Modal Expansion Modeling of the Electro-mechanical (e/m) Impedance Response of 1-d Structures

The electro-mechanical (E/M) impedance response of a 1-D structure interrogated by a PZT wafer active sensor is modeled from first principles. Equations of motion for the flexural vibrations under moment excitation from the PZT wafer are developed. Solution in terms of normal modes with internal damping is obtained. General expressions for pointwise dynamic stiffness and pointwise dynamic compliance are developed. 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. At structural resonance frequencies, the interaction between the real part of the structural dynamic stiffness and the PZT stiffness is directly reflected in the real part of the electro-mechanical impedance. The same behavior is also found in the electro-mechanical admittance. Both reflect the change in structural response, due to the presence of damage and internal flaws.