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在Lagrange坐标系中,根据流体力学的基本方程式,利用逐级近似法推导了计及二级近似的二维空间内平面波传播的波动方程式。以这组方程式为出发点分析了二层液态介质模型下,大振幅平面声波在平面分界面上的反射和折射。二级近似下的反射系数和透射系数不仅与介质的参数(包括非线性参数)有关,而且依赖于声源的位置。在斜投射时,一般而言,遵循线性声学反射和折射定律的二级近似反射波和折射波的波前上,波的幅度不再保持恒等。因之,除遵循线性声学反射和折射定律的二级近似反射波和折射波外,在其他方向上也有二级近似反射波和折射波。这个现象表明解释Muir等人的实验结果必须计及非线性效应。 相似文献
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非线性声波方程的传统二次谐波二阶近似解不够精确,对测量材料的非线性系数造成较大误差。利用摄动法展开非线性声波方程得到一系列非齐次偏微分方程,根据低阶解的性质拟定高阶特解的形式,通过符号计算求出高次谐波特解,对所有二次谐波成分求和最终获得二次谐波的高阶近似解。在水中开展非线性声学实验验证高阶近似解,结果表明:二次谐波相对幅度随传播距离和输入信号均呈现先增加后减小的趋势,高阶近似解即使在传播距离不太短和输入信号不太弱的宽泛条件下也能更好地吻合实验结果。得到的高阶近似解不仅弥补了现有二次谐波幅度理论公式的不足,进行非线性声学实验时还可扩展测量范围,充分利用实验数据也能提高非线性系数的测量精度。 相似文献
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本文研究了圆形活塞声源的有限振幅声波的反射。应用像源法计算已产生的谐波本身在边界上的反射,将它们看成是反射边界上振动的新声源所产生的辐射场,再应用弱冲击理论来计算这部分场自己产生的谐波场。在水池中作了二阶谐波的反射实验,反射界面是水池壁。结果表明,谐波声压随距离的平均衰减规律与理论符合得很好。实验还表明,反射谐波场沿纵向距离以及与它相垂直的横断面上有强烈的干涉现象,而纵向相干长度比横向相干长度大一个数量级。通过理论估计,认为这种现象是由于反射壁的有限厚度、它的两个平面之间有一个很小的角度以及发射波束有一定的宽度所造成的。这样估算出来的两个相干长度与实验符合。
关键词: 相似文献
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研究了一类非线性奇摄动方程的激波问题.利用Sinc-Galerkin方法,构造出边值问题的激波解,并由Newton法得到其近似解.
关键词:
非线性方程
激波
Sinc-Galerkin方法
Newton法 相似文献
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在微扰近似下,拉格朗日体系下的一阶、二阶波动方程解是具势运动,应用拉格朗日变动参数法来寻求积累解。在一般情况下,二阶波的波动方程在半空间会出现各式各样的积累解,它们沿着3个坐标变量的方向都有积累,在理想介质中它们不满足辐射条件。本文的结果表明,在考虑到介质的非理想性之后,也只有沿着平面边界面法线方向有积累的积累解才满足辐射条件,因而是收敛的。 相似文献
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A. Wünsche 《Annalen der Physik》1977,489(5):341-357
Reflection and Refraction of Light at the Boundary Plane between Two Anisotropic Media Relations for the amplitudes in the case of reflection and refraction of plane monochromatic waves at the boundary plane between two arbitrarily anisotropic media are derived from Maxwell equations with invariant methods. Solutions are represented with use of the refraction vectors and of the polarization vectors for the electric field. From the general solution of the problem the following essentially more simple special cases are obtained: 1. normal incidence, 2. optic axis in direction of the incident or reflected wave, 3. parallel and normal polarization of the partial waves in both media relatively to the plane of incidence. 相似文献
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A boundary problem in which a plane electromagnetic wave is reflected and refracted at a plane boundary of a semi-infinite optical medium with a quasi-zero refractive index has been solved. Such a medium has a random refractive index taking values in an interval from zero to some finite value less than unity. It means that the concept of a sharp interface between two media loses its meaning, the boundary of the medium becomes inhomogeneous, and laws of reflection and refraction of light become non-Fresnelian. Formulas for non-Fresnelian amplitudes of reflection and refraction have been derived. It is shown that a surface wave arises near the boundary of a medium with a quasi-zero refractive index. The wave propagates both on the inside and outside of the boundary. 相似文献
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本文构建了一种折射率梯度表面,并利用几何光学法对其物理机理作了研究,发现这种折射率梯度表面可以实现入射波到正常反射波,异常反射波,以及介质波的转换.当入射点介质折射率大于某一阈值时,异常反射波束方向角正弦值与入射波束方向角正弦值存在线性关系,意味着平行入射的波经介质后将平行出射到空气;而当折射率梯度常数大于某一阈值时,任何方向入射的波在透射到介质后,将发生全反射,被束缚在介质中.总而言之,通过调节结构参数,可以实现对波束方向与强度的人工调控,从而提供了一种人工可控的全介质梯度表面的工程实现思路. 相似文献
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We derive and evaluate boundary states for Maxwell’s equations, the linear, and the nonlinear Euler gas-dynamics equations to compute wave reflection from moving boundaries. In this study we use a Discontinuous Galerkin Spectral Element method (DGSEM) with Arbitrary Lagrangian–Eulerian (ALE) mapping for the spatial approximation, but the boundary states can be used with other methods, like finite volume schemes. We present four studies using Maxwell’s equations, one for the linear Euler equations, and one more for the nonlinear Euler equations. These are: reflection of light from a plane mirror moving at constant velocity, reflection of light from a moving cylinder, reflection of light from a vibrating mirror, reflection of sound from a plane wall and dipole sound generation by an oscillating cylinder in an inviscid flow. The studies show that the boundary states preserve spectral convergence in the solution and in derived quantities like divergence and vorticity. 相似文献
