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高功率激光系统中的热像效应可能导致光束的峰值功率剧烈增加,增益非线性介质会使这种光强增幅更为强烈。基于菲涅尔-基尔霍夫衍射理论和非线性近轴波动方程,对强激光在增益克尔介质工作在饱和区时的热像产生过程进行理论分析,将光束传输方程中增益饱和部分进行麦克劳林展开,取其近似,经过推导得出了介质薄近似时热像强度解析式和热像位置。通过数值模拟对解析结论预测的热像强度和位置进行验证。仿真结果表明,热像的位置在衍射物相对于介质对称处,热像强度解析结果与模拟结果相符,在薄介质时,解析解与模拟结果拟合较好。热像强度随非线性介质内非线性效应增强而停止增加,此外,讨论了热像强度随调制类型的变化。 相似文献
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气动声学的声比拟理论以密度、声压等标量为波动算子变量,建立非齐次波动方程,描述流体运动及与边界作用诱发声音的辐射,但标量无法直接描述声能量的传播过程和途径.在流体力学研究中,标量用于描述当前当地的物质状态,而矢量用于描述质量和能量的传输.借鉴上述思想,开展了矢量气动声学的研究,概述矢量气动声学的理论研究进展及应用,主要包括:(1)以声粒子速度为变量,采用声比拟理论的思想直接从Navier-Stokes方程出发推导建立了气动声学的矢量波动方程及两种频域解;(2)综合利用声压和声粒子速度的积分解,直接求解声源周围的瞬时和有功声强矢量场,直观显示声能量的传播途径,应用于旋转声源辐射声能量的传播分析,揭示了亚音速旋转声源辐射声能量的3种传播模式:螺旋模式、声学黑洞模式和R-A模式;(3)采用球谐级数展开方法建立旋转点/紧凑声源辐射噪声的声压和声粒子速度的频域解析解,在此基础上推导了声功率谱的频域解析解,建立了识别旋转叶片声源在空间域和频域分布特征的方法;(4)综合利用矢量气动声学方法和等效源方法,显示声源和散射边界周围声强矢量场的分布特征和能量传播途径,直接揭示了阻抗边界主要的吸声位置以及直接计算得到阻抗边界的吸收声功率. 相似文献
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考虑空气阻力的抛体射程 总被引:3,自引:0,他引:3
空气阻力对抛体的运动可以产生显著的影响.运用近似的方法处理超越方程,给出了考虑空气阻力的抛体运动落地时间和射程与抛射角的近似解析关系,并且与数值解进行了比较. 相似文献
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用李代数方法分分析了带电粒子在电磁交叉场分析器中的非线性传输,结果近似到三级近似.分析过程为:首先建立粒子在电磁交叉场分析器中的运动的Hamilton函数,然后将Hamilton函数在平衡轨道附近展开成幂级数,最后计算粒子的非线性轨迹到三级近似.根据需要,还可以推导出更高级的近似解. 相似文献
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An advanced time approach for acoustic analogy predictions 总被引:1,自引:0,他引:1
D. Casalino 《Journal of sound and vibration》2003,261(4):583-612
This paper deals with a new interpretation of the retarded time approach that is widely used in the prediction of acoustic fields from moving sources.A hierarchical inversion between the emission time and the reception time leads to advanced time approach. This consists in projecting the current status of a source in the observer time domain where the received signal is progressively built.The practical relevance of this methodology lies on two statements: no retarded time equations must be solved; an aerodynamic noise prediction can be processed parallelly to the aerodynamic computation.Theoretically, the advanced time approach differs from the retarded time approach only in one aspect. A signal emitted at a given instant by a point source, moving at subsonic as well as supersonic velocity, is received only one time by an observer moving at subsonic velocity. Consequently, only one value of the advanced time corresponds to a value of the emission time. The advanced time approach is herein applied to a retarded time solution of the Ffowcs Williams and Hawkings equation proposed by Farassat. The noise radiated by elementary acoustic sources in complex motion is then computed and checked against analytical solutions. 相似文献
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The subject of this paper is the development of a general solution procedure for the vibrations (primary resonance and nonlinear natural frequency) of systems with cubic nonlinearities, subjected to nonlinear and time-dependent internal boundary conditions—this is a commonly occurring situation in the vibration analysis of continuous systems with intermediate elements. The equations of motion form a set of nonlinear partial differential equations with nonlinear, time-dependent, and coupled internal boundary conditions. The method of multiple timescales, an approximate analytical method, is applied directly to each partial differential equation of motion as well as coupled boundary conditions (i.e. on each sub-domain and the corresponding internal boundary conditions for a continuous system with intermediate elements) which ultimately leads to approximate analytical expressions for the frequency-response relation and nonlinear natural frequencies of the system. These closed-form solutions provide direct insight into the relationship between the system parameters and vibration characteristics of the system. Moreover, the suggested solution procedure is applied to a sample problem which is discussed in detail. 相似文献
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Perturbation method of studying the EI Nifio oscillation with two parameters by using the delay sea-air oscillator model 下载免费PDF全文
The EI Nio-southern oscillation (ENSO) is an interannual phenomenon involved in tropical Pacific oceanatmosphere interactions. In this paper, we develop an asymptotic method of solving the nonlinear equation using the ENSO model. Based on a class of the oscillator of the ENSO model, a approximate solution of the corresponding problem is studied employing the perturbation method. 相似文献
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Ivana Kovacic 《Physics letters. A》2009,373(21):1839-1843
