Axisymmetric waves in a water-like cylinder

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Abstract

The results of an analytical study of the propagation of axisymmetric normal waves in a solid circular waveguide made of a water-like medium are presented. A water-like medium is a medium in which the velocity of shear waves is significantly lower than the velocity of longitudinal waves. It is shown that the propagation velocities of normal waves are approximately equal to the propagation velocities in a liquid cylinder. This result is radically different from the common statement in the literature that the propagation velocities of normal waves at high frequencies are approximately equal to the velocity of a Rayleigh wave at a flat boundary. The correction to the water-like approximation is calculated, and the contributions of the longitudinal and shear components of the fields for normal waves are obtained. An experimental illustration is provided confirming the results obtained.

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About the authors

M. A. Mironov

Andreev Acoustics Institute

Author for correspondence.
Email: mironov_ma@mail.ru
Russian Federation, 4 Shvernik str., Moscow, 117292

P. A. Pyatakov

Andreev Acoustics Institute

Email: mironov_ma@mail.ru
Russian Federation, 4 Shvernik str., Moscow, 117292

O. A. Savitsky

Andreev Acoustics Institute

Email: mironov_ma@mail.ru
Russian Federation, 4 Shvernik str., Moscow, 117292

S. A. Shulyapov

Andreev Acoustics Institute

Email: mironov_ma@mail.ru
Russian Federation, 4 Shvernik str., Moscow, 117292

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Supplementary files

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2. Fig. 1. Circular elastic cylinder with a coordinate system

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3. Fig. 2. Phase (1, 3, 5, 7) and group (1’, 3’, 5’, 7’) velocities of axisymmetric waves in a liquid cylinder for the 1st, 3rd, 5th, 7th modes. The normalized frequency is plotted along the abscissa axis, and the normalized propagation velocities with normalization to the propagation velocity of longitudinal waves are plotted along the ordinate axis.

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4. Fig. 3. The modulus of the correction to the radial wave number for the 1st (1), 3rd (2) and 5th (3) eigenwaves as a function of frequency. The ratio of the longitudinal velocity to the transverse velocity S is 10. A loss factor of 0.02 is introduced.

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5. Fig. 4. Asymptotics of the radial wave number correction modulus calculated using formula (13). From top to bottom S = 5, 10, 20. The loss coefficient is 0.01.

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6. Fig. 5. The first mode, one and a half frequency, S = 5 and S = 10. 1 — Potential part of the field; 2 (S = 5), 3 (S = 10) — vortex part of the field

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7. Fig. 6. The third mode, double frequency. 1 — Potential part of the field; 2 (S = 5), 3 (S = 10) — vortex part of the field

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8. Fig. 7. The fourth mode, double frequency. 1 — Potential part of the field; 2 (S = 5), 3 (S = 10) — vortex part of the field

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9. Fig. 8. The seventh mode, double frequency. 1 — Potential part of the field, losses 0.0002; 2 (S = 5), 3 (S = 10) — vortex part of the field

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10. Fig. 9. Cylinder in the air. 1 — Electrical pickup signal, 2 — signal of the pulse passed through the cylinder.

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11. Fig. 10. Cylinder in water. 1 — Electrical pickup signal, 2 — signal of the pulse passed through the cylinder

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