scholarly journals Construction of the Courant-Snyder invariants for the non-linear equations of motion and criterion for the long-term stability of the beam in a storage ring

1993 ◽  
Author(s):  
V. Garczynski
Keyword(s):  
Storage Ring ◽  
Equations Of Motion ◽  
Linear Equations ◽  
Term Stability ◽  
Long Term Stability ◽  
Non Linear ◽  
Linear Equations Of Motion ◽  
Non Linear Equations

scholarly journals Multi-parametric Dynamic Analysis of a Rolling Bearings System

2021 ◽  
Vol 67 (9) ◽  
pp. 421-432
Author(s):  
Almatbek Kydyrbekuly ◽  
Gulama-Garip Alisher Ibrayev ◽  
Tangat Ospan ◽  
Anatolij Nikonov
Keyword(s):  
Harmonic Balance ◽  
Equations Of Motion ◽  
Linear Equations ◽  
Stiffness Coefficient ◽  
Rolling Bearings ◽  
Linear Characteristic ◽  
Non Linear ◽  
Linear Equations Of Motion ◽  
Oscillation Frequencies ◽  
Non Linear Equations

A method for calculating amplitudes and constructing frequency characteristics of forced and self-excited vibrations of a rotor-fluid-foundation system on rolling bearings with a non-linear characteristic based on the method of complex amplitudes and harmonic balance has been developed. Non-linear equations of motion of the rotor-fluid-foundation system are derived, and analytical methods of their solution are presented. Frequencies of fundamental and ultra-harmonic resonances are determined. The intervals between self-oscillation frequencies are estimated. The dependence of amplitudes on the amount of fluid in the rotor cavity, the mass of the foundation, linear imbalance, the value of the stiffness coefficient, and the damping coefficient is shown.

Stability and vibration of a non-linear vehicle and passenger system

2002 ◽  
Vol 216 (2) ◽  
pp. 109-116 ◽  
Author(s):  
K Yu ◽  
A C J Luo ◽  
Y He
Keyword(s):  
Equations Of Motion ◽  
Linear Equations ◽  
Dynamic Responses ◽  
Spring Stiffness ◽  
Torsional Spring ◽  
Non Linear ◽  
Linear Equations Of Motion ◽  
Safety Belts ◽  
The Stability ◽  
Non Linear Equations

A non-linear dynamic model to predict the passenger's response in a vehicle travelling on a rough pavement surface (or a rough terrain) is developed. The corresponding equilibrium and stability are investigated through the non-linear equations of motion for a vehicle and passenger system with impacts. The stability with respect to the torsional spring stiffness of safety belts is illustrated. Based on such a stability condition, the dynamic responses for the vehicle and passenger system with and without impacts are simulated numerically. This investigation shows that a strong torsional spring is required in order to reduce the vibration amplitudes of passengers and to avoid impacts between the vehicle and passenger.

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