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Table 1

Properties included in the calculation.

Variable Value Description
Voltage 35 [volt] Amplitude of excitation voltage
d 33 265e−12 [C/N] PZT piezoelectric charge constant (PIC181)
ε 33 1200 × 8.85e−12 PZT permittivity (PIC 181)
t smd 6.5e−3 [m] Thickness of titanium wall
c pzt 4221 [m/s] Longitudinal speed of sound in PZT4
c w 1480 [m/s] Speed of sound in water
c smd 6070 [m/s] Speed of sound in titanium (Engineering Toolbox)
ρ smd 4500 [kg/m3] Titanium density
ρ w 1000 [kg/m3] Water density
ρ pzt 7800 [kg/m3] PZT density (PIC 181)
ν pzt 0.34 Poisson ratio (PIC 181)
Y smd 102.7e9 [Pa] Young’s modulus of titanium GR2 (AmesWeb)
A S 1e−4 [m2] Area of transducer

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