用复数表示法建立质点的平面极坐标运动方程

用复数表示法建立质点的平面极坐标运动方程佘守宪廖耀发（北方交通大学北京１０００４４）（湖北工学院武汉４３００７０）（收稿日期：１９９６０５０８）１引言众所周知，用复数表示法分析交流电路、振动与波动学等问题在数学处理上较为简便．本文所介绍的复数表示...     

考虑损耗的压电陶瓷常用振动模的等效电路(Ⅰ)——电场垂直于长度的长度扩展杆

本文将复常数的概念扩广到所有四组压电方程。从复数压电方程出发推导了电场垂直于长度的长度扩展杆的等效图,从而说明建立考虑损耗的换能器等效图的一般方法。文中对考虑损耗时出现的复数参量的物理意义进行了阐述。并以自由振动情况为例,将考虑损耗时的等效图和不考虑损耗时的等效图作了对比,说明了考虑损耗的必要性。     

复数折射率介质中光束传输的Schro..dinger形式理论研究

将复数折射率介质的Helmholtz方程化为具有复数势能的Schredinger方程的形式,用进化算子的逆算子代替相应的共轭算子,定义了与实数折射率系统光束传输参数具有相似性质的力学量的复数平均值,证明复数光束质量因子守恒是复数ABCD定律成立的充要条件.利用推广的Heisenberg图象,从复数光束传输参数的进化方程得到了位置算子和动量算子的线性进化方程,进一步利用量子力学的表象和表示理论得到了一般复数ABCD系统的Huygens积分. 关键词： 复数折射率 Schrdinger方程 Heisenberg图象 ABCD定律     

复数折射率介质中光束传输的Schrdinger形式理论研究

将复数折射率介质的Helmholtz方程化为具有复数势能的Schr edinger方程的形式 ,用进化算子的逆算子代替相应的共轭算子 ,定义了与实数折射率系统光束传输参数具有相似性质的力学量的复数平均值 ,证明复数光束质量因子守恒是复数ABCD定律成立的充要条件 .利用推广的Heisenberg图象 ,从复数光束传输参数的进化方程得到了位置算子和动量算子的线性进化方程 ,进一步利用量子力学的表象和表示理论得到了一般复数ABCD系统的Huygens积分 .     

复数折射率介质中光束传输的Schrodinger形式理论研究

将复数折射率介质的Helmholtz方程化为具有复数势能的Schredinger方程的形式,用进化算子的逆算子代替相应的共轭算子,定义了与实数折射率系统光束传输参数具有相似性质的力学量的复数平均值,证明复数光束质量因子守恒是复数ABCD定律成立的充要条件.利用推广的Heisenberg图象,从复数光束传输参数的进化方程得到了位置算子和动量算子的线性进化方程,进一步利用量子力学的表象和表示理论得到了一般复数ABCD系统的Huygens积分.     

RPA的复数本征解与相变

应用推广的三能级可解模型,本文研究了满壳体系的相变、哈吹-福克(HF)解的稳定性和无规位相近似(RRA)方程的复数解,并较为仔细地讨论了相变与RPA方程复数解之间的关系.结果表明,RPA方程出现复数解时并不必然地预示着体系发生了相变.一般来说,复数解的出现乃是近似变坏的结果.     

水声作用下矩形弹性-粘弹性复合板的振动和散射声近场(Ⅱ)——矩形弹性-粘弹性复合板散射声近场研究

本文根据作者前一篇文章导出的复合粘-弹性薄板弯曲振动方程给出板振动简正模式的级数解,计算和分析了声波入射时,矩形复合粘弹性障板的振动;研究了密介质中,复合板简正模振动和其二次辐射场之间作用,以及不同模式振动之间由于辐射场引起的互耦合作用;数值计算了简支矩形板各号简正模的自耦合和互耦合系数随kl_1的变化关系,(r=l_2/l_1作为参变量,k为波数,l_1,l_2分别为板的两对边边长);并计算了复合障板在不同频率声波作用下各号模的复数振幅值;进而计算了不同频率声波作用下,板振动二次辐射声的近场声压分布。     

处理谐振电路的三角函数方法

在电磁学教学中,谐振电路的处理通常是用矢量图解法和复数方法,这需要了解振动的旋转矢量和复数表示.本文介绍一种直接的处理方式,即对振动函数(三角函数)进行运算,就可以得到最终的结果.这种处理方法还可以推广到一般的交流电路.该方法对预备知识的要求较低,适合在一些非物理专业大学物理课程中使用.     

