Applying Bending Wave equation in Plates?

[Jbosher]

Hi,

I am currently doing research on Distributed Mode Loudspeakers. These speakers consist of a flat panel set into vibration through an exciter mounted to the back. This causes bending waves to propagate across the panel, exciting the panels natural resonant modes. I have found equations dealing with the Euler beam theory, Kirchhoff plate theory and the Bending Wave theory. However, I am unsure how to apply the result of the equations in order to estimate the sound output of the speaker. The Bending wave formula leaves me with a phase velocity dependent on the frequency - the phase velocity increases with increasing frequency. How do I use this phase velocity?

Thanks

Jason

 

[GregLocock]

research coincidence frequency, and radiation efficiency

Cheers

Greg Locock


New here? Try reading these, they might help FAQ731-376

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[amanuensis]

So it can be supposed that you are able to determine the vibration response of the flat panel...

Now, you have to know a little bit about acoustic radiation.

First thing to know is that the vibration response of a structure can be replaced by a set of monopoles and dipôles.

Each monopole (or dipole) gonna interfere with others monopoles and dipôles depending on the phase relationship between them.

The good news is that when dealing with flat structure, only monopoles have to be considered. Dipôles have no influence.

To go further in this subject, you have to see the Rayleigh's integral which is a specific formulation of the integral equation applied to flat structures such as plate.

A remarkable phenomenom is the acoustic short-circuit. Indeed for a mode, every point of the deflection shape is in phase (0°) or out of phase (180°). Then points in phase and points out of phase annihilate (almost), and only points located near sides and corners of the structure gonna radiate a lot of acoustic energy.

 

[Jbosher]

Thanks for your replies, they have helped me understand it a lot more!

Another quick question,

I have come across the equation for determining the modal or eigeinfrequencies of a plate however I am a bit unsure how to apply it. From here:

http://www.mate.tue.nl/mate/pdfs/10230.pdf

the formula is stated in two ways, 2.1 and 2.2. I understand how the formula from 2.1 is derived, however I am unsure how to use 2.2 with the x and y variables. When I use the formula from 2.1 I do not get the same answers as the table shown in 2.2

Thanks

 

[amanuensis]

eigenfrequency and mode shape are not the same thing! They are related each other. You need to know both (with damping) in order to be able to get the vibration response.

But this is not the more difficult to understand...

Good luck!

 

[spongebob007]

If you have some money to spend look for books by Leo Beranek. They will point you in the right direction.

 

[GregLocock]

There's a lot more recent literature than Beranek, but it is mostly in papers or course notes, as we (automotive NVH) got interested in things like acoustic intensity and statistical energy analysis. But yes, Beranek is always a good place to start.



Cheers

Greg Locock


New here? Try reading these, they might help FAQ731-376

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