Electromechanical impedance response of a cracked functionally graded beam with imperfectly bonded piezoelectric wafers

Abstract

An analytical model of a cracked functionally graded beam with attached Lead Zirconate Titanate (PZT) actuator/sensors is proposed in the paper for structural health monitoring. In this model, the dynamic behavior of the piezoelectric patches is considered and a viscoelastic law is adopted to describe the bonding imperfection between the piezoelectric patches and the beam. A piecewisely homogeneous beam model is then employed to approximate the original inhomogeneous beam based on the Timoshenko beam theory. The crack in the beam is treated as a massless rotational spring. In order to develop the recursive formulations to reduce the dimension of the final equations in the method of reverberation-ray matrix (MRRM), new local scattering relations are established for this smart beam using a matrix reduction technique. An analytical expression of the electromechanical impedance (EMI) is derived based on the improved MRRM via the recursive formulations. Comparison with existent experimental results and those predicted by other methods, such as the conventional MRRM, the transfer matrix method (TMM), and the finite element method (FEM), is made to validate the proposed analysis. Furthermore, the effects of various parameters including the crack depth on the EMI signatures are highlighted.