Modeling of the Electro-mechanical (e/m) Impedance Response of a Damaged Composite Beam

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 electromechanical impedance directly reflects the pointwise structural resonances too. The same behavior is also found in the electromechanical 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. *Member, ASME Fellow, ASME INTRODUCTION Health monitoring of structures and machinery is a major concern of the engineering community. Flaws identification, early damage detection, and failure prevention are desiderates with far reaching implications in the management and preservation of nations aging infrastructure. Among structural health monitoring techniques, the electro-mechanical (E/M) impedance for structural health monitoring and non-destructive evaluation is an emerging method that offers distinct advantages. The electro-mechanical (E/M) impedance method has gained acceptance as an effective technique for structural health monitoring, damage detection, and failure prevention (Rogers and Giurgiutiu, 1999; Giurgiutiu and Rogers; 1999). The method uses small-size active sensors intimately bonded to an existing structure, or embedded into a new composite construction. Piezoelectric (PZT) wafer transducers have been widely used to this purpose. Experimental demonstrations have shown that the high-frequency impedance spectrum is directly affected by the presence of damage or defects in the monitored structure. A precursor to the electromechanical impedance method is the mechanical impedance method. This method evolved in the late 1970’s and early 1980’s and was based on measuring the response to force excitation applied normal to structural surface using conventional shakers and velocity transducers. Cawley (1984) studied the mechanical impedance method for nondestructive inspection (NDI). He excited the vibrations of bonded plates using a specialized transducer that simultaneously measures the applied normal force and the induced velocity. In his study, Cawley (1984) extended the work of Lange (1978), and studied the behavior of bonded thin plates, in order to identify local disbonds. Finite element analysis of the vibration of the bonded/disbonded plates was performed, and the impedance to excitation in the normal direction was predicted. The experimental work measured the normal-direction impedance at various locations. A small shaker was used to apply excitation through a force gauge and an accelerometer connected to the structure. The ASME Winter Annual Meeting, ASME Aerospace and Materials Divisions, Adaptive Structures And Material Systems Symposium, November 14-19, 1999, Nashville, TN, AD-Vol. 59, MD-Vol. 87, pp. 39-46.