Dynamic admittance matrix of piezoelectric cantilever bimorphs

The matrix that relates the harmonically varying driving parameters: a moment M at the tip, a force F at the tip, a uniformly applied body force p and voltage V to their response parameters: the tip rotation α, the tip deflection δ, the volumetric displacement V and the electrode charge Q, have been determined. The electrical element of this matrix is the (4,4) element, which is the electrical capacitance, hence we call this the dynamic admittance matrix. It is a four by four symmetric matrix having a purely electrical part, a purely elastic part and a mixed (piezoelectric) part. A common factor in nearly all elements describes the resonance frequencies that are to be expected