Propagation of plane longitudinal waves in a material with point defects | Mekhanika | kompozitsionnykh | materialov i konstruktsii
> Volume 25 > №4 / 2020 / Pages: 492-508

Propagation of plane longitudinal waves in a material with point defects

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In this paper, we study the propagation of plane longitudinal waves in an infinite medium with point defects located in an nonstationary inhomogeneous temperature field. The problem is considered in a self-consistent formulation, taking into account both the influence of the acoustic wave on the formation and movement of defects, and the influence of defects on the propagation features of the acoustic wave.It is shown that in the absence of heat diffusion, the system of equations reduces to a nonlinear evolution equation, which is a generalization of the Korteweg – de Vries – Burgers equation. By the method of truncated decompositions, an exact solution of the evolution equation in the form of a stationary shock wave with a monotonic decrease has been found. It is noted that dissipative effects due to the presence of defects prevail over the dispersion associated with the migration of defects in the medium. The influence of the initial temperature and type of defects on the main parameters of a stationary wave is studied: velocity, amplitude and front width. Nonlinear waves propagate faster in media with vacancies than in media with interstitials. An increase in the initial temperature leads to an increase in the velocity of the stationary wave if the defects are interstices and to a decrease if defects are vacancies. For harmonic waves, it is shown that the presence of defects in the medium promotes the appearance of frequency-dependent dissipation and dispersion. At low frequencies close to zero, wave attenuation is practically absent, and they propagate at a constant speed close to unity, which does not depend on the type of defects or on their presence. At high frequencies, the waves also propagate at a constant speed, which depends on the type of defects. Harmonic waves have a greater length and speed in media with interstitial than in media with vacancies. The influence of the diffusion parameter on the propagation of a harmonic wave is investigated.