Vibrational Black Hole for Torsional Waves Propagating Through a Rod of Variable Cross-Section

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Дәйексөз келтіру

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Аннотация

The propagation of torsional waves through rods of variable cross-section is considered. With a linear increase in the flattening of the rod, the propagation velocity of the torsional wave decreases linearly and turns to zero at the end of the rod. Yet, the propagation time to the sharpened end is equal to infinity. Such a decelerating structure is called a vibrational black hole in modern terminology. Exact solutions of the equation of torsional vibrations of a sharpened rod with a moment of inertia and a moment of torsion in the form of power functions are given. Corresponding expressions for the input impedance at the initial cross-section are obtained.

Толық мәтін

Рұқсат жабық

Авторлар туралы

M. Mironov

Andreev Acoustics Institute

Хат алмасуға жауапты Автор.
Email: mironov_ma@mail.ru
Ресей, 4 Shvernik str., Moscow, Russia, 117292

Әдебиет тізімі

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Әрекет
1. JATS XML
Жүктеу
2. Fig. 1. Elliptical cross-section rod with decreasing thickness — vibrational frequency resonance for torsional waves. The x-coordinate is measured from the thin cross-section of the rod.

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3. Fig. 2. Input impedance of the frequency resonance, δ = 0.01. The abscissa axis is the normalized frequency. The ordinate axis is the modulus of the frequency resonance impedance normalized to the input impedance of a homogeneous rod. 1 (dotted line) — homogeneous rod, 2 (solid) — ε = 0.1, 3 (dashed) — ε = 0.01.

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4. Fig. 3. Input impedance of the frequency resonance, δ = 0.1. Designations as in Fig. 2.

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5. Fig. 4. Ratio of imaginary parts of impedances of an ideal frequency resonance and a semi-infinite homogeneous rod as a function of frequency.

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6. Fig. 5. 1 — ratio of axes as a function of distance to the final section of a rod of elliptical section; 2 — asymptotics as X → 0.

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7. Fig. 6. Dependences of the thickness of the rod b(X) for a power-law dependence of its width a(X). m = 0, 0.25, 0.5, 1.0 (from top to bottom).

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