Admittance Function of Active Piezoelectric Elements Bonded on a Curved Cracked Beam

Abstract

The electric admittance function of active piezoelectric patches bonded on a circular beam with an open crack is presented, for the purpose of evaluating the health conditions of the cracked beam. A segment of beam covered with piezoelectric actuators is regarded as a piezoelectric sandwich; the motion equation of the sandwich is given by considering its in-plane bending vibration. A 7 × 7 equivalent impedance matrix representing the dynamics of the sandwich is derived, its degenerative form is a 6 × 6 impedance matrix representing the dynamics of the elastic beam. Dividing the whole cracked beam into four segments from the locations of the two ends of the sandwich and the crack location, modeling the open crack as linear spring, and considering the continuum conditions among these segments and the mechanical-electric boundary conditions, the piezoelectric admittance function is lastly obtained by solving these linear impedance equations of the four segments. The modal frequency parameters of the cracked beam system can be extracted from the piezoelectric admittance function. In numerical examples, the effect of the depth and location of the crack on the admittance is examined by analyzing changes in the frequencies of the system. Comparison between the calculated frequency results and the FEM results shows that the piezoelectric admittance function is properly built. The limitation of the present model is also discussed.