Acoustic Doppler and Radiation Pattern for Circular Disk A P

Acoustic Doppler and Radiation Pattern for Circular Disk A PZT circular disk having a material sound speed of 3, 800m/s, density rho =7, 500 kg/m3, relative dielectric constant epsilon_r = 1300, diameter 1.00cm, thickness t, vibrates at its fundamental thickness mode resonance at 1.500MHz. The element is free on its surfaces (ie no backing or matching layer that will effect the resonance frequency). Find the thickness of the disk? Find the next highest resonance of the disk through the thickness for the uniform electric field excitation through the thickness, (ie the material is polarized through the thickness) Plot/Sketch the directional factor in rectangular and polar coordinates. Estimate the Beamwidth? Estimate the Directivity D. What is the low frequency (far below resonance) Capacitance of the piezoelectric element. epsilon_0 = 8.854 times 10^-12 F/m.

Solution

The thickness of the disk is 45mm

Next highest resonance value is 56.

The bandwidth is 67.