External bonding of PZT patches to host structures as sensors and actuators has emerged as a popular method in
smart structural applications such as structural health monitoring and vibration and shape control. Due to the strong
material mismatches between the PZT patch and host structure, severe stress concentration can be induced along the
PZT-host structure interface, which can lead to interface debonding and premature failure of the smart structure. For this
reason, stresses along the PZT-host structure interface are of great research interest. To find the interface stresses,
existing studies commonly adopted a one-way coupling model to simulate the behavior of the piezoelectric patch, in
which the electric displacement field is assumed to be uniform through the thickness of the piezoelectric patch. In this
study, however, a two-way coupling model for the electrical and mechanical field interaction is proposed. The electrical
displacement field in the thickness direction of the piezoelectric patch is assumed to have a parabolic distribution.
Closed-form solutions of interface stresses and electric field are obtained. To verify the model and for comparison
purpose, a numerical example is calculated with different models, along with the numerical solution from finite element
A new damage detection technique using the roughness profile of structural mode shape is developed in this study. In this method, the spatially distributed signal (e.g., displacements or mode shapes) of a damaged structure is treated as an engineering surface. Irregularity of the surface induced by damage in beam-type structure is then treated as the roughness of the surface. A simple algorithm is developed to extract the roughness profile from the surface. The location and severity of damage is then determined by a sudden change on the roughness profile. This method is then applied to the mode shapes of cracked and delaminated beams obtained analytically, from which the damage location and size are determined successfully. As verifications, the proposed method is further applied on the experimentally measured curvature mode shapes to detect damage in carbon/epoxy composite beams. The successful detection of crack and delamination damage in the composite beams demonstrates that the new technique developed in this study can be used efficiently and effectively in damage identification and health monitoring of beam-type structures.