磁场中载流导体系统的解析逼近解

Analytical approximate solutions to oscillation of a current-carrying wire in a magnetic field

采用二阶牛顿-谐波平衡方法构造磁场中载流导体系统的解析逼近解,系统是一个具有非对称恢复力函数的保守振动系统,其恢复力形式导致系统具有强非线性。为提高方法的收敛速度,在对恢复力幂级数展开过程中保留二次项,借助线性化方程分两步求得系统的解析逼近周期与周期解。通过与数值方法构造的精确解对比,验证所得逼近解无论在小振幅还是大振幅情况下都具有较高精度。

In this paper,the second-order Newton harmonic balance method is used to construct the analytical approximation solution of the current-carrying conductor system in the magnetic field.The system is a conservative vibration system with asymmetric restoring force,and its restoring force form causes the system to have strong nonlinearity.In order to improve the convergence speed of the method,the quadratic term is retained in the expansion process of the restoring force power,and the analytical approximation period and periodic solution of the system are obtained in two steps with the help of linearization equation.By comparing with the exact solution constructed by the numerical method,it is verified that the approximate solution obtained has high accuracy for both small amplitude and large amplitude.