Study on Primary Resonance of Multi-Degree-of-Freedom Dynamic Systems With Strongly Non-Linearity Using the Homotopy Analysis Method

YUAN Pei-xin; LI Yong-qiang

doi:10.3879/j.issn.1000-0887.2010.10.010

Volume 31 Issue 10

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YUAN Pei-xin, LI Yong-qiang. Study on Primary Resonance of Multi-Degree-of-Freedom Dynamic Systems With Strongly Non-Linearity Using the Homotopy Analysis Method[J]. Applied Mathematics and Mechanics, 2010, 31(10): 1229-1238. doi: 10.3879/j.issn.1000-0887.2010.10.010

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Study on Primary Resonance of Multi-Degree-of-Freedom Dynamic Systems With Strongly Non-Linearity Using the Homotopy Analysis Method

doi: 10.3879/j.issn.1000-0887.2010.10.010

YUAN Pei-xin¹,
LI Yong-qiang²

1.
Mechanical Engineering and Automation School, Northeastern University, Shenyang 110004, P. R. China;

Received Date: 1900-01-01
Rev Recd Date: 2010-09-03
Publish Date: 2010-10-15

Abstract

Abstract

The homotopy analysis method (HAM) was presented for the primary resonance of multidegree-of-freedom system with strongly non-linearity excited by harmonic forces.The validity of the HAM is independent of whether or not there are small parameters in the considered equation.The HAM has provided a simple way to adjust and control the convergence region of the series solution by means of an auxiliary parameter h.Two examples were presented to show that the HAM solutions agree well with the results of the modified Linstedt-Poincarémethod and the incremental harmonic balance method.
- homotopy analysis method,
- primary resonance,
- strongly non-linearity,
- series solution,
- multi-degree-of-freedom

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References(23)

References

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