電動力學中衰減機械系統的非線性振蕩方法

Abstract

衰減機械系統的非線性振蕩可用來研究長約瑟夫遜結的電動力學方程式，而這方程式等同於弱衰減機械系統的非線性振蕩。本文應用的方法是將控制方程線性化及結合諧波平衡法（線性諧波平衡法）而產生色散關係，再把平均法應用在弱非線性的耗散系統中得到非常準確的瞬變反應。在此提出的方法不僅考慮能量耗散，而且利用簡單的線性代數等式關係來代替冗長及覆雜的分析近似解。

The nonlinear oscillation of damped mechanical systems is applied to investigate the electrodynamics of long Josephson junction. The latter has been shown as equivalent to the weakly damped mechanical nonlinear oscillation system. This paper applies the combination of linearized governing equation and harmonic balancing method (LHBM) to yield the dispersion relation. The application of the method of averaging is then employed to achieve very accurate transient responses of the weekly dissipative system. The proposed approach herein not only accounts for energy dissipation but also presents the relationship of simple linear algebraic equations instead of lengthy and complicated analytical approximate solutions.