An admittance function of active piezoelectric elements bonded on a cracked beam

The electric admittance function of the piezoelectric patches bonded on a beam with an open crack is presented, for the purpose of theoretically evaluating the health conditions of the cracked beam. At first, a sandwich beam with two layers of piezoelectric actuators is regarded as a piezoelectric bimorph, and the dynamics of the bimorph is represented by a 5×5 piezoelectric impedance matrix. Secondly, the dynamics of the elastic beam is also represented by a 4×4 impedance matrix, which is a degenerative form of piezoelectric impedance. Thirdly, the open crack is modeled as rotational massless spring and an expression of the equivalent stiffness is adopted, then the spring is used to connect the adjacent elastic beam segments. Furthermore, the cracked beam is represented by three elastic beam segments and one piezoelectric bimorph segment together with one spring. The admittance function of the piezoelectric elements is obtained by solving the linear impedance equations considering the mechanical–electric boundary conditions and the continuum conditions between the beam segments and the spring. Lastly, the effects of the crack depth and location on the admittance are examined in two numeric examples. It is found that the frequency changes and the admittance amplitude changes of the beam due to the crack can be predicted by the piezoelectric admittance function, and the modal frequencies calculated by the proposed method are accord with the results obtained by experiments and other methods. The possible application of the admittance function to detect the crack on the beam is discussed at the end of the paper as well.