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Z. Zhang, and C. Cheng, "Vibrations of Loudspeaker Cones in the Transitional Range," J. Audio Eng. Soc., vol. 54, no. 7/8, pp. 589-603, (2006 July.). doi: Z. Zhang, and C. Cheng, "Vibrations of Loudspeaker Cones in the Transitional Range," J. Audio Eng. Soc., vol. 54 Issue 7/8 pp. 589-603, (2006 July.). doi:
Abstract: The vibration of the loudspeaker conical diaphragm is analyzed in the transitional frequency range, where the bending waves appear on the cone’s outer part and with increasing frequency gradually cover the entire diaphragm. The displacement patterns in the transitional range are described analytically and numerically along with characteristic frequency equations and the axial admittance. The solution of the equations shows a strong coupling between longitudinal and bending motions. For practical applications, the resonance spacing formula is derived as well as the expression for the first nonbending frequency, which may be considered the theoretical upper limit of the loudspeaker frequency response.

@article{zhang2006vibrations,
author={zhang, zhi-liang and cheng, chang-jun},
journal={journal of the audio engineering society},
title={vibrations of loudspeaker cones in the transitional range},
year={2006},
volume={54},
number={7/8},
pages={589-603},
doi={},
month={july},} @article{zhang2006vibrations,
author={zhang, zhi-liang and cheng, chang-jun},
journal={journal of the audio engineering society},
title={vibrations of loudspeaker cones in the transitional range},
year={2006},
volume={54},
number={7/8},
pages={589-603},
doi={},
month={july},
abstract={the vibration of the loudspeaker conical diaphragm is analyzed in the transitional frequency range, where the bending waves appear on the cone’s outer part and with increasing frequency gradually cover the entire diaphragm. the displacement patterns in the transitional range are described analytically and numerically along with characteristic frequency equations and the axial admittance. the solution of the equations shows a strong coupling between longitudinal and bending motions. for practical applications, the resonance spacing formula is derived as well as the expression for the first nonbending frequency, which may be considered the theoretical upper limit of the loudspeaker frequency response.},}

TY - paper
TI - Vibrations of Loudspeaker Cones in the Transitional Range
SP - 589 EP - 603
AU - Zhang, Zhi-liang
AU - Cheng, Chang-jun
PY - 2006
JO - Journal of the Audio Engineering Society
IS - 7/8
VO - 54
VL - 54
Y1 - July 2006 TY - paper
TI - Vibrations of Loudspeaker Cones in the Transitional Range
SP - 589 EP - 603
AU - Zhang, Zhi-liang
AU - Cheng, Chang-jun
PY - 2006
JO - Journal of the Audio Engineering Society
IS - 7/8
VO - 54
VL - 54
Y1 - July 2006
AB - The vibration of the loudspeaker conical diaphragm is analyzed in the transitional frequency range, where the bending waves appear on the cone’s outer part and with increasing frequency gradually cover the entire diaphragm. The displacement patterns in the transitional range are described analytically and numerically along with characteristic frequency equations and the axial admittance. The solution of the equations shows a strong coupling between longitudinal and bending motions. For practical applications, the resonance spacing formula is derived as well as the expression for the first nonbending frequency, which may be considered the theoretical upper limit of the loudspeaker frequency response.