Viscoelastically coupled multi-layered spectral elements for analyzing ultrasonic-guided wave propagation in layered structural waveguides: part 2 - TMM

This paper presents an analysis of wave propagation in infinitely periodic multi-layered structural waveguides, approximated as higher-order frame structures combining Mindlin-Herrmann rod and Timoshenko beam theories. The inter-layer interface bonding layer is modeled using distributed systems of spring-dashpot elements to capture its viscoelastic nature. This approach allows for simulating various levels of interface bonding between layers by assigning different values to the spring and damping constants. The analysis employs the Transfer Matrix Method (TMM), which requires identifying unit cells that consist of all unique features. Shear correction factors needed for higher-order frames are computed by comparing the cut-off frequencies of shear and lateral contraction modes with the respective Lamb wavemodes. The TMM yields an overall transfer matrix that relates state vectors at the output end to those at the input end of the unit cell. Bloch’s theorem is then applied to compute dispersion curves, illustrating the behavior of traveling waves within the waveguide. Additionally, the Fourier transform-based Spectral Finite Element Method is utilized to compute time-domain responses. The developed model is used to investigate the impact of unit cell length, interface bonding layer strength, and damping in the interface bonding layer on dispersion curves and time-domain responses. The validity of the model is established by comparing the obtained dispersion curves with those from the Dispersion Calculator and the time-domain responses with the Finite Element responses from COMSOL simulations.