PSI - Issue 23

Viacheslav Mokryakov et al. / Procedia Structural Integrity 23 (2019) 143–148 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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plane, and the stresses on the axis and on the surface differ insignificantly. Such a case has been described in many sources (see, for example, [6]). On the contrary, for high frequencies (more than 2 MHz), both relations exponentially tend to zero with increasing frequency. That is, the maximum stresses on the surface are much higher than on the axis. The phase velocity is close to the Rayleigh velocity c R ; the wavelength is less than the radius of the rod. The calculation of the stress-strain state shows that with increasing frequency, the wave is localized at the surface, and tends to the shape of the Rayleigh wave. This effect is also known, it can be considered as confirmation of the correctness of calculations. Let us now consider waves whose lengths are comparable with the thickness of the rod (this corresponds approximately to the range of 0.7 MHz < ω < 1.2 MHz). As the plot shows, the ratio R tension reaches 3.164 at a frequency of 824 kHz. Also, the ratio R shear reaches 4.056 at a frequency of 949 kHz. Fig. 3 represents the distribution of σ 1 over the longitudinal section of the rod; fig. 4 shows the distribution of σ Mises . Both graphs show that at these frequencies, the maximum stresses are localized on the axis of the rod.

Fig. 1. Dispersion relation for axisymmetric longitudinal Pochhammer – Chree waves