### Abstract

In the analysis of a discrete nonlinear system, one of the important problems is to derive a steady solution for the nonlinear difference equation characterizing the system. However, the study for the solution method of the difference system has not been sufficient, and examples of the methods being applied to the parametric oscillation are few. This paper presents a method which derives the steady solution for the quasi‐linear difference equation containing a periodic parametric excitation in its weakly nonlinear function with small parameter e. In this method the harmonic balance and the averaging methods used in the solution of the continuous nonlinear differential equation are applied to the discrete system. Since the nonlinear term in the equation is bounded by ε the discrete waveform in the steady state is almost sinusoidal. This paper presents numerical examples for the solutions by the two methods, assuming the solution as the discrete oscillation corresponding to the sinusoid of the continuous system. As a result, the same solution is obtained by either method. Comparing the result with the output waveform obtained directly by the numerical calculation for the fundamental equation, the validity of the approximate solution by the proposed method was verified.

Original language | English |
---|---|

Pages (from-to) | 100-108 |

Number of pages | 9 |

Journal | Electronics and Communications in Japan, Part III: Fundamental Electronic Science (English translation of Denshi Tsushin Gakkai Ronbunshi) |

Volume | 72 |

Issue number | 10 |

DOIs | |

Publication status | Published - 1989 |

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### ASJC Scopus subject areas

- Electrical and Electronic Engineering

### Cite this

*Electronics and Communications in Japan, Part III: Fundamental Electronic Science (English translation of Denshi Tsushin Gakkai Ronbunshi)*,

*72*(10), 100-108. https://doi.org/10.1002/ecjc.4430721010

**Experimental approximate solutions of nonlinear discrete oscillation with parametric excitation.** / Tanaka, Toshiyuki.

Research output: Contribution to journal › Article

*Electronics and Communications in Japan, Part III: Fundamental Electronic Science (English translation of Denshi Tsushin Gakkai Ronbunshi)*, vol. 72, no. 10, pp. 100-108. https://doi.org/10.1002/ecjc.4430721010

}

TY - JOUR

T1 - Experimental approximate solutions of nonlinear discrete oscillation with parametric excitation

AU - Tanaka, Toshiyuki

PY - 1989

Y1 - 1989

N2 - In the analysis of a discrete nonlinear system, one of the important problems is to derive a steady solution for the nonlinear difference equation characterizing the system. However, the study for the solution method of the difference system has not been sufficient, and examples of the methods being applied to the parametric oscillation are few. This paper presents a method which derives the steady solution for the quasi‐linear difference equation containing a periodic parametric excitation in its weakly nonlinear function with small parameter e. In this method the harmonic balance and the averaging methods used in the solution of the continuous nonlinear differential equation are applied to the discrete system. Since the nonlinear term in the equation is bounded by ε the discrete waveform in the steady state is almost sinusoidal. This paper presents numerical examples for the solutions by the two methods, assuming the solution as the discrete oscillation corresponding to the sinusoid of the continuous system. As a result, the same solution is obtained by either method. Comparing the result with the output waveform obtained directly by the numerical calculation for the fundamental equation, the validity of the approximate solution by the proposed method was verified.

AB - In the analysis of a discrete nonlinear system, one of the important problems is to derive a steady solution for the nonlinear difference equation characterizing the system. However, the study for the solution method of the difference system has not been sufficient, and examples of the methods being applied to the parametric oscillation are few. This paper presents a method which derives the steady solution for the quasi‐linear difference equation containing a periodic parametric excitation in its weakly nonlinear function with small parameter e. In this method the harmonic balance and the averaging methods used in the solution of the continuous nonlinear differential equation are applied to the discrete system. Since the nonlinear term in the equation is bounded by ε the discrete waveform in the steady state is almost sinusoidal. This paper presents numerical examples for the solutions by the two methods, assuming the solution as the discrete oscillation corresponding to the sinusoid of the continuous system. As a result, the same solution is obtained by either method. Comparing the result with the output waveform obtained directly by the numerical calculation for the fundamental equation, the validity of the approximate solution by the proposed method was verified.

UR - http://www.scopus.com/inward/record.url?scp=84989423189&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84989423189&partnerID=8YFLogxK

U2 - 10.1002/ecjc.4430721010

DO - 10.1002/ecjc.4430721010

M3 - Article

VL - 72

SP - 100

EP - 108

JO - Electronics and Communications in Japan, Part III: Fundamental Electronic Science (English translation of Denshi Tsushin Gakkai Ronbunshi)

JF - Electronics and Communications in Japan, Part III: Fundamental Electronic Science (English translation of Denshi Tsushin Gakkai Ronbunshi)

SN - 1042-0967

IS - 10

ER -