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1.
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   

2.
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   

3.
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   

4.
特解边界元法数值解三维Pennes方程及其应用   总被引:2,自引:0,他引:2  
应用特解边界元法对非稳态的三维Pennes方程求解,将解分为一满足泊松方程的通解与一特解之和,通解按照边界元法求解,特解用分离变量法给出,与位置有关的部分采用截断多项式,逐时间段计算边界元的温度及热流值,然后计算域内点的值,并将该方法用于热疗温度场的数值实例计算。  相似文献   

5.
曾天海  王海雷  张向东 《物理》2012,41(6):382-386
文章讨论了偏振高斯光束在空气-手征介质界面的反射和折射问题,发现了反射和折射光束的异常自旋霍尔效应.在某些特定的角度下,反射高斯光束重心的移动可以达到几十个波长的量级,通过调节手征参数,甚至会出现折射光重心移动方向由正到负的转变.文章还讨论了任意偏振高斯光束在空气-运动介质界面的反射和透射问题,当介质垂直于入射平面运动时,反射和透射光束的横向移动可以达到几个波长的量级,甚至在某些运动速度下可以实现移动方向正负的改变.这些研究对控制光的自旋霍尔效应提供了可能的途径.  相似文献   

6.
一类非线性方程激波解的Sinc-Galerkin方法   总被引:1,自引:0,他引:1       下载免费PDF全文
吴钦宽 《物理学报》2006,55(4):1561-1564
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   

7.
吴宁  韩庆邦  仲晓敏 《声学学报》2020,45(4):594-600
应用二阶势理论研究了P波入射到固-固界面情况下的二阶谐波场。运用变动参数法求解二阶非齐次势函数方程的边值问题,数值计算了二阶谐波位移与入射角的关系,结果表明当入射角到达某个角度时,二阶谐波场的位移会急剧增大。同时,当入射角度为θw时,特解位移趋近无限大的有关现象依然出现,关于边界面的影响也做了讨论。   相似文献   

8.
孟宗  刘彬 《物理学报》2008,57(3):1329-1334
建立一类含广义非线性弹性力的两质量相对转动系统的非线性动力学方程. 应用变量梯度法构造李雅普诺夫函数,研究相对转动非线性自治系统的稳定性. 应用摄动法求得相对转动非线性非自治系统在两种不同频率谐波共同激励下的组合谐波响应的近似解. 关键词: 相对转动 非线性动力系统 稳定性 组合谐波响应  相似文献   

9.
钱祖文 《声学学报》2018,43(5):850-854
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   

10.
读者 作者     
对“大振幅平面声波的反射和折射(Ⅱ)——二维情况”一文的批评声学学报编辑部: 我读了“大振幅平面声波的反射和折射(Ⅱ)——二维情况”一文(文献[1]之后,发现该文的定解条件和它要解决的问题(平面半空间的反射与折射)是自相矛盾的,因为该文在推导二阶势函数所满足的波动方程时,强行令一阶声场势函数必须满足只有在无界空间才满足的单向波条件,而该文要处理的空间却是有界空间(平面半空间),方程与实际情况相悖,因而该文得到的二阶声场表达式没有科学根据,其分析如下。  相似文献   

11.
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   

12.
有限振幅声波在平面界面上的反射和折射   总被引:2,自引:0,他引:2       下载免费PDF全文
在文献[1]的基础上,进一步研究了有限振幅声波在平面界面上的反射和折射,求得了两种介质中的场,并对界面条件和折射关系作了讨论。 关键词:  相似文献   

13.
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   

14.
折射率梯度表面机理的研究   总被引:1,自引:0,他引:1       下载免费PDF全文
刘晓波  施宏宇  陈博  蒋延生  徐卓  张安学 《物理学报》2014,63(21):214201-214201
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   

15.
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   

16.
顾国锋  吕耀平  唐国宁 《中国物理 B》2010,19(5):50515-050515
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   

17.
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   

18.
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   

19.
20.
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   

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