Stability analysis for parametric resonances of frame structures using dynamic axis-force transfer coefficient

Structures ◽  
2021 ◽  
Vol 34 ◽  
pp. 3611-3621
Author(s):  
Wei Liu ◽  
Yuchun Li
Keyword(s):  
Stability Analysis ◽  
Transfer Coefficient ◽  
Frame Structures ◽  
Force Transfer ◽  
Parametric Resonances

Destabilization of a vortex by acoustic waves

2000 ◽  
Vol 414 ◽  
pp. 315-337 ◽  
Author(s):  
STÉPHANE LEBLANC
Keyword(s):  
Stability Analysis ◽  
Vortex Core ◽  
Acoustic Waves ◽  
Periodic Potential ◽  
Three Dimensional ◽  
Basic Flow ◽  
Almost Periodic ◽  
The Core ◽  
Parametric Resonances ◽  
Time Periodic

The linear stability of a circular vortex interacting with two plane acoustic waves propagating in opposite directions is investigated. When the wavelength is large compared to the size of the vortex, the core is subjected to time-periodic compressions and strains. A stability analysis is performed with the geometrical optics approximation, which considers short-wavelength perturbations evolving along the trajectories of the basic flow. On the vortex core, the problem is reduced to a single Hill–Schrödinger equation with periodic or almost-periodic potential, the solution to which grows exponentially when parametric resonances occur. On interacting with the acoustic waves, the circular vortex is thus unstable to three-dimensional perturbations.

scholarly journals Identifying Critical Loads of Frame Structures with Equilibrium Equations in Rate Form

2015 ◽  
Vol 2015 ◽  
pp. 1-17
Author(s):  
Zhaohui Qi ◽  
Xianchao Kong ◽  
Gang Wang
Keyword(s):  
Stability Analysis ◽  
Critical Load ◽  
Large Scale ◽  
Frame Structures ◽  
Engineering Practice ◽  
Nonlinear Stability Analysis ◽  
Governing Equations ◽  
Equilibrium Equations ◽  
Stiffness Matrices ◽  
Rate Form

Frame structures are widely used in engineering practice. They are likely to lose their stability before damage. As an indicator of load-carrying capability, the first critical load plays a crucial role in the design of such structures. In this paper, a new method of identifying this critical load is presented, based on the governing equations in rate form. With the presented method, a great deal of well-developed numerical methods for ordinary differential equations can be used. As accurate structural tangent stiffness matrices are essential to stability analysis, the method to obtain them systematically is discussed. To improve the computational efficiency of nonlinear stability analysis in large-scale frame structures, the corotational substructure elements are formulated as well to reduce the dimension of the governing equations. Four examples are studied to illustrate the validity and efficiency of the presented method.

Stability analysis of frame structures by bubble-function method

2009 ◽  
Vol 45 (8-9) ◽  
pp. 495-500 ◽  
Author(s):  
Xuanneng Gao ◽  
Haoming Zhu ◽  
Renhui Wang
Keyword(s):  
Stability Analysis ◽  
Function Method ◽  
Frame Structures ◽  
Bubble Function

Vibration and Stability Analysis of Axially Moving Beams with Variable Speed and Axial Force

2014 ◽  
Vol 14 (06) ◽  
pp. 1450015 ◽  
Author(s):  
Bozkurt Burak Özhan
Keyword(s):  
Stability Analysis ◽  
Axial Force ◽  
Multiple Time Scales ◽  
Axially Moving Beam ◽  
Multiple Time ◽  
Vibration Model ◽  
Moving Beam ◽  
Parametric Resonances ◽  
Axially Moving ◽  
Beam Parameters

The well-known vibration model of axially moving beam is considered. Both axial moving speed and axial force are assumed to vary harmonically. The Method of Multiple Time Scales (a perturbation method) is used. The natural vibrations of beam are considered for different values of beam parameters. Resonances are obtained for seven different conditions. Solvability conditions for each resonance case are found analytically. Effects of transport velocity, axial force, rigidity and damping are discussed. Stability analysis are obtained for principal parametric resonances. Stable and unstable regions are obtained regarding velocity and force effects separately and together.

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