Based on the Church-Hoff model, the nonlinear oscillations of a single encapsulated microbubble with a finite thickness shell are theoretically studied. The effects of viscoelasticity on radial oscillations and the fu...Based on the Church-Hoff model, the nonlinear oscillations of a single encapsulated microbubble with a finite thickness shell are theoretically studied. The effects of viscoelasticity on radial oscillations and the fundamental and harmonic components are researched. The peaks of radial oscillations and magnitudes of power spectra of the fundamental and harmonic components all increase gradually with the shear modulus of shell varying from 0 to 10 MPa by an interval of 0. 1 MPa at the same shear viscosity, while they decrease as the shear viscosity increases from 0 to 1 Pa · s by an interval of 0. 01 Pa · s at the same shear modulus. The fluctuation ranges of subharmonic and ultraharmonic signals are much larger than both the fundamental and second harmonic components. It means that the effect of viscoelasticity on the subharmonic and ultraharmonic signals is greater than that on the fundamental and second harmonic components. So adjusting the viscoelasticity of the shell is a potential method to obtain a perfect microbubble contrast agent used for the subharmonic and ultraharmonic imaging. Four points with significant fundamental and harmonic components are chosen as an example： a shear viscosity of 0. 39 Pa · s with shear modulus of 3.9, 6. 6, and 8.6 MPa, respectively; a shear modulus of 6.6 MPa with a shear viscosity of 0.42 Pa · s.展开更多
Based on Biot’s wave equation, this paper discusses the transient response of a spherical cavity with a partially sealed shell embedded in viscoelastic saturated soil. The analytical solution is derived for the trans...Based on Biot’s wave equation, this paper discusses the transient response of a spherical cavity with a partially sealed shell embedded in viscoelastic saturated soil. The analytical solution is derived for the transient response to an axisymmetric surface load and fluid pressure in Laplace transform domain. Numerical results are obtained by inverting the Laplace transform presented by Durbin, and are used to analyze the influences of the partial permeable property of boundary and relative rigidity of shell and soil on the transient response of the spherical cavity. It is shown that the influence of these two parameters is remarkable. The available solutions of permeable and impermeable boundary without shell are only two extreme cases of this paper.展开更多
The authors study a 3 x 3 rate-type viscoelastic system, which is a relaxation approximation to a 2 x 2 quasi-linear hroerbolic system, including the well-known p-system. The nonlinear stability of two-mode shock wave...The authors study a 3 x 3 rate-type viscoelastic system, which is a relaxation approximation to a 2 x 2 quasi-linear hroerbolic system, including the well-known p-system. The nonlinear stability of two-mode shock waves in this relaxation approximation is proved.展开更多
The authors study a 3×3 rate-type viscoelastic system, which is a relaxation approximationto a 2×2 quasi-linear hyperbolic system, including the well-known p-system. It is shown thatthe rarefaction waves are...The authors study a 3×3 rate-type viscoelastic system, which is a relaxation approximationto a 2×2 quasi-linear hyperbolic system, including the well-known p-system. It is shown thatthe rarefaction waves are nonlinear asymptotically stable in this relaxation approximation.展开更多
基金The National Basic Research Program of China ( 973Program) ( No. 2011CB933503)the National Natural Science Foundation of China ( No. 50872021, 60725101, 31000453)
文摘Based on the Church-Hoff model, the nonlinear oscillations of a single encapsulated microbubble with a finite thickness shell are theoretically studied. The effects of viscoelasticity on radial oscillations and the fundamental and harmonic components are researched. The peaks of radial oscillations and magnitudes of power spectra of the fundamental and harmonic components all increase gradually with the shear modulus of shell varying from 0 to 10 MPa by an interval of 0. 1 MPa at the same shear viscosity, while they decrease as the shear viscosity increases from 0 to 1 Pa · s by an interval of 0. 01 Pa · s at the same shear modulus. The fluctuation ranges of subharmonic and ultraharmonic signals are much larger than both the fundamental and second harmonic components. It means that the effect of viscoelasticity on the subharmonic and ultraharmonic signals is greater than that on the fundamental and second harmonic components. So adjusting the viscoelasticity of the shell is a potential method to obtain a perfect microbubble contrast agent used for the subharmonic and ultraharmonic imaging. Four points with significant fundamental and harmonic components are chosen as an example： a shear viscosity of 0. 39 Pa · s with shear modulus of 3.9, 6. 6, and 8.6 MPa, respectively; a shear modulus of 6.6 MPa with a shear viscosity of 0.42 Pa · s.
文摘Based on Biot’s wave equation, this paper discusses the transient response of a spherical cavity with a partially sealed shell embedded in viscoelastic saturated soil. The analytical solution is derived for the transient response to an axisymmetric surface load and fluid pressure in Laplace transform domain. Numerical results are obtained by inverting the Laplace transform presented by Durbin, and are used to analyze the influences of the partial permeable property of boundary and relative rigidity of shell and soil on the transient response of the spherical cavity. It is shown that the influence of these two parameters is remarkable. The available solutions of permeable and impermeable boundary without shell are only two extreme cases of this paper.
文摘The authors study a 3 x 3 rate-type viscoelastic system, which is a relaxation approximation to a 2 x 2 quasi-linear hroerbolic system, including the well-known p-system. The nonlinear stability of two-mode shock waves in this relaxation approximation is proved.
文摘The authors study a 3×3 rate-type viscoelastic system, which is a relaxation approximationto a 2×2 quasi-linear hyperbolic system, including the well-known p-system. It is shown thatthe rarefaction waves are nonlinear asymptotically stable in this relaxation approximation.
