Propagation of nonlinear waves in a gas-liquid medium. Exact and approximate analytical solutions of wave equations

A number of exact and approximate analytical solutions of the equations for one-dimensional and weakly non-one-dimensional waves propagating in a liquid with gas bubbles are presented for the case where the bubble distribution density is a continuous function of the bubble radius and spatial coordinates.     

非均匀吸收介质中地震波的广义传播矩阵解法

本文在复频域内,通过应用混合变量粘弹性波方程和线性常微分方程组的指数矩阵解法,给出了一种计算非均匀吸收介质中地震波传播的广义传播矩阵解法。该方法适用于各种粘弹性模型,可模拟任意震源及所产生的各种体波、面波,数值结果表明具有很高的计算精度。     

Spatial shapes of magnetoelastic shear body waves at the transmission edges in a periodically inhomogeneous magnetostrictive medium

The spatial shapes of magnetoelastic shear body waves at the transmission edges in a periodically inhomogeneous magnetostrictive medium are studied. Numerical results are obtained for a two-component composition of ferrite and nonmagnetic dielectric __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 3, pp. 61–69, March 2006.     

Stability of the Korteweg-de Vries solitary wave solution

ＳＴＡＢＩＬＩＴＹＯＦＴＨＥＫＯＲＴＥＷＥＧ－ＤＥＶＲＩＥＳＳＯＬＩＴＡＲＹＷＡＶＥＳＯＬＵＴＩＯＮＬｕＸｉａｎ－ｑｉｎｇ（吕咸青）（ＳｈａｎｄｏｎｇＥｄｕｃａｔｉｏｎＣｏｌｌｅｇｅ,Ｊｉｎａｎ）（ＲｅｃｅｉｖｅｄＪｕｎｅ１８,１９９３,Ｃｏｍｍｕｎ...     

Propagation of pressure waves in a gas-liquid medium with a cluster structure

Propagation of a stepwise shock wave in a liquid containing spherical gas-liquid clusters is experimentally studied. Measured results are compared with available theoretical models. It is shown that resonant interaction of gas-liquid clusters in the wave can increase the amplitude of oscillations in the shock wave. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 3, pp. 50–60, May–June, 2005.     

Propagation of Elastic Waves in Periodically Inhomogeneous Media

The structural theory of waves and vibrations in periodically inhomogeneous media is set out. Relevant research results are presented. Emphasis is on the principles of the theory, surface waves, and other surface effects     

Propagation of magnetoelastic shear waves across layers in a periodically layered medium

The paper is concerned with magnetoelastic shear waves propagating in regularly layered magnetostrictive media at a right angle to the layer interfaces __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 6, pp. 54–60, June 2006.     

The parameter perturbation method on elastic wave equation in inhomogeneous medium

I.IntroductionTheelasticwaveininhomogeneousmediumiscomplicatedbecauseofthediffracting,scattering,andtransmutingofthewavetapes.Exceptforsomesimpleandregularmediummode1s,thesolutionofelasticwavehasnotbeengotyet.Nowadays,theresearchoftheelasticwavescattering…     

On the dynamic behavior of gas bubbles in an inhomogeneous standing wave

The motion of gas bubbles in an inhomogeneous standing wave is examined. The nonlinear system of equations is solved by the averaging method. Stationary solutions (bubble clusters) are found, and the conditions for their stability are established __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 5, pp. 88–94, May 2006.     

Effect of a periodic action on average flow in an inhomogeneous liquid-saturated porous medium

The problem of the average flow of a viscous incompressible fluid saturating a stationary porous incompressible matrix under a periodic action is considered. It is shown that a spatial inhomogeneity of the medium porosity leads to an average fluid flow, quadratically dependent on the action amplitude, in the direction of increase in porosity. In particular, this means that wave action on an oil reservoir could lead to fluid flow on the interfaces from low-porosity,weakly permeable collector regions into high-porosity regions, for example, to flow from blocks to fractures in fractured porous reservoirs, which makes it possible to enhance oil production. It is shown that in the presence of a constant pressure gradient the flow component generated by a periodic action can provide a substantial proportion of the total flow, especially on the boundaries with low-porosity strata or blocks. With increase in amplitude this may significantly exceed the component associated with the constant pressure gradient.     

