有界窄带激励下扬声器静圈振动系统的主共振

摘要

Dynamic model of static coil vibration system of loudspeakers was established based on Lagrange-Maxwell equation.By means of the multi-scale method,the first approximation solution and its steady state solution to the static coil vibration system of loudspeakers subjected to narrow-band random excitation were obtained.Its ITO stochastic differential equation was deduced.Using the moment method,the mean-square response equation of the system was derived and the numerical calculation was done.The influences of parameters of the static coil vibration system of loudspeakers on the primary resonance response curves and their mean-square values were analyzed.It was shown that the sufficient and necessary conditions for the stability of the primary resonance are the same as those for the first order moment and the second order moment of the response of the system;with increase in the random disturbance intensity,the limit cycle of the system becomes the limit cycle of diffusion;with increase in length of the coil and the magnetic field strength,the mean square values of the primary resonance of the system increase;the mean-square values of the primary resonance of the system decrease with increase in resistance and damping coefficient of the static coil vibration system.%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γ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。