有界窄带激励下扬声器静圈振动系统的主共振

杨志安 1,王帅 2

振动与冲击 ›› 2016, Vol. 35 ›› Issue (23) : 51-55.

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PDF(1345 KB)
振动与冲击 ›› 2016, Vol. 35 ›› Issue (23) : 51-55.
论文

有界窄带激励下扬声器静圈振动系统的主共振

  • 杨志安 1 , 王帅 2
作者信息 +

Primary response of static coil vibration system of loudspeakers Subjected to Narrow-Band Random Excitation

  • YANG Zhi-an1,  WANG Shuai2
Author information +
文章历史 +

摘要

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

Key words

 Loudspeaker / static coil / Lagrange-Maxwell equation / the method of multiple scales method; primary resonance / mean square response

引用本文

导出引用
杨志安 1,王帅 2. 有界窄带激励下扬声器静圈振动系统的主共振[J]. 振动与冲击, 2016, 35(23): 51-55
YANG Zhi-an1, WANG Shuai2. Primary response of static coil vibration system of loudspeakers Subjected to Narrow-Band Random Excitation[J]. Journal of Vibration and Shock, 2016, 35(23): 51-55

参考文献

[1] 王以真. 静电扬声器的理论与实践[J]. 电声技术,2002,02(2):47-51.
   WANG Yi-zhen. Theory and practice of electrostatic loudspeaker [J]. Electro acoustic technology,2002,02(2): 47-51.   
[2] 宗丰德,张志良. 扬声器低频谐波失真的数值分析[J]. 声学技术,2003,22(2):83-86.  
   ZONG Feng-de, ZHANG Zhi-liang. Numerical analysis of total harmonic distortion of a loudspeaker in low frequency range[J]. Acoustic technology,2003,22(2): 83-86.
[3] 陶擎天,倪皖荪,谬国庆,张志良. 强迫力非线性对动圈扬声器跳变现象的影响[J]. 电声技术,1989,04:1-5.
   CHENG Qing-tian, NI Wan-sun, LIAO Guo-qing, ZHANG Zhi-liang. The Influence of Exacted Force Nonlinearity about Jamp Phenomenon in Moving-coil Loudspeakers[J].Electro acoustic technology,1989,04: 1-5.
[4] 杨志安,张玉佳. 扬声器动圈振动系统主共振[C]// 中国力学学会《工程力学》编委会. 第21届全国结构工程学术会议论文集第Ⅲ册[C]. 中国力学学会《工程力学》编委会:
   2012. 439-443.
   YANG Zhi-an, ZHANG Yu-jia. Primary Resonance of Moving Coil Vibration System of Loudspeakers [C]// 《Engineering mechanics》editorial board of the mechanical institute of China. The third book of proceedings of the 21th national conference on structure engineering: 2012. 439-443.
[5] 李健. 扬声器系统非线性振动动力学的研究[D]. 唐山: 河北联合大学,2013
   LI Jian, Study on nonlinear vibration dynamics of loudspeaker systems[D]. Tangshan: Hebei University ,2013.
[6] 徐伟,方同,戎海武. 有界窄带激励下具有黏弹项的Duffing振子[J]. 力学学报,2002,34(5):764-771.
   XU Wei, FANG Tong, RONG Hai-wu. Duffing Oscillator with visco-elastic term under Narrow-Band Random Excitation [J]. Journal of mechanics,2002,34(5): 764-771.
[7] RONG Hai-wu, XU Wei, FANG Tong. Principal Response of Duffing Oscillator to Combined Deterministic and Narrow-Band Random Parametric Excitation[J]. Journal of Sound and Vibration, 1998, 210(4): 483-515.
[8] RONG Hai-wu, MENG Guang, Fang Tong. On the almost-sure asymptotic stability of second-order linear stochastic system[J]. Journal Sound and Vibration,2000,229(3): 491-503.
[9] ZHU WQ. Stochastic Jump and Bifurcation of A Duffing Oscillator Under Narrow-Band Excitation[J]. Acta Mechanica Sinica,1994,01: 73-81.
[10] 朱位秋. 随机振动[M]. 北京:科学出版社,1992.
ZHU WQ. Random Vibration[M], Beijing: Science Press,
1992. 
[11] Nayfeh AH, Serhan SJ.Response statistics of nonlinear systems to combined deterministic and random excitation[J]. International Journal of Nonlinear Mechanics, 1990, 25(5): 493-509.

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