Study on high performace averaging method for systems based on quadratic spring system with strong nonlinearity

Tadashi Okabe, Takahiro Kondou, Hideyuki Tsumura

Research output: Contribution to journalArticle

Abstract

In order to obtain a highly accurate periodic solution for systems based on strongly quadratic nonlinear oscillators, an averaging method improved through the use of the Jacobian elliptic function is proposed. In the improved averaging method, the Jacobian elliptic sine function is incorporated as the generating solution. The stability criterion for the approximate solutions obtained by this method is also presented. The proposed method is then applied to several different typical nonlinear oscillators. The efficiency of the proposed method is demonstrated by comparing the computational results with those obtained by the shooting method and the conventional averaging method. It is confirmed that the proposed method provides a more accurate solution than the conventional averaging method, which uses a trigonometric function as the generating solution.

Original languageEnglish
Pages (from-to)5-12
Number of pages8
JournalNihon Kikai Gakkai Ronbunshu, C Hen/Transactions of the Japan Society of Mechanical Engineers, Part C
Volume71
Issue number1
Publication statusPublished - Jan 1 2005
Externally publishedYes

Fingerprint

Stability criteria

All Science Journal Classification (ASJC) codes

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

Cite this

@article{58022c8fdebb454796f1f7b77f8cc444,
title = "Study on high performace averaging method for systems based on quadratic spring system with strong nonlinearity",
abstract = "In order to obtain a highly accurate periodic solution for systems based on strongly quadratic nonlinear oscillators, an averaging method improved through the use of the Jacobian elliptic function is proposed. In the improved averaging method, the Jacobian elliptic sine function is incorporated as the generating solution. The stability criterion for the approximate solutions obtained by this method is also presented. The proposed method is then applied to several different typical nonlinear oscillators. The efficiency of the proposed method is demonstrated by comparing the computational results with those obtained by the shooting method and the conventional averaging method. It is confirmed that the proposed method provides a more accurate solution than the conventional averaging method, which uses a trigonometric function as the generating solution.",
author = "Tadashi Okabe and Takahiro Kondou and Hideyuki Tsumura",
year = "2005",
month = "1",
day = "1",
language = "English",
volume = "71",
pages = "5--12",
journal = "Nippon Kikai Gakkai Ronbunshu, C Hen/Transactions of the Japan Society of Mechanical Engineers, Part C",
issn = "0387-5024",
publisher = "The Japan Society of Mechanical Engineers",
number = "1",

}

TY - JOUR

T1 - Study on high performace averaging method for systems based on quadratic spring system with strong nonlinearity

AU - Okabe, Tadashi

AU - Kondou, Takahiro

AU - Tsumura, Hideyuki

PY - 2005/1/1

Y1 - 2005/1/1

N2 - In order to obtain a highly accurate periodic solution for systems based on strongly quadratic nonlinear oscillators, an averaging method improved through the use of the Jacobian elliptic function is proposed. In the improved averaging method, the Jacobian elliptic sine function is incorporated as the generating solution. The stability criterion for the approximate solutions obtained by this method is also presented. The proposed method is then applied to several different typical nonlinear oscillators. The efficiency of the proposed method is demonstrated by comparing the computational results with those obtained by the shooting method and the conventional averaging method. It is confirmed that the proposed method provides a more accurate solution than the conventional averaging method, which uses a trigonometric function as the generating solution.

AB - In order to obtain a highly accurate periodic solution for systems based on strongly quadratic nonlinear oscillators, an averaging method improved through the use of the Jacobian elliptic function is proposed. In the improved averaging method, the Jacobian elliptic sine function is incorporated as the generating solution. The stability criterion for the approximate solutions obtained by this method is also presented. The proposed method is then applied to several different typical nonlinear oscillators. The efficiency of the proposed method is demonstrated by comparing the computational results with those obtained by the shooting method and the conventional averaging method. It is confirmed that the proposed method provides a more accurate solution than the conventional averaging method, which uses a trigonometric function as the generating solution.

UR - http://www.scopus.com/inward/record.url?scp=18344366384&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=18344366384&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:18344366384

VL - 71

SP - 5

EP - 12

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 - 1

ER -