Jg. Smits et A. Ballato, DYNAMIC ADMITTANCE MATRIX OF PIEZOELECTRIC CANTILEVER BIMORPHS, Journal of microelectromechanical systems, 3(3), 1994, pp. 105-112
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 f
orce p and voltage V to their response parameters: the tip rotation al
pha, the tip deflection delta, the volumetric displacement V and the e
lectrode charge Q, have been determined, The electrical element of thi
s matrix is the (4,4) element, which is the electrical capacitance, he
nce we call this the dynamic admittance matrix, It is a four by four s
ymmetric matrix having a purely electrical part, a purely elastic part
and a mixed (piezoelectric) part, A common factor in nearly all eleme
nts describes the resonance frequencies that are to be expected. [88]