轴向运动弦线横向振动的频域分析

轴向运动弦线是多种工程系统的模型。为明确轴向运动横向振动的频域特性，及探索频域方法的应用特点．本文用频域方法分析轴向运动弦线的横向振动。基于轴向运动弦线横向振动方程和边界条件．通过Laplace变换导出频率域中的控制方程，并将该控制方程和边界条件用状态变量表示。由状态空间中的控制方程导出特征方程，从而求出固有频率。由轴向运动弦线的矩阵函数计算得到系统的传递函数，然后用留数定理计算传递函数的Laplace逆变换．这样就可以得到时域响应。最后分析了轴向运动弦线的横向共振，若简谐外激励的频率与系统固有频率相同，系统响应将随时间无限增加。

Frequency Domain Analysis for Transverse Vibration of Axially Moving Strings

Axially moving strings can represent many engineering devices. In order to understand the transverse vibration in the frequency domain, and to explore the application of frequency domain analysis, the transverse vibration of axially moving strings was analyzed by the frequency domain mehtod. The Laplace transform was applied to change the governing equation of the transverse vibration of axially moving strings from time domain into frequency domain. The transformed governing equation and boundary conditions were expressed in terms of the state variables. The characteristic equation was derived from the governing equation in the state space, and the natural frequencies were solved from the characteristic. The transfer function was derived from the matrix function of axialy moving strings. Then the inverse Laplace transform, with the residue theorem, was employed to calculate the time domain response from the frequency domain response. Finally the transverse resonance of axially moving strings was easily analyzed. It is found that the response would increase with the time if the frequency of the external simple harmonic excitation is equal to one of the string's natural frequencies.