and moderately thick DSM formulations, and influences of L/r 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  h/r is small and L/r is large, without any observation of shear locking.

Funder

National Natural Science Foundation of China

Publisher

Hindawi Limited

Subject

Mechanical Engineering,Mechanics of Materials,Geotechnical Engineering and Engineering Geology,Condensed Matter Physics,Civil and Structural Engineering

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