Resonance and antiresonance of symmetric cantilevered piezoelectric flexors

The resonances of dynamically excited symmetric piezoelectric bimorphs have been determined from the equations of state. Under the effect of sinusoidal stimuli: an electrode voltage V, a moment exerted at the tip M, a force exerted perpendicular to the plane of the bimorph also applied at the tip F, and a uniformly applied pressure p, they respond with a sinusoidal electrode charge Q, tip rotation α, tip deflection δ, and volume displacement ν. All of the former are related to all of the latter through a dynamic admittance matrix B. We have found the antiresonance frequency of the capacitance C, while also antiresonance in off-diagonal elements is determined. The latter indicate that at these frequencies the bimorph does not work as an actuator or sensor in the particular domain of the off-diagonal. The mode shape at these antiresonance frequencies has been determined. The antiresonance of b₁₄ determines that for this frequency the tip has deflection but no rotation, while the antiresonance of b₂₄ indicates that the tip has rotation but no deflection. No antiresonance in the volume displacement is found, indicating that the bimorph is a pressure converter (microphone) at all frequencies