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

Tadashi Okabe; Takahiro Kondou; Hirofumi Watanabe

doi:10.1299/kikaic.74.1971

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

Tadashi Okabe, Takahiro Kondou, Hirofumi Watanabe

Dynamics of Mechanical Systems

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

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
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
DOIs	https://doi.org/10.1299/kikaic.74.1971
Publication status	Published - Aug 2008

All Science Journal Classification (ASJC) codes

Mechanics of Materials
Mechanical Engineering
Industrial and Manufacturing Engineering

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10.1299/kikaic.74.1971

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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.",

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AU - Kondou, Takahiro

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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.

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

Abstract

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