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This paper uses the two-dimensional Brusselator model to study reflection and refraction of chemical waves.It presents some boundary conditions of chemical waves,with which occurence of observed phenomena at interface as refraction and reflection of chemical waves can be interpreted.Moreover,the angle of reflection may be calculated by using the boundary conditions.It finds that reflection and refraction of chemical waves can occur simultaneously even if plane wave goes from a medium with higher speed to a medium with lower speed,provided the incident angle is larger than the critical angle. 相似文献
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M. M. Carroll 《Applied Physics A: Materials Science & Processing》1979,19(3):321-329
A time-sinusoidal circularly polarized plane standing wave solution is obtained for isotropic lossless dielectric media with
arbitrary nonlinearity. The spatial variation of the standing wave depends on the nonlinearity and is found by solving a problem
of centralforce motion in which the electric complementary energy density furnishes the potential and the spatial coordinate
has the role of time. Two special nonlinear dielectric response laws-cubic and quintic-are treated, and explicit solutions
for the spatial variation of the wave amplitude and phase are obtained in terms of elliptic functions and elliptic integrals,
respectively. The standing-wave solution is applied to give steady state solutions of two reflection/transmission problems
(a) reflection from, or resonance modes between, ideally conducting planes and (b) reflection and transmission at a plane
interface between two nonlinear dielectric media. 相似文献
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An analysis of the parameters of nonlinear waves transmitted through a layer of a randomly inhomogeneous medium is carried
out. The layer is modeled by a two-dimensional phase screen. Passing through the screen plane, the wave acquires a random
phase shift. The wave front becomes distorted, and randomly located regions of ray convergence and divergence are formed,
in which the nonlinear evolution of the wave alters profoundly. The problem is solved in the approximation of geometrical
acoustics. The ray pattern of a plane wave transmitted through the regular screen is constructed. The solution that describes
the spatial structure of the field and the evolution of an arbitrary temporal wave profile behind the screen is obtained.
Statistical characteristics of the discontinuity amplitude are calculated for different distances from the screen. A random
modulation is shown to result in a faster (in comparison with the case of a homogeneous medium) nonlinear attenuation of the
wave and in the smoothing of the shock profile. The distribution function of the wave field parameters becomes broader because
of random focusing effects. 相似文献
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Reflection and refraction of longitudinal and transverse acoustic waves at a plane boundary between an antiferromagnet and a dielectric are studied. The antiferromagnet is assumed to have an easy-plane anisotropy and to be in the state near the orientational phase transition in the magnetic field. A possibility of controlling the angles of the wave-type transformation upon reflection and the refraction angles, as well as all four coefficients of the wave transformation upon reflection and refraction, by the magnetic field is demonstrated. Conditions for the formation of the critical angles of internal reflection and the effect of the magnetic field on their values are specified. A possibility of the radiation of a grazing wave into the material bulk in the vicinity of the phase transition is analyzed. 相似文献