Wave Propagation in Multi-Layered Elastic Beam

In this paper, a spectral finite element model (SFEM) is developed for an n-layered elastic beam and subsequently used to investigate its dynamic response and wave propagation characteristics. Each layer of the beam is idealized by a Timoshenko beam, in which shear deformation as well as rotational inertia are included. This higher order theory is critical to capture high frequency response of the multi-layered beam structures. Semi-analytical solutions were determined for the governing equations in order to construct the SFEM. Our frequency predictions were validated by the results of two and three-layer beams in the literature and good correlations were achieved. Fewer elements were used in our SFEM compared to conventional finite element based approaches, which substantially benefits the ultrasonic frequency simulations. Wave propagation responses were calculated for a two-layer beam, in which a notch in the top layer was assumed to represent the damage case. Wave reflection from the notch was observed to indicate the existence of damage. This newly developed SFEM can be served as a platform to conduct comprehensive simulations in order to capture wave propagation characteristics in multi-layered beam structures.