Piezoelectric Modes of Vibration

Vibration ModeDimensionsConstants to be calculated
L-Length W-Width T-Thickness D-DiameterPiezoelectricMechanical
Transverse Length ModeTransverse length mode

T, W > L/3

k31, d31, g31, ε33Ts11 D, s11E, Q31
Radial Mode

T, W > D > 5T

kp, ε33 s, ε33TσE, s12E, Qp
Thickness Extension Mode


Kt, ε33 sc33 D, c33 E, s13E Qt
Longitudinal Length Mode

D > L/5

k33, d33, g33, ε33Ts33 D, s33E, Q33
Thickness Shear Mode

L, W > 8T

k15, d15, g15, ε11T, ε11sc55 D, s55 D, s55E Q15