Weakly Nonlinear Analysis on Two Types of Elastic Waves in a Beam with Geometric Nonlinearity

Kikuchi, Yusei; Uchiyama, Yusuke; Kanagawa, Tetsuya

doi:10.1299/jsmedmc.2020.147

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“…Based on the method of multiple scales, 46) our group has theoretically studied ultrasound propagation in liquids containing many microbubbles without a shell. [47][48][49][50][51][52][53][54][55][56][57][58][59][60] Recently, we extended the previously established theory 47,50) to the case of bubbles with shells, 61) that is, by using Hoff's model 23) for a single encapsulated bubble, we succeeded in deriving a nonlinear evolution equation [i.e. Korteweg-de Vries-Burgers (KdVB) equation] for ultrasound propagation in liquids containing many encapsulated bubbles, which is different from the equation derived by Ma et al 28) In this paper, the derivation process of the KdVB equation briefly described in Ref.…”

Section: Introductionmentioning

confidence: 99%

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Weakly nonlinear theory on ultrasound propagation in liquids containing many microbubbles encapsulated by visco-elastic shell

Kikuchi

Kanagawa

2021

Jpn. J. Appl. Phys.

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Aimed towards an application of ultrasound diagnosis using contrast agents, the dynamics of encapsulated bubbles has been theoretically investigated under the restriction of a single bubble. In this paper, we extend the theory for single bubble or some bubbles to that for many bubbles, and theoretically investigate weakly nonlinear propagation of ultrasound in an initially quiescent incompressible liquid, uniformly containing many microbubbles encapsulated by the shell as a viscoelastic body (Kelvin–Voigt model). As a result, we derived the Korteweg–de Vries–Burgers equation for a low-frequency long wave and clarified that the shell affects the advection, nonlinear, and dissipation (not dispersion) effects of ultrasound propagation. In particular, shell rigidity, surface tension, and shell viscosity increased the advection, nonlinear, and dissipation effects, respectively.

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Section: Introductionmentioning

confidence: 99%

“…Finally, we evaluate typical UCAs by comparing the coefficients in the KdVB equation. 61) 2. Formulation of the problem 2.1.…”

Section: Introductionmentioning

confidence: 99%

Weakly nonlinear theory on ultrasound propagation in liquids containing many microbubbles encapsulated by visco-elastic shell

Kikuchi

Kanagawa

2021

Jpn. J. Appl. Phys.

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Weakly Nonlinear Analysis on Two Types of Elastic Waves in a Beam with Geometric Nonlinearity

Cited by 1 publication

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Weakly nonlinear theory on ultrasound propagation in liquids containing many microbubbles encapsulated by visco-elastic shell

Weakly nonlinear theory on ultrasound propagation in liquids containing many microbubbles encapsulated by visco-elastic shell

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