Parameters
Silicon Diaphragm (P-type, (100))
Si(100) effective: E_eff = 130 GPa | ν = 0.28 | ρ = 2329 kg/m³
Piezoelectric Film (AlN sputtered — default values)
Acoustic Input & Fluid
Added mass coeff. α = 0.6691 (Lamb, clamped circular plate, 1st mode)
Plot Frequency Range
f₀ in air
—
Hz
f₀ in water
—
Hz
Output Voltage V_oc
—
V (open-circuit)
Peak Deflection w_max
—
nm
Physical Model Summary
Clamped circular diaphragm (Kirchhoff-Love) under uniform pressure → bending strain field → piezoelectric voltage via e₃₁ coupling.
Clamped circular diaphragm (Kirchhoff-Love) under uniform pressure → bending strain field → piezoelectric voltage via e₃₁ coupling.
w₀ = P·a⁴ / (64·D) (static), D = E·h³/(12(1−ν²))
Fluid loading (added mass, Lamb 1921): submerged operation shifts resonance downward.f₀water = f₀air / √(1 + α·ρ_f·a / (ρ_Si·h_Si)) α = 0.6691
Open-circuit voltage from inner electrode (ρ < 1/√2), where S_r+S_θ > 0:V_oc = −(e₃₁/ε₃₃) · h_p · <S_r+S_θ>_avg
Dynamic response uses single-mode 2nd-order transfer function with in-water f₀. Piezo film mechanical contribution neglected (h_p < h_Si/10).