An analytical approach to determine the approximate solution for the periodic motion of non-conservative oscillators with a fractional-order restoring force and slowly varying parameters is presented. The solution has the form of the first-order differential equation for the amplitude and phase of motion. The method used is based on the combination of the Krylov-Bogoliubov method with Hamilton's variational principle with the uncommutative rule for the variation of velocity. The conservative systems with slowly varying parameters are also considered. The corresponding adiabatic invariant is obtained. Two examples are given to illustrate derived theoretical results. 相似文献
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Perturbation method of studying the EI Niño oscillation with two parameters using delay sea—air oscillator model 下载免费PDF全文
The EI Niño-southern oscillation (ENSO) is an interannual phenomenon involved in the tropical Pacific ocean-atmosphere interactions. In this paper, we develop an asymptotic method of solving the nonlinear equation using the ENSO model. Based on a class of oscillator of the ENSO model, a approximate solution of the corresponding problem is studied employing the perturbation method. 相似文献
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An asymptotic solving method for the periodic solution of a class of disturbed nonlinear evolution equation 下载免费PDF全文
<正>A class of disturbed evolution equation is considered using a simple and valid technique.We first introduce the periodic traveling-wave solution of a corresponding typical evolution equation.Then the approximate solution for an original disturbed evolution equation is obtained using the asymptotic method.We point out that the series of approximate solution is convergent and the accuracy of the asymptotic solution is studied using the fixed point theorem for the functional analysis. 相似文献
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A. Beléndez E. Gimeno M.L. Álvarez D.I. Méndez A. Hernández 《Physics letters. A》2008,372(39):6047-6052
An analytical approximate technique for conservative nonlinear oscillators is proposed. This method is a modification of the rational harmonic balance method in which analytical approximate solutions have rational form. This approach gives us the frequency of the motion as a function of the amplitude of oscillation. We find that this method works very well for the whole range of parameters, and excellent agreement of the approximate frequencies with the exact one has been demonstrated and discussed. The most significant features of this method are its simplicity and its excellent accuracy for the whole range of oscillation amplitude values and the results reveal that this technique is very effective and convenient for solving conservative truly nonlinear oscillatory systems with complex nonlinearities. 相似文献
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The scope of the spectral index method for solving general planar waveguiding problems is analysed by first showing how simple it is to set up a closed-form transcendental equation whose solution is very accurate; the solution is so fast that the method can be used as a subroutine, making it possible to solve many two-dimensional problems fully, even for coupled rib waveguides, without using effective index approximations. The method is then extended to the uniformly buried waveguide of rectangular cross-section, and the corresponding coupler, thereby unifying the effective index, transverse resonance and spectral index methods for the first time, and giving an asymptotic expression for the coupling length without using overlap integrals. Finally, sample numerical results and optical field profiles are given for the rib waveguide and rib waveguide coupler. 相似文献
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In the current research paper, a conservative system comprising of a mass grounded by linear and nonlinear springs in series connection is studied. The equation of motion for the aforementioned system has been derived as a nonlinear ordinary differential equation with inertia and static–type cubic nonlinearities. The global residue harmonic balance method is applied to obtain an approximate analytical frequency and periodic solution of the problem. Using the obtained analytical expressions, the influences of the hardening and softening nonlinear spring on the non–dimensional frequency are investigated. The results show that developing the system nonlinearity leads the displacement of the mass and the deflection of linear spring to approach each other. Moreover, comparison of the results obtained using the proposed procedure with those achieved by other methods such as numerical method, variational iteration method and harmonic balance approach demonstrates the accuracy and advantages of the current approach. 相似文献