单芯偏心电缆的磁场

利用复数坐标系z上的分式线性变换,计算单芯偏心电缆的磁场,并给出磁感线方程.     

新书推荐

正内容简介内容简介:《云端脚下》是一本视界垂直的书,讲述从一元二次方程、三次方程、四次方程到代数不可解的五次方程,引出复数与超复数、线性代数以及群论,最终成就了量子力学、相对论和规范场论的伟大历程,     

多级阻振质量阻隔振动波的传递特性研究

利用波动理论的分析、处理方法,分析了多级平行阻振质量阻隔振动波传递的特性,给出了多级阻振质量对平面弯曲波传递的阻抑公式,讨论了平面弯曲波传递时形成的穿透频段和堵塞频段,并进行了相应的算例分析,采用有限元法对多级阻振质量的隔振性能进行了数值计算,结果表明:阻振质量对偏离法向角的弯曲波分量的阻抑较强,传递能量的损失较大;多级阻振质量能够较好地阻抑结构声的传递,且阻抑效果随着阻振级数的增加而增大;在有几个阻振质量的情况下,通过改变它们的平行性,可以提高其隔振效果;且如果将不同质量、不同横截面形状的阻振质量前后交错配置,同样可以使总的隔振效果提高,这对于多级阻振质量在船体结构减振降噪中的应用具有重要的参考意义。     

Influence des ondes de “galerie a echo” sur la diffusion d'une onde ultrasonore plane par un cylindre

An experimental method which allows measurement of the frequency (ka) of circumferential wave resonances which propagate in aluminium cylinders is described. It is also possible to deduce the number of wavelenghts on the circumference or the vibration mode of circumferential waves. This study allows a better understanding of the complex structures of the form function in the far field. It specifies the theoretical results which show the effect of each circumferential wave in the angular diagram.     

Amplification of light in one-dimensional vibrating metal photonic crystal

Photon–phonon interaction on the analogy of electron–phonon interaction is considered in one-dimensional metal photonic crystal. When lattice vibration is artificially introduced to the photonic crystal, a governing equation of electromagnetic field is derived. A simple model is numerically analyzed, and the following novel phenomena are found out. The lattice vibration generates the light of frequency which added the integral multiple of the vibration frequency to that of the incident wave and also amplifies the incident wave resonantly. On a resonance, the amplification factor increases very rapidly with the number of layers. Resonance frequencies change with the phases of lattice vibration. The amplification phenomenon is analytically discussed for low frequency of the lattice vibration and is confirmed by numerical works.     

磁流变液构成的类梯度结构振动传递特性

提出了一种磁流变液构成的类梯度结构,并通过理论建模、数值计算和实验研究了该结构的振动传递特性.磁流变液在磁场作用下具有液固转换的特殊理化性质,而液固转换过程就是磁流变液的振动传递阻抗变化过程.因此,基于磁流变液的这一特性,通过控制磁场,构建了类梯度结构.基于弹性波传递的一维波动方程,建立了垂直入射的弹性波在类梯度结构中传递的波动方程.然后,使用连续介质的离散化方法和传递矩阵法进行求解,得到振级落差的表达式,对其进行数值计算,分析类梯度结构的振级落差随弹性波频率和磁场强度的变化趋势.最后,对类梯度结构的振动传递特性进行了实验研究,分析了磁场强度对类梯度结构振动传递特性的影响.研究结果表明,与均匀场作用的磁流变液相比,类梯度结构对弹性波的衰减效果更好,且该结构具备良好的可调控特性.     

7-羟基香豆素红外光谱的密度泛函理论研究

红外光谱是化合物结构鉴定的重要信息来源,对天然有机药物的分子结构及其生物活性研究意义重大。而随着理论计算方法更加合理、计算精度不断提高,理论计算在红外光谱模拟、振动模式归属指认等方面优势更加明显,对红外光谱解析等实验研究具有重要参考价值。本研究利用密度泛函理论(density functional theory, DFT)/B3LYP方法,在6-311G(d,p)基组水平对7-羟基香豆素进行了几何结构优化和红外光谱计算,得到稳定结构及全部振动模式。计算结果显示7-羟基香豆素红外光谱吸收峰主要分布于波数3 700～3 500,3 150～3 000,1 750～1 400,1 400～1 000,1 000～50 cm-1几个区域。除波数3 700～3 500,3 150～3 000 cm-1范围内振动相对独立,分别归属为O—H伸缩振动和芳环C—H伸缩振动外,其他几个区域均较为复杂,谱峰不同程度由多个振动模式叠加而成。最后,根据振动模式理论及振动图像分析,对所有振动模式进行了详细指认。并通过线性回归方法,利用相关系数值r研究了7-羟基香豆素红外光谱主要吸收峰波数理论计算值和实验数据的相关性。结果表明,计算值和实验值基本吻合,相关系数值等于0.998 5,相关性较好;采用密度泛函理论在该基组水平对7-羟基香豆素红外光谱的理论计算较为可靠。     

