Impedance and admittance matrices of symmetric piezoelectric annular bimorphs and their applications

The 5 x 5 impedance and admittance matrices of a symmetric triple-layer piezoelectric annular bimorph (PAB) are presented and the PAB with the piezoelectric layers partially covering the shim layer in harmonic motion is analyzed using the matrices. The electromechanical flow vectors are defined as the mechanical displacements and rotations at the inner and outer boundaries and the electric current of the piezoelectric layer; the conjugate parameters, i.e., the electromechanical effort vectors, are accordingly defined. The impedance matrix which relates the flow vector with the effort vector is divided into three matrices, the mechanical, electrical, and electromechanical coupling impedance matrices; each matrix is represented by a block network with five ports. The resonance and the antiresonance frequencies and the effective electromechanical coupling factors of the PAB excited by the partially covering piezoelectric layers are then calculated for various boundary conditions imposed at the inner and outer surfaces. The numerical results by the impedance matrix are compared with those by the finite element methods; they are in excellent agreement with each other. It is also shown that the matrix representations can be easily applied to the piezoelectric circular bimorph (PCB) with the extended shim layer.