Free vibration of multi-layered circular cylindrical shell with cross-ply walls, including shear deformation by using spline function method

2008 ◽  
Vol 22 (11) ◽  
pp. 2062-2075 ◽  
Author(s):  
K. K. Viswanathan ◽  
Kyung Su Kim ◽  
Jang Hyun Lee ◽  
Hee Seung Koh ◽  
Jae Beom Lee
1983 ◽  
Vol 50 (3) ◽  
pp. 544-548 ◽  
Author(s):  
T. Irie ◽  
G. Yamada ◽  
Y. Muramoto

An analysis is presented for the free vibration of a circular cylindrical shell restrained by axially spaced elastic springs. The governing equations of vibration of a circular cylindrical shell are written as a coupled set of first-order differential equations by using the transfer matrix of the shell. Once the matrix has been determined, the entire structure matrix is obtained by the product of the transfer matrices and the point matrices at the springs, and the frequency equation is derived with terms of the elements of the structure matrix under the boundary conditions. The method is applied to circular cylindrical shells supported by axially equispaced springs of the same stiffness, and the natural frequencies and the mode shapes of vibration are calculated numerically.


1991 ◽  
Vol 113 (4) ◽  
pp. 511-516 ◽  
Author(s):  
M. Takayanagi

A procedure for analyzing parametric resonance of liquid storage axisymmetric shells is proposed that is an extension of the procedure presented at PVP-89 for parametric resonance of empty axisymmetric shells with lumped weights. Free vibration modes of axisymmetric shells containing liquid are calculated considering the effect of initial stress due to static liquid pressure by using a conical shell finite element. The calculated free vibration modes are used to expand the free vibration modes of the axisymmetric shell with lumped weights and internal liquid. A type of Mathieu equation is derived considering the effects of the translational motion of the attached weight in the radial direction or the effects of the beam-type motion of the shell without lumped weight. The harmonic balance method is used to obtain the parametric resonance regions. Principal resonance of a circular cylindrical shell with an attached weight and combination resonance of a liquid storage circular cylindrical shell without attached weights are analyzed. Analytical results show good agreement with experimental results.


Author(s):  
Saeed Sarkheil ◽  
Mahmud S Foumani ◽  
Hossein M Navazi

Based on the Sanders thin shell theory, this paper presents an exact solution for the vibration of circular cylindrical shell made of two different materials. The shell is sub-divided into two segments and the state-space technique is employed to derive the homogenous differential equations. Then continuity conditions are applied where the material of the cylindrical shell changes. Shells with various combinations of end boundary conditions are analyzed by the proposed method. Finally, solving different examples, the effect of geometric parameters as well as BCs on the vibration of the bi-material shell is studied.


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