Estimation of the Critical Flutter Load of a Tapered Beam Simultaneously Subjected to a Follower Force and an Axial Force

2009 ◽  
Author(s):  
I. Takahashi
Keyword(s):  
Axial Force ◽  
Follower Force ◽  
Tapered Beam ◽  
Flutter Load

Critical Speeds of Shaft-Disk Systems Subjected to Longitudinal Forces

1997 ◽  
Author(s):  
Lien-Wen Chen ◽  
Hong-Cheng Sheu
Keyword(s):  
Axial Force ◽  
Longitudinal Force ◽  
Numerical Results ◽  
Follower Force ◽  
Numerical Techniques ◽  
Disk System ◽  
Critical Speeds ◽  
Whirl Speed ◽  
The Right ◽  
Left Portion

Abstract The critical speeds of a spinning Timoshenko shaft with an intermediate attached disk subjected to a longitudinal force are analytically solved. The expressions of whirl speed equations for hinged-hinged, hinged-clamped, clamped-hinged, and clamped-clamped rotors are given respectively. The critical speeds of each shaft-disk system are sought from its corresponding whirl speed equation by using simple numerical techniques. The effects of the disk location and the longitudinal force on the critical speeds of the shaft-disk systems are investigated. Numerical results reveal that if the disk locates in the left portion of the shaft, both the primary forward and backward critical speeds for the rotor subjected to a follower force are larger than those subjected to an axial force with the same magnitude. The results are contrary while the disk locates in the right portion of the shaft.

Nonconservative Stability of Gyroscopic Rotor Systems

1993 ◽  
Author(s):  
Hwang-Kuen Chen ◽  
Der-Ming Ku ◽  
Lien-Wen Chen
Keyword(s):  
Direct Method ◽  
Equations Of Motion ◽  
Beam Theory ◽  
Follower Force ◽  
The Finite Element Method ◽  
Nonconservative System ◽  
Rotor Systems ◽  
Eigenvalue Sensitivity ◽  
The Stability ◽  
Flutter Load

Abstract The stability behavior of a cantilevered shaft, rotating at a constant speed and subjected to a follower force at the free end, is studied by the finite element method. The equations of motion for such a gyroscopic system are formulated by using deformation shape functions developed from Timoshenko beam theory. The effects of translational and rotatory inertia, gyroscopic moments, bending and shear deformations are included. In order to determine the critical load of the present nonconservative system more quickly and efficiently, a simple and direct method that utilizes the eigenvalue sensitivity with respect to the follower force is introduced. The numerical results show that for the present nonconservative system, the onset of flutter instability occurs when the first and second backward whirl speeds are coincident. And also, due to the effect of the gyroscopic moments, the critical flutter load decreases as the rotational speed increases.

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