达芬-谐波振子解析逼近的新方法

A New Method for Analytical Approximate Solutions to the Duffing-Harmonic Oscillator

LI Peng-song¹,SUN Wei-peng²

(1. College of Science, Northeast China Institute of Electric Power Engineering, Jilin 132012, Jilin Province, China;2. College of Mathematics, Jilin University, Changchun 130012, China)

Received:2005-03-28 Revised:1900-01-01 Online:2006-03-26 Published:2006-03-26
Contact: SUN Wei-peng

Abstract

Abstract: This paper deals with analytical approximate solutions to the Duffing-Harmonic oscillator by a new method. By combining the Newton method and the method of harmonic balance into the rewritten governing equation, we have established improved analytical approximations to the frequency and the corresponding periodic solution of the oscillator. The improved analytical approximations show excellent agreement with the accurate solution, and are valid for the total range of oscillation amplitudes, including the two extreme cases of the oscillation amplitudes respectively approaching zero and infinity.

Key words: Duffing-Harmonic oscillator, Newton method, harmonic balance

CLC Number:

O322

LI Peng-song,SUN Wei-peng. A New Method for Analytical Approximate Solutions to the Duffing-Harmonic Oscillator[J].J4, 2006, 44(02): 170-174.

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A New Method for Analytical Approximate Solutions to the Duffing-Harmonic Oscillator

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