Semi-analytical hybrid approach for the simulation of layered waveguide with a partially debonded piezoelectric structure

This paper presents an efficient semi-analytical hybrid approach for simulating the dynamic interaction of perfectly bonded or damaged piezoelectric structures with a layered elastic waveguide. In the proposed approach, the frequency domain spectral element method is utilized for the discretization of the finite-sized surface mounted piezoelectric structure, and the semi-analytical boundary integral method is employed for the evaluation of wave phenomena in the host laminate structure. While the spectral element method allows cost-effective simulation of dynamics of a complex-shaped transducer (e.g. curvilinear or with wrapped electrodes), the analytically-based technique reliably describes wave excitation and propagation in multi-layered structures. The coupling of these methods is achieved through the rigorous fulfillment of the boundary conditions at the area of waveguide-transducer contact. Three various combinations of approximation polynomials and surface-load interpolation functions are applied in order to obtain the solution in a frequency domain. The time-domain solution is evaluated employing the inverse Laplace transform. Convergence of the method is confirmed for different bonding conditions. The paper demonstrates the efficiency of the proposed method for the multi-parameter analysis of the dependence of the resonance characteristics on the debonding parameters and contact conditions. The approach can be used for such a crucial task as diagnosing failures of piezoelectric devices incorporated into a structural health monitoring system based on guided waves.