Affiliations: [a] The Aeronautic Key Laboratory for Smart Materials
& Structures, College of Aerospace Engineering, Nanjing University of
Aeronautics and Astronautics, Yudao Street 29, Nanjing, 210016, P.R.
China
Abstract: 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
α, the tip deflection δ, 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.
Keywords: Piezoelectric fiber, metal core, half coated, constitutive equation, sensor and actuator
