A Simple Collocation Scheme for Obtaining the Periodic Solutions of the Duffing Equation , and its Equivalence to the High Dimensional Harmonic Balance Method : Subharmonic Oscillations

@inproceedings{Dai2012ASC,
  title={A Simple Collocation Scheme for Obtaining the Periodic Solutions of the Duffing Equation , and its Equivalence to the High Dimensional Harmonic Balance Method : Subharmonic Oscillations},
  author={Hong-Hua Dai and Matt Schnoor and Satya N. Atluri},
  year={2012}
}
In this study, the harmonic and 1/3 subharmonic oscillations of a single degree of freedom Duffing oscillator with large nonlinearity and large damping are investigated by using a simple point collocation method applied in the time domain over a period of the periodic solution. The relationship between the proposed collocation method and the high dimensional harmonic balance method (HDHB), proposed earlier by Thomas, Dowell, and Hall (2002), is explored. We demonstrate that the HDHB is not a… CONTINUE READING
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