Dynamic Response Analysis and Comparative Study of Circular Cylindrical Shell Subjected to Radial Impact

2007 ◽  
Vol 51 (02) ◽  
pp. 94-103
Author(s):  
Li Xuebin
Keyword(s):  
Cylindrical Shell ◽  
Dynamic Response ◽  
Normal Mode ◽  
Shell Theory ◽  
Circular Cylindrical Shell ◽  
Equations Of Motion ◽  
Response Analysis ◽  
Mode Theory ◽  
Normal Mode Theory ◽  
Exact Derivation

Following Flu¨ gge's exact derivation for the buckling of cylindrical shells, the equations of motion for dynamic loading of a circular cylindrical shell under external hydrostatic pressure have been formulated. The normal mode theory is used to provide transient dynamic response for the equations of motion. The responses of displacements, strain, and stress are obtained for the area of impact, while those outside the area of impact are also calculated. The accuracy of normal mode theory and Timoshenko shell theory are examined in this paper.

Application of Normal Mode Theory and Pseudoforce Methods to Solve Problems With Nonlinearities

1976 ◽  
Vol 98 (2) ◽  
pp. 151-156 ◽  
Author(s):  
A. J. Molnar ◽  
K. M. Vashi ◽  
C. W. Gay
Keyword(s):  
Normal Mode ◽  
Nuclear Reactor ◽  
Equations Of Motion ◽  
Basic Structure ◽  
Type Analysis ◽  
Mode Theory ◽  
Hypothetical Accident ◽  
Normal Mode Theory ◽  
Nonlinear Equations Of Motion ◽  
Tie Rods

In the design of structural systems such as nuclear reactor coolant loops consisting of piping, supports, bumpers, and tie rods, the basic structure is linear. For transient analysis of piping loops under conditions of earthquake and hypothetical accident of pipe rupture, the linear system becomes nonlinear because of forces due to bottoming in gaps, plastic action in the bumper stops or tie rods, etc. The dynamic analysis of such a structure normally employs the direct integration of the governing nonlinear equations of motion. A technique is presented in this paper where conventional normal mode theory is used even though there are nonlinearities. Nonlinearities such as bumper-gap elements, plasticity, etc., are defined as functions of motion and incorporated as generalized pseudoforces. This approach can, to a considerable degree, preserve the benefits of modal type analysis such as physical understanding in terms of frequencies and modes, and adequate and economical solutions using a reduced number of modes.

Approximate Formulas for Cylindrical Shell Free Vibration Based on Vlasov’s and Enhanced Vlasov’s Semi-Momentless Theory

2018 ◽  
Author(s):  
Igor Orynyak ◽  
Yaroslav Dubyk
Keyword(s):  
Cylindrical Shell ◽  
Boundary Conditions ◽  
Circular Cylindrical Shell ◽  
Equations Of Motion ◽  
Middle Surface ◽  
Axial Direction ◽  
Mode Shapes ◽  
Natural Mode ◽  
Transverse Deflection ◽  
Approximate Formulas

Simple approximate formulas for the natural frequencies of circular cylindrical shells are presented for modes in which transverse deflection dominates. Based on the Donnell-Mushtari thin shell theory the equations of motion of the circular cylindrical shell are introduced, using Vlasov assumptions and Fourier series for the circumferential direction, an exact solution in the axial direction is obtained. To improve the results assumptions of Vlasov’s semimomentless theory are enhanced, i.e. we have used only the hypothesis of middle surface inextensibility to obtain a solution in axial direction. Nonlinear characteristic equations and natural mode shapes, are derived for all type of boundary conditions. Good agreement with experimental data and FEM is shown and advantage over the existing formulas for a variety of boundary conditions is presented.

scholarly journals A normal‐mode theory of shallow‐water reverberation

1993 ◽  
Vol 94 (3) ◽  
pp. 1785-1785 ◽  
Author(s):  
Renhe Zhang ◽  
Guoliang Jin ◽  
Dinghua Guan ◽  
Wenhua Li ◽  
Xinfang Qiu
Keyword(s):  
Shallow Water ◽  
Normal Mode ◽  
Mode Theory ◽  
Normal Mode Theory

Normal mode theory for electron-beam plasma amplification

Microwaves ◽  
1963 ◽  
pp. 333-337
Author(s):  
M. Chodorow ◽  
J. C. Eidson ◽  
G. S. Kino
Keyword(s):  
Electron Beam ◽  
Normal Mode ◽  
Mode Theory ◽  
Beam Plasma ◽  
Normal Mode Theory ◽  
Electron Beam Plasma
Sign in / Sign up

Export Citation Format

Share Document