### Abstract

An improved averaging method is proposed in order to obtain a highly accurate periodic solution composed of only odd order harmonics in a strongly nonlinear dynamical system. In this method, sum of the Jacobian elliptic cosine (en) and sine (sn) function is incorporated as the generating solution. The proposed method is applicable to relatively general nonlinear systems based on Duffing equation. The stability of the solution is analyzed by obtaining the characteristic multipliers of the variational equation. The numerical results for typical nonlinear oscillators are shown. The effectiveness of the proposed method is verified by comparing the computational results with those obtained by the shooting method.

Original language | English |
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Pages (from-to) | 1971-1978 |

Number of pages | 8 |

Journal | Nihon Kikai Gakkai Ronbunshu, C Hen/Transactions of the Japan Society of Mechanical Engineers, Part C |

Volume | 74 |

Issue number | 8 |

Publication status | Published - Aug 1 2008 |

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### All Science Journal Classification (ASJC) codes

- Mechanics of Materials
- Mechanical Engineering
- Industrial and Manufacturing Engineering

### Cite this

*Nihon Kikai Gakkai Ronbunshu, C Hen/Transactions of the Japan Society of Mechanical Engineers, Part C*,

*74*(8), 1971-1978.

**An elliptic averaging method using sum of Jacobian elliptic cosine and sine functions.** / Okabe, Tadashi; Kondou, Takahiro; Watanabe, Hirofumi.

Research output: Contribution to journal › Article

*Nihon Kikai Gakkai Ronbunshu, C Hen/Transactions of the Japan Society of Mechanical Engineers, Part C*, vol. 74, no. 8, pp. 1971-1978.

}

TY - JOUR

T1 - An elliptic averaging method using sum of Jacobian elliptic cosine and sine functions

AU - Okabe, Tadashi

AU - Kondou, Takahiro

AU - Watanabe, Hirofumi

PY - 2008/8/1

Y1 - 2008/8/1

N2 - An improved averaging method is proposed in order to obtain a highly accurate periodic solution composed of only odd order harmonics in a strongly nonlinear dynamical system. In this method, sum of the Jacobian elliptic cosine (en) and sine (sn) function is incorporated as the generating solution. The proposed method is applicable to relatively general nonlinear systems based on Duffing equation. The stability of the solution is analyzed by obtaining the characteristic multipliers of the variational equation. The numerical results for typical nonlinear oscillators are shown. The effectiveness of the proposed method is verified by comparing the computational results with those obtained by the shooting method.

AB - An improved averaging method is proposed in order to obtain a highly accurate periodic solution composed of only odd order harmonics in a strongly nonlinear dynamical system. In this method, sum of the Jacobian elliptic cosine (en) and sine (sn) function is incorporated as the generating solution. The proposed method is applicable to relatively general nonlinear systems based on Duffing equation. The stability of the solution is analyzed by obtaining the characteristic multipliers of the variational equation. The numerical results for typical nonlinear oscillators are shown. The effectiveness of the proposed method is verified by comparing the computational results with those obtained by the shooting method.

UR - http://www.scopus.com/inward/record.url?scp=55549138071&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=55549138071&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:55549138071

VL - 74

SP - 1971

EP - 1978

JO - Nippon Kikai Gakkai Ronbunshu, C Hen/Transactions of the Japan Society of Mechanical Engineers, Part C

JF - Nippon Kikai Gakkai Ronbunshu, C Hen/Transactions of the Japan Society of Mechanical Engineers, Part C

SN - 0387-5024

IS - 8

ER -