Internal inertia gradient effect on two mode magneto-elastic wave propagation

In this study, two-mode harmonic wave propagation for thick rods subjected to a transverse magnetic field is addressed. The analysis is based on the Mindlin-Herrmann rod theory and the unified strain/inertia gradient model. The effects of the strain and inertial gradient parameters on lower and upper modes under different magnetic field intensities are presented in detail and discussed. This study also includes the single-mode wave propagation analysis based on the Rayleigh-Bishop rod theory, as a special case. An overview of the analysis results shows that the wave propagations in the lower and the upper modes are affected by the strain and inertial gradient parameters, as expected. However, some significant differences are observed in the effects of the internal inertial gradient parameter on these modes. In addition, this analysis reveals the relationship between the inertial gradient and cut-off frequency.