Comparative analysis of the profile evolutions of an elastic harmonic wave caused by the second and third harmonics

The influence of the second and third harmonics on the evolution of a harmonic longitudinal wave propagating through a nonlinearly elastic material has been simulated for real composite materials (the most typical plots are presented for a granulated composite with copper granules and molybdenum matrix). The frequency and initial amplitude are varied beginning from conditionally small values (at which visible distortions appear after a great number of oscillations) to extremely large values (at which the profile becomes distorted already after the second or third oscillation). Four and three different stages of profile evolution due to the influence of the second and third harmonics, respectively, are observed. It is found out that the effect of the initial amplitude on the evolution process is weaker for the second harmonic, and the effect of the frequency on the evolution process is weaker for the third harmonics. It is also revealed that the ranges of frequencies and initial amplitudes within which the evolution caused by different harmonics is very intensive are different-the effect of the third harmonic is stronger at larger values of both parameters. The effects of both harmonics are tantamount within the boundary ranges where the second harmonic is already predominant and the third harmonic is at the early stage of development.