径向非均匀压电介质中圆孔对SH波的散射

利用复变函数理论对SH波作用下含圆孔径向非均匀压电介质的反平面动力特性进行了研究。压电介质的密度沿径向按幂函数形式变化,但压电参数、弹性参数、介电参数均为常数。利用变量替换法将非均匀压电介质的变系数波动方程组转化为标准的Helmholtz方程组,得到了满足边界条件的波函数解析表达式。通过数值算例分析了入射角度、入射波频率、幂次等对应力集中系数和电场强度集中系数的影响,并与已有文献进行比较。结果表明,某些参数组合下,动应力集中系数与电场强度集中系数均随幂次增大而增大。     

不均匀磁电弹板中的厚度扭曲波的传播

压电-压磁复合材料或结构的许多应用是与弹性波的传播密切相关的,这要求人们首先从理论的角度弄清楚弹性波的传播规律。本文研究由多个不均匀磁电弹介质组成的薄板厚度扭曲波的传播性质,从磁电弹全耦合场三维方程出发得到了其精确解,根据所得到的解分析了波的传播特征,这些结果对于理解和设计谐振器、滤波器以及声波元件提供了有价值的理论基础。     

Propagation of electromagnetic wave in the three phases soil media

IntroductionItisofparamountimportancetogetgeotechnicalparameterssuchasmoisture ,compactness,andshearstrengthforgeotechnicalengineeringtransaction .Butthemethodtofetchthesoilsamplesforlaboratorytestcannotavoidbringingthedisturbance ,andmakethetestresultsinconsistenttotheactualstatusofsoil.Inrecentyears,theapplicationofEMwaveinthedetectinghiddentroublesindamsandundergroundfoundationsdevelopedrapidly .Buttherearestillsomefactorsthatrestricttheadvanceofapplication .Firstly ,thesoilconstitutesthr…     

Existence and breaking property of real loop-solutions of two nonlinear wave equations

Dynamical analysis has revealed that, for some nonlinear wave equations, loop- and inverted loop-soliton solutions are actually visual artifacts. The so-called loopsoliton solution consists of three solutions, and is not a real solution. This paper answers the question as to whether or not nonlinear wave equations exist for which a ＂real＂ loopsolution exists, and if so, what are the precise parametric representations of these loop traveling wave solutions.     

Propagation of liquid surface waves over finite graphene structured arrays of cylinders

Based on the multiple scattering method, this paper investigates a benchmark problem of the propagation of liquid surface waves over finite graphene (or honeycomb) structured arrays of cylinders. Comparing the graphene structured array with the square structured and with triangle structured arrays, it finds that the finite graphene structure can produce more complete band gaps than the other finite structures, and the finite graphene structure has less localized ability than the other finite structures.     

A boundary element method for calculating the SH waves scattering from arbitrarily shaped holes in an anisotropic medium

The scattering problem of elastic wave by arbitrarily shaped cavities in an infinite anisotropic medium is investigated by the boundary integral equation (BIE) method. The formulations of BIE are derived with the help of generalized Green's formula. The discretization of BIE is based upon constant elements. After confirmation of the accuracy of the present method, some numerical examples are given for various cavities in a full space, in which an isotropic body with a circular cylinder hole is used for comparison and good agreement is observed. It has been proved that the method developed in this paper is effective.     

On the approximation of local efflux/influx bed discharge in the shallow water equations based on a wave propagation algorithm

In cities, flood waves may propagate over street surfaces below which lie complicated pipe networks used for storm drainage and sewage. The flood and pipe flows can interact at connections between the underground pipes and the street surface. The present paper examines this interaction, using the shallow water equations to model the flood wave hydrodynamics. Sources and sinks in the mass conservation equation are used to model the pipe inflow and outflow conditions at bed connections. We consider the problem reduced to one dimension. The shallow water equations are solved using a Godunov‐type wave propagation scheme. Wave speeds are modified in the wave propagation algorithm to enable flows to be simulated over nearly dry beds and dry states. First, the model is used to simulate vertical flows through finite gaps in the bed. Next, the interaction of the vertical flows with a dam break flow is considered for both dry and wet beds. An efflux number, En, is defined based on the vertical efflux velocity and the gap length. Comparisons are made with numerical predictions from STAR‐CD, a commercial Navier–Stokes solver that models the free‐surface motions, and a parameter study is undertaken to investigate the effect of the one‐dimensional approximation of the present model, for a range of non‐dimensional efflux numbers. It is found that the shallow flow model gives sensible predictions at all time provided En<0.5, and for long durations for En>0.5. Dam break flow over an underground connecting pipe is also considered. Copyright © 2010 John Wiley & Sons, Ltd.     

Initial value problem for a class of fourth-order nonlinear wave equations

In this paper, existence and uniqueness of the generalized global solution and the classical global solution to the initial value problem for a class of fourth-order nonlinear wave equations are studied in the fractional order Sobolev space using the contraction mapping principle and the extension theorem. The sufficient conditions for the blow up of the solution to the initial value problem are given.     

Exact traveling wave solutions for an integrable nonlinear evolution equation given by M. Wadati

By using the method of dynamical systems, the travelling wave solutions of for an integrable nonlinear evolution equation is studied. Exact explicit parametric representations of kink and anti-kink wave, periodic wave solutions and uncountably infinite many smooth solitary wave solutions are given.