根据拉格朗日麦克斯韦方程建立扬声器静圈振动系统的动力学模型,应用多尺度法得到在有界窄带随机激励下扬声器静圈振动系统的一次近似解及其稳态解,导出系统的Ito随机微分方程。采用矩法得到系统均方响应方程,并进行数值计算。分析扬声器静圈系统参数对主共振响应曲线和均方值的影响。主共振稳态解稳定的充分必要条件与系统一阶矩和二阶矩存在的充分必要条件是一样的;系统相轨随着随机扰动强度 的增大,极限环变为扩散的极限环;增大音圈长度、磁场强度可以增大系统主共振的均方值;增大静圈电阻、阻尼系数可以减小系统主共振的均方值。
Abstract
Dynamics model of static coil vibration system of loudspeakers is established based on Lagrange-Maxwell equation. By means of the method of multiple scales to the static coil vibration system of loudspeakers subjected to narrow-band random excitation, the first approximation solution and corresponding to the steady state solution and Ito stochastic differential equation have been obtained. Using moment method the mean-square response equation of the system is derived and numerical analysis is carried out. The influence of the parameters of the static coil vibration system of loudspeakers on the primary resonance response curves and mean-square values have been analyzed. The sufficient and necessary condition for the stability of the primary resonance is the same as the first order moment and the second order moment stability of the system. With the increase of the random disturbance intensity, the limit cycle becomes limit cycle of diffusion and the width increases. Increasing the length of the coil and the magnetic field strength can increase the average value and resonance region of the primary resonance of the system. The mean-square value and the resonance region of the primary resonance can be reduced by increasing the resistance and damping coefficient of the system.
关键词
扬声器 /
静圈 /
拉格朗日麦克斯韦方程 /
多尺度 /
主共振 /
均方响应
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Key words
Loudspeaker /
static coil /
Lagrange-Maxwell equation /
the method of multiple scales method; primary resonance /
mean square response
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