Non-Linear Torsional Vibration of a Two-Degree-of-Freedom System Having Variable Inertia

1965 ◽  
Vol 7 (1) ◽  
pp. 101-113 ◽  
Author(s):  
B. Porter
Keyword(s):  
Normal Mode ◽  
Torsional Vibration ◽  
Large Amplitude ◽  
Critical Speed ◽  
Degree Of Freedom ◽  
Reciprocating Engine ◽  
Non Linear ◽  
Two Degree Of Freedom

A variant of Kryloff and Bogoliuboff's method is used to analyse the periodic vibrations of a non-linear two-degree-of-freedom system which is an idealization of the crankshaft of a two-cylinder in-line reciprocating engine. It is shown that there are two critical speed ranges associated with each normal mode of the system within which periodic harmonic or subharmonic vibrations of large amplitude can occur as a result of variable-inertia excitation. Extensions of the results to homogeneous in-line engines having any number of cylinders are indicated.

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.

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