Semi-analytical hybrid approach for modelling smart structures and guided wave-based SHM systems for a laminate with multiple delaminations and surface-mounted inhomogeneities

Abstract

An advanced semi-analytical hybrid approach for simulating the dynamic behaviour of guided waves-based SHM system is proposed here. The proposed numerical method simulates wave excitation, scattering and sensing in a multi-layered elastic waveguide with a system of internal delaminations and piezoelectric/elastic inhomogeneities mounted on the surface the waveguide. The frequency domain spectral element method is applied to describe wave motion in surface-mounted obstacles (piezoelectric transducers, stringers, joints etc.), while the advanced boundary integral equation method is employed to calculate piezo-induced or scattered wave-fields propagating in the multi-layered waveguide with multiple delaminations. The crack opening displacements at the delaminations are interpolated via weighted Chebyshev polynomials of the second kind taking into account square-root behaviour at the tips of delaminations. The collocation and Galerkin methods are applied to satisfy boundary conditions in the contact area between surface-mounted inhomogeneities and the multi-layered waveguide. The convergence, the accuracy and the computational costs of the hybrid method are analysed, and the comparison with the finite element method is provided. The presented novel hybrid method grants opportunity to analyse resonance frequencies of a laminate with multiple delaminations and surface mounted inhomogeneties, calculate energy flow transferred from an actuator into the waveguide and provide fast parametric analysis of guided wave propagation in the considered structures.