Enhancement in modelling Guided Wave propagation by Semi-Analytical Finite Element method for Ultrasonic Nondestructuive Evaluation purposes

The Semi-Analytical Finite Element (SAFE) method for modelling stress guided wave propagation is extended to account for linear viscoelastic materials. The framework is based on the three-dimensional theory of linear elasticity and viscoelastic materials are counted by allowing for complex constitutive tensors in the stress-strain relations. The method describes the wave propagation displacements coupling an approximate field over the waveguide’s cross-section, via finite elements, with exact time harmonic functions in the propagation direction. For plate-like systems and axisymmetric waveguides the displacement field can be best described by using mono-dimensional finite elements while for generic cross-sections (square rod, rail, I beam, etc.), plane bi-dimensional elements must be used. The discretization of the energy balance equation leads the wave equation to a set of algebraic equations. The guided wave dispersive solutions are found by solving a twin-parameter eigenvalue problem in the frequency and wavenumber domain. Dispersive characteristics of viscoelastic waveguides, such as wave phase velocities, wave attenuations, wave energy velocities and wavestructures are obtained. The addition of material damping is proven to have considerable impact on the design of any structural health monitoring technique that uses ultrasonic guided waves for long range inspection. Some successful experimental applications will be presented