Vibration reduction by using the idea of phononic crystals in a pipe-conveying fluid

Flexural vibration in a pipe system conveying fluid is studied. The pipe is designed using the idea of the phononic crystals. Using the transfer matrix method, the complex band structure of the flexural wave is calculated to investigate the gap frequency range and the vibration reduction in band gap. Gaps with Bragg scattering mechanism and locally resonant mechanism can exist in a piping system with fluid loading. The effects of various parameters on the gaps are considered. The existence of flexural vibration gaps in a periodic pipe with fluid loading lends new insight into the vibration control of pipe system.     

Apertureless SNOM imaging of the surface phonon polariton waves: what do we measure?

The apertureless scanning near-field microscope (ASNOM) mapping of surface phonon polariton (SPP) waves being excited at the surface of the SiC polar crystal at a frequency corresponding to the lattice resonance was investigated. The wave with well-defined direction and source position, as well as a well-known propagation law, was used to calibrate the signal of an ASNOM. An experimental proof is presented showing that the signal collected by the ASNOM in such a case is proportional (as a complex number) to the local field amplitude above the surface, regardless of the tip response model. It is shown that the expression describing an ASNOM response, which is, in general case, rather complicated nonlinear function of a surface/tip dielectric constants, wavelength, tip vibration amplitude, tip shape etc., can be dramatically simplified in the case of the SPP waves mapping in a mid-IR range, due to a lucky combination of the tip and surface parameters for the case being considered. A tip vibration amplitude is much less than a running SPP wave field decay height in a normal direction. At the same time, the tip amplitude is larger than a characteristic distance at which a tip–surface electromagnetic near-field interaction plays a significant role.     

Separability of amplitude,phase and polarization information in the Jones calculus

The two-component Jones vector is cast in a form that achieves the separation of the information on the polarization ellipse from that on the amplitude and phase of the light wave. The shape, sense of rotation and orientation of the elliptic vibration of the electric field are described by the complex polarization variable χ while the amplitude a (size) and temporal phase ? of that vibration are described by the complex amplitude A = aexp(i?). The transformation of the complex amplitude of the wave A after passing through an optical system leads to a complex-amplitude transfer function (CATF) which is a nonanalytic function of the complex polarization variable χ. The CATF is, in turn, separable into polarization-dependent (real) amplitude and phase transfer functions (ATF and PHTF). Together with the polarization transfer function PTF (the transformation of χ), the ATF and PHTF provide a useful set of tools that complement the well-known Jones calculus.     

Wave structure analysis of guided waves in a bar with an arbitrary cross-section

Both dispersion curves and wave structures, which are displacement distributions on a bar cross-section, are essential for guided wave NDEs. Theoretical dispersion curves and wave structures for a bar with an arbitrary cross-section are derived in this paper using a special modeling technique called the semi-analytical finite element method (SAFEM). The guidelines for guided wave NDEs of bar-like structures are also shown based on wave structure and modal analysis. First, the relationship between the dispersion curves and their corresponding wave structures were obtained for a square rod. Modes with longitudinal vibration have higher group velocities and torsional modes have constant phase and group velocities. Next, the relationship between the dispersion curves and wave structures for a rail are detailed. The rail is used to represent a bar with a complex cross-section. Similar to the square rod results, the rail's longitudinal modes have higher group velocities. However, the rail contains modes with local vibration. Finally, single mode detection and excitation techniques are introduced. A single mode can be obtained by detecting and exciting with a weighted function that corresponds to a specific mode's wave structure.     

Transverse and torsional complex vibration systems for ultrasonic seam welding of metal plates

Transverse and torsional complex vibration systems for ultrasonic seam welding of metal plate specimens, using a 27 kHz complex vibration disk welding tip vibrating in transverse and torsional vibration modes, were studied. Using a complex vibration welding system with a welding tip vibrating in elliptical or circular locus, thick plate specimens can be welded with a more uniform and larger area compared to a conventional ultrasonic welding system. The disk welding tip vibrates in an elliptical or circular locus. The complex vibration system can continuously weld multiple parts of metal plate specimens such as heat sinks with a large number of fins.