Numerical verification of an efficient coupled SAFE-3D FE analysis for guided wave ultrasound excitation

Numerical verification of a method to simulate piezoelectric transducers exciting infinite elastic waveguides is presented. The method, referred to as SAFE-3D, combines a 3D finite element (FE) model of a transducer with a 2D semi-analytical finite element (SAFE) model of the waveguide and accounts for the dynamics of the transducer. An interpolation procedure is employed to transfer forces and displacements between the SAFE and 3D FE models, and therefore nodes at the interface between the two models are not required to be coincident. An Abaqus/Explicit analysis, employing a thermal equivalent piezoelectric model and absorbing boundary conditions to prevent end reflections, is used to verify the accuracy of the SAFE-3D model. A piezoelectric transducer attached to the web of a rail and driven with frequency content which excites a mode cut-off is considered. A driving signal which does not contain cut-off frequencies is used for comparison. Time domain displacement results computed using Abaqus/Explicit and SAFE-3D are compared directly. Several methods to alleviate the numerical difficulties encountered by the SAFE-3D method, when transforming frequency domain displacements to the time domain, close to cut-off frequencies are evaluated. It is shown that post-processing methods have a similar effect to adding damping, but are less numerically expensive if iterative tuning of parameters is required. A SAFE-based method to extract modal amplitudes from Abaqus/Explicit time domain results is used to evaluate the accuracy of SAFE-3D in the frequency domain. Good agreement between the SAFE-3D method and results computed using Abaqus/Explicit is achieved, despite the Abaqus/Explicit and SAFE-3D models predicting slightly different cut-off frequencies.