Coupled Periodic Motion in free Undamped Non-Linear Two-Degree-of-Freedom Systems

1962 ◽  
Vol 4 (2) ◽  
pp. 149-155 ◽  
Author(s):  
R. F. Henry
Keyword(s):  
Periodic Motion ◽  
Degree Of Freedom ◽  
Non Linear ◽  
Two Degree Of Freedom

Non-linear torsional oscillation of a two-degree-of-freedom system incorporating a Hooke joint

1964 ◽  
Vol 277 (1368) ◽  
pp. 92-106 ◽  
Keyword(s):  
Large Amplitude ◽  
Critical Speed ◽  
Torsional Oscillation ◽  
Degree Of Freedom ◽  
Non Linear ◽  
Two Degree Of Freedom

The non-linear torsional oscillation of the system is analyzed by means of a variant of Kryloff and Bogoliuboff’s method. It is shown that each mode of the system can perform oscillations of large amplitude in a number of critical speed ranges, and that hysteresis effects and discontinuous jumps in amplitude are to be expected in these speed ranges if the damping is light.

Forced Oscillations of Non-Linear Two-Degree-of-Freedom Systems

1966 ◽  
Vol 8 (3) ◽  
pp. 252-258 ◽  
Author(s):  
G. N. Bycroft
Keyword(s):  
Numerical Integration ◽  
Transient Response ◽  
Internal Resonance ◽  
Perturbation Technique ◽  
Degree Of Freedom ◽  
Forced Oscillations ◽  
Oscillatory Systems ◽  
Non Linear ◽  
Two Degree Of Freedom ◽  
Good Agreement

This paper shows how the Lighthill-Poincaré perturbation technique may be used to determine the transient response of ‘lightly coupled’ non-linear multi-degree-of-freedom oscillatory systems subject to arbitrary forcing functions. The results in general are complex but simplify in many important cases. A comparison is made between the analytical results and results obtained by a numerical integration of the equations on a computer. Good agreement is noted. The method fails under conditions of ‘internal resonance’ of the system.

Analytical Stability Improvement of the Periodic Vibro-Impact Processes

1999 ◽  
Author(s):  
Jan Awrejcewicz ◽  
Krzysztof Tomczak
Keyword(s):  
Periodic Orbits ◽  
Periodic Motion ◽  
Feedback Loop ◽  
Degree Of Freedom ◽  
Loop Control ◽  
Analytical Stability ◽  
Impact Processes ◽  
Delay Loop ◽  
Sufficient Stability ◽  
Two Degree Of Freedom

Abstract In this paper an attention is focused on stabilisation improvement of periodic orbits of a one- and two-degree-of-freedom nonautonomous vibro-impact systems. This approach, among others, includes two problems. 1. A possibility of a sufficient stability improvement of the considered vibro-impact periodic motion using a feedback loop control is presented. 2. An original analytical averaging technique applied to a one-degree-of-freedom system is demonstrated. It enables to predict the efficient delay loop coefficients in order to achieve the desired stabilisation. In addition, an efficient delay loop control applied to two-degree-of-freedom system is proposed and illustrated.

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