A field method in the study of weakly non-linear two-degree-of-freedom oscillatory systems

2004 ◽  
Vol 271 (1-2) ◽  
pp. 464-468 ◽  
Author(s):  
Ivana Kovacic
Keyword(s):  
Field Method ◽  
Degree Of Freedom ◽  
Oscillatory Systems ◽  
Non Linear ◽  
Two Degree Of Freedom

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.

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.

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