摘要
In the present paper the propagation property of nonlinear waves in a thin viscoelastic tube filled with incom- pressible inviscid fluid is studied. The tube is considered to be made of an incompressible isotropic viscoelastic material described by Kelvin-Voigt model. Using the mass conservation and the momentum theorem of the fluid and radial dynamic equilibrium of an element of the tube wall, a set of nonlinear partial differential equations governing the propagation of nonlinear pressure wave in the solid-liquid coupled system is obtained. In the long-wave approximation the nonlinear far-field equations can be derived employing the reductive perturbation technique （RPT）. Selecting the expo- nent c~ of the perturbation parameter in Gardner-Morikawa transformation according to the order of viscous coefficient 7, three kinds of evolution equations with soliton solution, i.e. Korteweg-de Vries （KdV）-Burgers, KdV and Burgers equations are deduced. By means of the method of traveling-wave solution and numerical calculation, the propagation properties of solitary waves corresponding with these evolution equations are analysed in detail. Finally, as a example of practical application, the propagation of pressure pulses in large blood vessels is discussed.
In the present paper the propagation property of nonlinear waves in a thin viscoelastic tube filled with incom- pressible inviscid fluid is studied. The tube is considered to be made of an incompressible isotropic viscoelastic material described by Kelvin-Voigt model. Using the mass conservation and the momentum theorem of the fluid and radial dynamic equilibrium of an element of the tube wall, a set of nonlinear partial differential equations governing the propagation of nonlinear pressure wave in the solid-liquid coupled system is obtained. In the long-wave approximation the nonlinear far-field equations can be derived employing the reductive perturbation technique （RPT）. Selecting the expo- nent c~ of the perturbation parameter in Gardner-Morikawa transformation according to the order of viscous coefficient 7, three kinds of evolution equations with soliton solution, i.e. Korteweg-de Vries （KdV）-Burgers, KdV and Burgers equations are deduced. By means of the method of traveling-wave solution and numerical calculation, the propagation properties of solitary waves corresponding with these evolution equations are analysed in detail. Finally, as a example of practical application, the propagation of pressure pulses in large blood vessels is discussed.
基金
Project supported by the National Natural Science Foundation of China (Grant No. 10772129)
