Forced vibrations of a bubble in a liquid-filled elastic vessel
Geometry and dimensions of a bubble located in the middle of a cylindrical blood vessel. are the global coordinates, and are the local coordinates on the bubble surface. A, B, and C are monitoring points for analysis of numerical results.
The deformed shapes of the vessel wall and the bubble at the end of the insonation period (deformations are shown magnified by 20 times). (a) = 1 MHz, (b) = 2 MHz, (c) = 3 MHz. = 3 , = 4 , = 1 , = 0 , = 5 MPa, = 0.5.
Variation of relative pressure in liquid at points A, B, and C [Figs. 1(a) and 1(b)], and the spectra of the incident pressure pulse described by Eq. (9) and pressure oscillations at points B and C (c). = 3 , = 4 , = 1 , = 0 , = 5 MPa, = 0.5, = 1 MHz < 2.3 MHz.
Same as Fig. 3, = 2 MHz 2.3 MHz.
Same as Fig. 3, = 3 MHz > 2.3 MHz.
Dispersion of the phase speed according to the results of the FEM calculations in comparison with the theoretical Eqs. (3), (6), and (7). = 3 , = 4 , = 5 MPa, = 0.5.
Variation of the propagated wavelength with the frequency. The results are obtained based on the phase speed dispersion spectra shown in Fig. 6.
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