A Method for the Measurement of the k Factor in Lossy Piezoelectric Materials: FEM and Experimental Results

Abstract — In general the coupling factor k is a dimensionless parameter, defined as a particular combination of the dielectric, elastic and piezoelectric constants, which may be useful for the internal energy conversion description in piezoelectric materials. In previous works it was demonstrated that it is possible to define the k factor also in dynamic situations as ratio of energies, and this definition was extended to lossy materials. A method to measure this parameter in these materials was also developed: by using the 1–D analytical model of a piezoelectric element vibrating in the length extensional (rod) mode, it was demonstrated that the dynamic coupling factor can be evaluated by measuring the velocity on the element external surfaces orthogonal to the wave propagation direction, and the voltage across the element. The velocity and the voltage must be measured by supplying the piezoceramic with a current generator, working at the element electrical antiresonance frequency. In this paper a FEM commercial code (ANSYS) is used to test the proposed measurement method; the obtained results confirm those obtained by means of the 1–D model and show that the method can be applied to any vibration mode. We also checked if the method can be applied when an AC voltage generator is used to supply the piezoelectric element; the obtained results confirm its validity an applicability. Finally, the method was applied to measure the dynamic coupling factor of a piezoelectric cylinder vibrating in the rod mode, obtaining results close to numerical previsions.