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This problem is on the modeling of an unfocused receiving acoustic transducer and compute the electric signal due to the pressure field. I have come up with this simple model in 2D. Basically, the transducer has a flat surface S and the surface is assumed moving in the direction normal to its surface, i.e. direction of the force F.

To the best of my knowledge, the force F is proportionally to the induced electric signal. So the problem becomes computing the F on the transducer surface from the pressure field. The finite difference time-domain method is used to calculate the pressure P and the particle velocity Uy and Uz as shown in the figure.

I have found two possible ways to calculate the force and need some feedback.

a) Linearly interpolate the pressure field on S, and

[tex] F = \int p dl [/tex]

where dl is some small distance on the surface and p denotes the pressure.

b) Linearly interpolate Uy and Uz on S. Since the transducer surface only moves in the direction of F, I could calculate the net velocity

[tex]

U = U_y\sin\theta-U_z\cos\theta

[/tex]

Then, calculate the force through

[tex]

F = -\rho \frac{\partial } {\partial t} U \Delta l

[/tex]

where the next velocity U at the two adjacent time steps are needed for the time derivative.

Since I have not worked with transducer before, firstly, I am not sure if this modeling is correct (the surface is about 3~2 cm in diameter for ultrasound imaging application). Secondly, I am not sure which one (a) or (b) is the proper way to compute the electric signal. My feeling is (b) as it takes into account of the direction. Any discussion or any reference on this kind of modeling is welcome.

Thank you.

Elgen

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# Modeling of an acoustic transducer and calculation of force

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