Dynamic stability of a rectangular plate with four free edges subjected to a follower force

AIAA Journal ◽  
1990 ◽  
Vol 28 (7) ◽  
pp. 1300-1305 ◽  
Author(s):  
Ken Higuchi ◽  
Earl H. Dowell
Keyword(s):  
Rectangular Plate ◽  
Dynamic Stability ◽  
Follower Force ◽  
Free Edges

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.

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