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Loudspeaker Driver - damping

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Hi,

I have noticed that for spider and suspension the Rayleigh damping is specified. The beta parameter is specified as a ratio of certain coefficient (0.14 for spider and 0.46 for suspension) and "omega0". Does anyone know how those coefficients have been obtained? Are those values empirical or somewhere from the literature?

Also, it is also not fully clear to me what is understood by parameter f0 (frequency at which loss factor is given). Could anyone explain that as well?

Thanks in advance!

Regards,

Michal

1 Reply Last Post 03.03.2014, 05:32 GMT-5
Henrik Sönnerlind COMSOL Employee

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Posted: 1 decade ago 03.03.2014, 05:32 GMT-5
Hi,

The data is essentially empirical. The numbers could be estimated from specification sheets for loudspeakers.

Part of the explanation is given by the following quote from the model documentation:

"In most loudspeaker specifications, the suspension is characterized by a mechanical compliance Cs and resistance Rs. In order to keep the resistance constant over a range of frequencies, the material needs to have a damping factor that increases linearly with the frequency or, equivalently, Rayleigh damping with αdM = 0 and a constant βdK = η0/ω0, where η0 is the loss factor measured at the angular frequency ω0. In this model, the frequency where the loss factor is measured is chosen to be near the lowest mechanical resonance of the driver."

Note that the system essentially has one mechanical natural frequency in the interesting frequency band, so it is there that the damping must be tuned.

The relative damping at a certain angular frequency can for Rayleigh damping be written as



Since the loss factor is related to the relative damping by



a frequency proportional loss factor can be obtained with only the beta term in the Rayleigh damping:



So to summarize: You need to know the damping at a certain frequency (which in general is arbitrary) to set beta. Alternatively, you could enter the damping as frequency dependent loss factor, in which case the expression for the loss factor would be e.g. 0.14*freq/40 if the loss factor is 0.14 at 40 Hz.

Regards,
Henrik
Hi, The data is essentially empirical. The numbers could be estimated from specification sheets for loudspeakers. Part of the explanation is given by the following quote from the model documentation: "In most loudspeaker specifications, the suspension is characterized by a mechanical compliance Cs and resistance Rs. In order to keep the resistance constant over a range of frequencies, the material needs to have a damping factor that increases linearly with the frequency or, equivalently, Rayleigh damping with αdM = 0 and a constant βdK = η0/ω0, where η0 is the loss factor measured at the angular frequency ω0. In this model, the frequency where the loss factor is measured is chosen to be near the lowest mechanical resonance of the driver." Note that the system essentially has one mechanical natural frequency in the interesting frequency band, so it is there that the damping must be tuned. The relative damping at a certain angular frequency can for Rayleigh damping be written as [math] \zeta =\frac{ \alpha}{2 \omega} + \frac{\beta \omega}{2} [/math] Since the loss factor is related to the relative damping by [math] \eta = 2 \zeta [/math] a frequency proportional loss factor can be obtained with only the beta term in the Rayleigh damping: [math] \eta = \beta \omega [/math] So to summarize: You need to know the damping at a certain frequency (which in general is arbitrary) to set beta. Alternatively, you could enter the damping as frequency dependent loss factor, in which case the expression for the loss factor would be e.g. 0.14*freq/40 if the loss factor is 0.14 at 40 Hz. Regards, Henrik

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