Exact static solutions to piezoelectric smart beams including peel stresses: I: Theoretical formulation

This paper presents exact static solutions to smart beams with perfectly bonded or partially debonded piezoelectric (PZT) actuators and sensors including peel stresses. When a PZT patch is bonded on the surface of a beam, both shear and peel stresses exist in the adhesive between the PZT patch and the host beam. In Part I, non-dimensional differential governing equations for infinitesimal elements of the PZT patch and the host beam are formulated firstly, and then the ordinary differential equation (ODE) of the coupled shear and peel stresses are completely solved analytically. The exact solutions are applicable to smart beams with PZT actuators and sensors. When the PZT patches are used as actuators, the solutions give the formulations for the energy transferring shear and peel stresses in the adhesive actuated by the applied voltages, and for the actuated stress resultants and displacements in the host beam. When the PZT patches are used as sensors, the solutions give the shear and peel stresses in the adhesive caused by the loadings, and also the sensing electric charges. When PZT patches are not perfectly bonded to the host beam, i.e., partially debonded, the developed solutions can be tailored to the case of edge debondings, i.e., PZTs with the shortened length