The shock formation distance in a bounded sound beam of finite amplitude

2003 ◽  
Vol 114 (1) ◽  
pp. 114-121 ◽  
Author(s):  
Chao Tao ◽  
Jian Ma ◽  
Zhemin Zhu ◽  
Gonghuan Du ◽  
Zihong Ping
Keyword(s):  
Finite Amplitude ◽  
Shock Formation ◽  
Sound Beam

A more general model equation of nonlinear Rayleigh waves and their quasilinear solutions

2016 ◽  
Vol 30 (08) ◽  
pp. 1650096 ◽  
Author(s):  
Shuzeng Zhang ◽  
Xiongbing Li ◽  
Hyunjo Jeong
Keyword(s):  
Rayleigh Waves ◽  
General Equation ◽  
Wave Motion ◽  
Numerical Solutions ◽  
Second Harmonic ◽  
Approximate Equation ◽  
Finite Amplitude ◽  
Sound Beam ◽  
Quasilinear Theory ◽  
Sound Beams

A more general two-dimensional wave motion equation with consideration of attenuation and nonlinearity is proposed to describe propagating nonlinear Rayleigh waves of finite amplitude. Based on the quasilinear theory, the numerical solutions for the sound beams of fundamental and second harmonic waves are constructed with Green’s function method. Compared with solutions from the parabolic approximate equation, results from the general equation have more accuracy in both the near distance of the propagation direction and the far distance of the transverse direction, as quasiplane waves are used and non-paraxial Green’s functions are obtained. It is more effective to obtain the nonlinear Rayleigh sound beam distributions accurately with the proposed general equation and solutions. Brief consideration is given to the measurement of nonlinear parameter using nonlinear Rayleigh waves.

QUALITATIVE ANALYSIS OF THE KHOKHLOV–ZABOLOTSKAYA–KUZNETSOV (KZK) EQUATION

2008 ◽  
Vol 18 (05) ◽  
pp. 781-812 ◽  
Author(s):  
ANNA ROZANOVA-PIERRAT
Keyword(s):  
Blow Up ◽  
Viscous Medium ◽  
Finite Amplitude ◽  
Mean Value ◽  
Nonlinear Propagation ◽  
Step Method ◽  
Fractional Step Method ◽  
Sound Beam ◽  
Kzk Equation ◽  
Zero Viscosity

The Khokhlov–Zabolotskaya–Kuznetzov (KZK) equation is considered as a model of nonlinear acoustic which describes the nonlinear propagation of a finite-amplitude focused sound beam which is essentially one-directional, in the thermo-viscous medium.1,7,8 The aim of this paper is the study of the existence, uniqueness, stability, regularity, continuous dependence on the initial value and blow-up of solution of the KZK equation in Sobolev spaces Hs of periodic on x functions and with mean value zero. Existence of shock waves for the model with zero viscosity is proved using S. Alinhac's method.2 Global existence in time of the beam's propagation in viscous media is established for small enough initial data. Existence result is proved by two methods: first by the fractional step method in the particular case ℝ3 and s = 3 to justify the numerical results of Thierry Le Pollès25 and second for the general case ℝn and s > [n/2] + 1 by the approach used in Refs. 12 and 13 for the Kadomtsev–Petviashvili (KP) equation.

Distortion and harmonic generation in the nearfield of a finite amplitude sound beam

1984 ◽  
Vol 75 (3) ◽  
pp. 749-768 ◽  
Author(s):  
Sigurd Ivar Aanonsen ◽  
Tor Barkve ◽  
Jacqueline Naze Tjo/tta ◽  
Sigve Tjo/tta
Keyword(s):  
Harmonic Generation ◽  
Finite Amplitude ◽  
Sound Beam

scholarly journals Directional Loudspeaker Using a Parametric Array

10.14311/862 ◽  
2006 ◽  
Vol 46 (4) ◽  
Author(s):  
A. Ritty
Keyword(s):  
Carrier Frequency ◽  
Nonlinear Acoustics ◽  
Finite Amplitude ◽  
Sound Beam ◽  
Sound Reproduction ◽  
Audible Sound ◽  
Parametric Array ◽  
Film Transducer

The theory for sound reproduction of parametric arrays is based on nonlinear acoustics. Due to the nonlinearity of the air, a finite amplitude ultrasound interacts with itself and generates audible secondary waves in the sound beam. A special feature of this loudspeaker is its sharper directivity compared to conventional loudspeakers of the same aperture size.This paper describes the basis of the theory used for parametric arrays, and presents the influence of the main parameters, e.g., carrier frequency. It also describes some signal pre-processing needed to obtain the desired audible sound. A PVDF (polyvinylidenefluoride) film transducer is also studied in order to produce a prototype to confirm the theory. 

The transmission of finite amplitude sound beam in multi-layered biological media

2007 ◽  
Vol 362 (1) ◽  
pp. 50-56 ◽  
Author(s):  
Xiaozhou Liu ◽  
Junlun Li ◽  
Chang Yin ◽  
Xiufen Gong ◽  
Dong Zhang ◽  
...  
Keyword(s):  
Finite Amplitude ◽  
Sound Beam ◽  
Biological Media

Numerical modeling of finite-amplitude sound beams: Shock formation in the near field of a cw plane piston source

2001 ◽  
Vol 110 (1) ◽  
pp. 95-108 ◽  
Author(s):  
V. A. Khokhlova ◽  
R. Souchon ◽  
J. Tavakkoli ◽  
O. A. Sapozhnikov ◽  
D. Cathignol
Keyword(s):  
Numerical Modeling ◽  
Near Field ◽  
Finite Amplitude ◽  
Shock Formation ◽  
Sound Beams
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