The electro-mechanical (E/M) impedance method has gained acceptance as an effective technique for structural health monitoring, damage detection, and failure prevention. In spite of extensive experimental validation of this novel method, very little work has been dedicated to its modeling. This paper develops a model of the E/M impedance response of a damaged composite beam interrogated by a PZT wafer active sensor. The electromechanical model for the interaction between the beam and the active sensor is developed from first principles. The effective axial force and bending moments induced by the PZT wafer into the beam are considered. Equations of motion for the flexural vibrations of a composite beam under moment excitation are developed. Solution in terms of normal modes with internal damping is obtained. The resulting response and the applied force are utilized to deduce general expressions for pointwise dynamic stiffness and pointwise dynamic compliance. Effective stiffness of the PZT wafer is also calculated, and the complex stiffness ratio for the PZT-structure interaction is determined. Hence, the complex electro-mechanical impedance and admittance are deduced.
A numerical example is given to illustrate the method and test its effectiveness. It is found that the real part of the effective pointwise dynamic stiffness interacts at par with the PZT stiffness at structural resonance frequencies. The imaginary part of the complex stiffness ratio directly reflects the pointwise structural resonances. Consequently, the real part of the electro-mechanical impedance directly reflects the pointwise structural resonances too. The same behavior is also found in the electro-mechanical admittance. Thus, the real part of the E/M impedance and the real part of the E/M admittance are found to be direct measures of the structural response, reflective of damage presence.