Exact Solutions of the Autonomous Duffing Equation and Their Computation : Expression of Solutions and Trial Calculation of a Characteristic Parameter) : Vibration, Control Engineering, Engineering for Industry

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概要

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• Exact solutions of the autonomous Duffing equation, including the so-called snap-through spring system, are obtained in the Fourier expansion using elliptic functions. The characteristic parameter J in Fourier coefficients and/or the governing parameter m (or the complementary parameter m_1) of the complete elliptic integral of the first kind, K(m), must be determined to satisfy conditions which are characterized by the situation of the system as well as the natural (non-dimensional) frequency ν. In this paper, three algorithms are established to compute parameter m or m_1 exactly, by a trial method, and also three approximate formulae to express J are proposed. The solutions are grouped into five classes according to the characteristics of the spring system and the type of wave form of the vibration. The frequency responses and some salient features of the solutions are examined and illustrated generally. The numerical results of J(ν) are shown in tabular form, in which the relative error is about 10^<-14>.

• 一般社団法人日本機械学会の論文

著者

• TAMURA Hideyuki

  Faculty of Engineering, Kyushu University

• Tamura H

  Dept. Of Mechanical Engineering Faculty Of Engineering Kyushu University

• MATSUDA Yoshiaki

  Faculty of Engineering, Miyazaki University

• Tamura Hideyuki

  Faculty Of Engineering Kyoto University

• Matsuda Yoshiaki

  Faculty Of Engineering Miyazaki University

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