On the Propagation of Finite-Amplitude Acoustic Waves in Mono-Relaxing Media

被引：0

作者：

Jordan, P. M. ^{[1
]}

Norton, G. V. ^{[1
]}

Chin-Bing, S. A. ^{[1
]}

Warn-Varnas, A. ^{[1
]}

机构：

[1] USN, Res Lab, Stennis Space Ctr, Code 7180, Stennis Space Ctr, MS 39529 USA

来源：

CONTINUUM MECHANICS, FLUIDS, HEAT | 2010年

关键词：

Nonlinear acoustics; Abel's equation; Lambert W-function; kinematic-wave theory;

D O I：

暂无

中图分类号：

O414.1 [热力学];

学科分类号：

摘要：

The propagation of finite-amplitude acoustic traveling waves in a class of mono-relaxing media is considered. The resulting associated ordinary differential equation (ODE), which is of the Abel type, is analyzed and exact, approximate, and asymptotic solutions are derived. In addition, numerical simulations are presented, special cases are discussed, and connections to other fields are noted. The analysis carried out here also serves to highlight some of the many applications of Abel's equation and the Lambert W-function, a relatively recent addition to the family of special functions, in the physical sciences.

引用

页码：67 / +

页数：2

共 16 条

[1] Time-domain modeling of finite-amplitude sound in relaxing fluids [J].

Cleveland, RO ;

Hamilton, MF ;

Blackstock, DT .

JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA, 1996, 99 (06) :3312-3318

[2] On the Lambert W function [J].

Corless, RM ;

Gonnet, GH ;

Hare, DEG ;

Jeffrey, DJ ;

Knuth, DE .

ADVANCES IN COMPUTATIONAL MATHEMATICS, 1996, 5 (04) :329-359

[3]

Davis H.T., 1962, Introduction to Nonlinear Differential and Integral Equations

[4] Solitary and compactlike shear waves in the bulk of solids [J].

Destrade, Michel ;

Saccomandi, Giuseppe .

PHYSICAL REVIEW E, 2006, 73 (06)

[5]

Hill J M., 1992, Differential Equations and Group Methods for Scientists and Engineers

[6]

Howison S.D., 2005, PRACTICAL APPL MATH

[7]

Lamb H., 1945, HYDRODYNAMICS, P541

[8]

Landau LD, 1976, Mechanics, V1

[9]

Makarov S, 1996, ACUSTICA, V82, P579

[10] Traveling-wave solutions for a discrete Burgers equation with nonlinear diffusion [J].

Mickens, Ronald E. .

MATHEMATICS AND COMPUTERS IN SIMULATION, 2009, 80 (04) :855-859

← 1 2 →