Harmonic Balance Analysis of Snap-Through Orbits in an Undamped Duffing Oscillator

2015 ◽  
Vol 137 (6) ◽  
Author(s):  
Smruti R. Panigrahi ◽  
Brian F. Feeny ◽  
Alejandro R. Diaz
Keyword(s):  
Approximate Solution ◽  
Phase Space ◽  
Large Amplitude ◽  
Harmonic Balance ◽  
Duffing Oscillator ◽  
Solution Properties ◽  
Harmonic Balance Analysis ◽  
Balance Analysis ◽  
Large Amplitude Vibrations

A simple nonlinear undamped Duffing oscillator has been studied for its snap-through behavior at large-amplitude vibrations. We present an algorithm that uses the harmonic balance (HB) method to find amplitude and frequency relationships in two- and three-term approximations for solutions that lie outside the separatrix in the phase space. Trends of the approximate solution properties are examined with reference to an analysis of the limit as the trajectory approaches the separatrix.

Harmonic Balance for Large-Amplitude Vibrations in Snap-Through Structures

2014 ◽  
Author(s):  
Smruti R. Panigrahi ◽  
Brian F. Feeny ◽  
Alejandro R. Diaz
Keyword(s):  
Phase Space ◽  
Large Amplitude ◽  
Harmonic Balance ◽  
Duffing Oscillator ◽  
Harmonic Balance Method ◽  
Balance Method ◽  
Large Amplitude Vibrations

A simple nonlinear Duffing oscillator has been studied for its snap-through behavior at large-amplitude vibrations. Using the harmonic balance method we have developed an algorithm to find particular amplitude and frequency relations in two-term and three-term approximations when the solution lies outside of the separatrix on the phase space, i.e. when the oscillator exhibits snap-through behavior.

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