EFFECT OF A CRACK ON THE DYNAMIC STABILITY OF A FREE–FREE BEAM SUBJECTED TO A FOLLOWER FORCE

2000 ◽  
Vol 233 (1) ◽  
pp. 119-135 ◽  
Author(s):  
K.-H. KIM ◽  
J.-H. KIM
Keyword(s):  
Dynamic Stability ◽  
Follower Force ◽  
Free Beam

Dynamic stability of a free-free cylindrical shell under a follower force

AIAA Journal ◽  
2000 ◽  
Vol 38 ◽  
pp. 1070-1077
Author(s):  
Si-Hyoung Park ◽  
Ji-Hwan Kim
Keyword(s):  
Cylindrical Shell ◽  
Dynamic Stability ◽  
Follower Force

Dynamic Stability and Response of Inclined Beams Under Moving Mass and Follower Force

2020 ◽  
pp. 2043004
Author(s):  
D. S. Yang ◽  
C. M. Wang ◽  
J. D. Yau
Keyword(s):  
Dynamic Stability ◽  
Moving Load ◽  
Dynamic Responses ◽  
Follower Force ◽  
Load Force ◽  
Moving Mass ◽  
Concentrated Mass ◽  
Spatial Part ◽  
Method Of Solution ◽  
Fourier Sine Series

This paper is concerned with the dynamic stability and response of an inclined Euler–Bernoulli beam under a moving mass and a moving follower force. The extended Hamilton’s principle is used to derive the governing equation of motion and the boundary conditions for this general moving load/force problem. Considering a simply supported beam, one can solve the problem analytically by approximating the spatial part of the deflection with a Fourier sine series. Based on the formulation and method of solution, sample dynamic responses are determined for a beam that is inclined at 30[Formula: see text] with respect to the horizontal. It is shown that the dynamic response of the beam under a moving mass is rather different from an equivalent moving follower force. Also investigated herein are the dynamic stability of inclined beams under moving load/follower force which are described by four key variables, viz. the speed of the moving mass/follower force, concentrated mass to the beam distributed mass, vibration frequency and the magnitude of the moving mass/follower force. The critical axial load and the critical follower force are different when they are located at different positions in the beam; except for the special case when they are at the end of the beam.

Dynamic Stability of Fluttered Systems Subjected to Parametric Random Excitations

2002 ◽  
Vol 8 (3) ◽  
pp. 291-310 ◽  
Author(s):  
T. H. Young ◽  
T. C. Tseng ◽  
L. S. Song
Keyword(s):  
White Noise ◽  
Dynamic Stability ◽  
Aerodynamic Force ◽  
Normal Modes ◽  
Stochastic Averaging ◽  
Stochastic Averaging Method ◽  
Follower Force ◽  
Spanwise Direction ◽  
White Noise Excitation ◽  
Sample Stability

A general solution for dynamic stability of the fluttered mode of damped, fluttered systems subjected to parametric random excitations is presented in this paper. First, the system equations are pairwisely uncoupled by a modal analysis based on normal modes of the system at the onset of fluttering. The stochastic averaging method is then applied to obtain Ito's equation governing the amplitude of the fluttered mode. Finally, the Lyapunov exponent of the fluttered mode is derived, from which the criterion for asymptotic sample stability of the mode is determined. A cantilevered beam acted upon by a static follower force and a white noise parametric excitation at the free end, and a skew panel subjected to an aerodynamic force in the chordwise direction and a white noise excitation in the spanwise direction are demonstrated as examples. Numerical results show that, although the static follower force or the aerodynamic force exceeds the flutter load, the fluttered mode of the beam or the panel may remain stable in the sense of asymptotic sample stability due to the presence of the white noise excitation.

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