On the instability of the equilibrium for a Lagrangian system with gyroscopic forces

1994 ◽  
Vol 1 (4) ◽  
pp. 313-322 ◽  
Author(s):  
Alessandra Celletti ◽  
Piero Negrini
Keyword(s):  
Lagrangian System ◽  
Gyroscopic Forces

Vibration and Stability Control of Spinning Flexible Shaft via Integration of Smart Materials Technology

2000 ◽  
Author(s):  
Ohseop Song ◽  
Liviu Librescu ◽  
Nam-Heui Jeong
Keyword(s):  
Smart Materials ◽  
Stability Control ◽  
Rotational Axis ◽  
Rotating Shaft ◽  
Nonconservative System ◽  
Gyroscopic Forces ◽  
Points Of View ◽  
The Stability ◽  
Spinning Speed ◽  
Static Character

Abstract Within this paper problems related with the vibration and stability control of circular flexible shafts spinning about their rotational axis are addressed. Due to the occurrence, as a result of the spinning speed, of gyroscopic forces in the system, the rotating shaft can experience, in some conditions, instabilities of the same nature as any nonconservative system, namely divergence and flutter instabilities. Whereas the former instability is of a static character, the latter one is of dynamic character and the results of its occurrence are catastrophic. By including collocated sending and actuating capabilities via integration in the system of piezoelectric devices and of a feedback control law, it is shown that a dramatic enhancement of both the free dynamic response and of the stability behavior from both the divergence and flutter points of view can be achieved. This implies that via the implementation of this technology an increase of the spinning speed can be achieved without the occurrence of these instabilities. Numerical simulations documenting these findings are provided and pertinent conclusions are outlined. It is also worthy to mention that the shaft is modeled as a thin-walled cylinder made of an anisotropic material and incorporating a number of non-classical features.

A Lagrangian system with an exponential-type potential

2003 ◽  
Vol 317 (1-2) ◽  
pp. 120-126
Author(s):  
Toshio Yoshikawa
Keyword(s):  
Exponential Type ◽  
Lagrangian System ◽  
Type Potential

On the covering of a Hill’s region by solutions in systems with gyroscopic forces

2017 ◽  
Vol 148 ◽  
pp. 138-146 ◽  
Author(s):  
Valery Kozlov ◽  
Ivan Polekhin
Keyword(s):  
Gyroscopic Forces
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