Parametric Resonance of a Self-Excited System Under External Force and Time Delay Influence

2013 ◽  
Author(s):  
Jerzy Warminski ◽  
Anna Warminska
Keyword(s):  
Time Delay ◽  
External Force ◽  
Parametric Resonance ◽  
Parametric Excitation ◽  
Multiple Time ◽  
Frequency Locking ◽  
Scale Method ◽  
Rayleigh Function ◽  
Excited System ◽  
Multiple Time Scale Method

Vibrations of a nonlinear self-excited system driven by parametric excitation are presented in the paper. The considered model with one DOF includes a self-excitation term represented by a nonlinear Rayleigh function and also a periodically varied stiffness coefficient which represents parametric excitation. The influence of the external force or/and time delay, treated as a control signal, is demonstrated. Nonlinear parametric resonance is determined numerically and analytically by the multiple time scale method. The influence of time delay on the resonance zones and the frequency locking phenomenon is analysed.

VIBRATION ANALYSIS OF A SELF-EXCITED SYSTEM WITH PARAMETRIC FORCING AND NONLINEAR STIFFNESS

1999 ◽  
Vol 09 (03) ◽  
pp. 493-504 ◽  
Author(s):  
GRZEGORZ LITAK ◽  
GRZEGORZ SPUZ-SZPOS ◽  
KAZIMIERZ SZABELSKI ◽  
JERZY WARMIŃSKI
Keyword(s):  
Floquet Theory ◽  
Multiple Time ◽  
Nonlinear Stiffness ◽  
Multiple Time Scale ◽  
Van Der Pol ◽  
Scale Method ◽  
Excited System ◽  
Excited Oscillator ◽  
Parametric Forcing ◽  
Multiple Time Scale Method

Vibrations of a self-excited oscillator under parametric excitation with nonlinear stiffness were investigated in this paper. Differential equation of motion includes van der Pol, Mathieu and Duffing terms. Vibrations synchronization, stability of solutions were examined by means of the multiple time scale method and Floquet theory. Chaotic solutions were found by means of Lyapunov exponent.

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