The constitutive equations of half coated metal core piezoelectric fiber

The half coated metal core piezoelectric fiber (HMPF) is one of the new type piezoelectric devices for sensors and actuators. The constitutive equations of cantilevered HMPFs under various mechanical and electrical loading conditions are derived. The equations can describe the behavior of HMPF subjected to an external voltage V on the electrodes, a bending moment M at the free end of the beam, a lateral force F at the tip of the beam and a uniformly distributed load p on the whole length. The internal energy density of the beam is expressed in mechanical strain and electrical field. The internal energy is calculated by integrating the energy density over the whole volume of the beam. The voltage V, bending moment M, lateral force F, and distributed load p are generalized force acting on the fiber and their corresponding generalized displacement are the charge Q on the electrodes, the tip angle alpha, the tip deflection delta, the areal displacement A of the fiber. The constitutive equations give the dependence of the generalized displacements upon generalized forces. The equations are given in the direct form, with external parameters (M, V), (F, V), and (p, V) as independent variables and also in a linear combination with (M, F, p, V) as variables. The constitutive equations derived in this paper can be used for further analysis of HMPF sensors and actuators. Two experiments, in which a HMPF was used as a sensor or an actuator, were performed to verify the constitutive equations. The experimental results are compared with the numerical results.