The subharmonic bifurcation solution of nonlinear Mathieu's equation and Euler dynamic buckling problems

1988 ◽  
Vol 4 (4) ◽  
pp. 350-362 ◽  
Author(s):  
Chen Yushu ◽  
W. F. Langford
Keyword(s):  
Dynamic Buckling ◽  
Subharmonic Bifurcation ◽  
Mathieu’S Equation ◽  
Bifurcation Solution

scholarly journals Swaying gel: chemo-mechanical self-oscillation based on dynamic buckling

Matter ◽  
2021 ◽  
Author(s):  
Mutian Hua ◽  
Cheolgyu Kim ◽  
Yingjie Du ◽  
Dong Wu ◽  
Ruobing Bai ◽  
...  
Keyword(s):  
Dynamic Buckling

Dynamic Buckling of Cylindrical Shells under Axial Impact in Hamiltonian System

2012 ◽  
Vol 13 (1) ◽  
Author(s):  
Jia-Bin Sun ◽  
Xin-Sheng Xu ◽  
Chee-Wah Lim
Keyword(s):  
Hamiltonian System ◽  
Critical Load ◽  
Impact Load ◽  
Dynamic Buckling ◽  
Inertia Force ◽  
Elastic Cylindrical Shell ◽  
Symplectic Method ◽  
Buckling Mode ◽  
Axial Impact ◽  
Dual Variables

AbstractIn this paper, the dynamic buckling of an elastic cylindrical shell subjected to an axial impact load is analyzed in Hamiltonian system. By employing a symplectic method, the traditional governing equations are transformed into Hamiltonian canonical equations in dual variables. In this system, the critical load and buckling mode are reduced to solving symplectic eigenvalues and eigensolutions respectively. The result shows that the critical load relates with boundary conditions, thickness of the shell and radial inertia force. And the corresponding buckling modes present some local shapes. Besides, the process of dynamic buckling is related to the stress wave, the critical load and buckling mode depend upon the impacted time. This paper gives analytically and numerically some new rules of the buckling problem, which is useful for designing shell structures.

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