NON-LINEAR VIBRATION AND THERMAL BUCKLING OF AN ORTHOTROPIC ANNULAR PLATE WITH A CENTRIC RIGID MASS

A computational analysis of the non-linear vibration and thermal post-buckling of a heated orthotropic annular plate with a central rigid mass is examined for the cases of immovably hinged as well as clamped constraint conditions of the outer edge. First, based on von Karman's plate theory and Hamilton's principles, the governing equations, in terms of the displacements of the middle plane, of the problem are derived. Then, upon assuming that harmonic responses of the system exist, the non-linear partial differential equations are converted into the corresponding non-linear ordinary differential equations through elimination of the time variable by using the Kantorovich time-averaging method. Finally, by applying a shooting method, the fundamental responses of the non-linear vibration and thermal post-buckling of the plate are numerically obtained. For some prescribed values of the parameters, such as the material rigidity ratio, temperature rise and so on, the curves of the fundamental frequency versus specified amplitude and the thermal post-buckled equilibrium paths of the plate are numerically presented.     

鱼洗振型浅析

本在普通物理的层次上建立鱼洗的物理模型，应用柱面坐标的波动方程和模拟鱼的简化边界条件解出其自激振荡振型，与应用激光全息手段拍摄的鱼洗振型基本一致亦与锤击实验中测得的鱼洗侧壁位移相符，从而初步揭示了鱼洗的喷水机理。     

谐振系统能量Ek+Ep=1/2kA2的涵义

在文献[4]的基础上，举例论证谐振动就是动、势能在平衡位置附近相互转化，因此，参考点一般应选取在平衡位置．     

GENERATION OF ENTANGLED FOCK STATES OF TWO NONLOCAL CAVITY MODES WITH DIFFERENT FREQUENCIES

We present a method to generate entangled Fock states of two nonlocal cavity modes with different frequencies. We send an atom with three levels g,e, and f across two cavities. The atomic transition frequency between level g and e is resonant with the first cavity frequency, while the atomic transition frequency between level g and f is resonant with the second cavity frequency. The detection of the atomic state leaves the pure field in an entangled Fock state.     

RESEARCH ON VIBRATION MODES OF THE CHINESE CHIME STONE

Nearfield acoustical holography is a powerful tool for imaging of acoustic sources. In this article, the basic theory treating steady-state acoustic radiation with generalized holography has been discussed. By holographic imaging, the vibration characteristics of irregular objects, the Chinese ancient musical instrument, the one-tone chime stone and the two-tone chime stone provided by the Institute of Archaeology, the Museum of Hubei Province, have been researched. The results show that the ancient chime stone has two main vibration modes, which make up the base of sound produced by the instrument. As for the two-tone chime stone, it is not so long and wide as the single-tone chime stone, but thicker and smoother than the single-tone chime stone. When it is excited at different positions, although it radiates sounds of different frequencies, its vibration modes are similar. This may be related to its dimensions and shape. The research is helpful for studying the sound producing system and the radiated field characteristics of the chime stone.     

RESEARCH ON VIBRATION MODES OF THE CHINESE CHIME STONE

Nearfield acoustical holography is a powerful tool for imaging of acoustic sources. In this article, the basic theory treating steady-state acoustic radiation with generalized holography has been discussed. By holographic imaging, the vibration characteristics of irregular objects, the Chinese ancient musical instrument, the one-tone chime stone and the two-tone chime stone provided by the Institute of Archaeology, the Museum of Hubei Province, have been researched. The results show that the ancient chime stone has two main vibration modes, which make up the base of sound produced by the instrument. As for the two-tone chime stone, it is not so long and wide as the single-tone chime stone, but thicker and smoother than the single-tone chime stone. When it is excited at different positions, although it radiates sounds of different frequencies, its vibration modes are similar. This may be related to its dimensions and shape. The research is helpful for studying the sound producing system and the radiated field characteristics of the chime stone.     

圆板在匀布重压下所生之挠曲

本文所研究者,为一周缘夹紧之圆板,在匀布之侧向重压下所生之巨大挠曲。本文用圆板中点之挠曲距离与板厚之比率为参数,逐步求得本题之近似解答,藉此避免前人Way氏之幂级数法中繁重之数字计算。圆板周缘呈现委屈现象之条件,亦可求得,其结果与McPherson,Ramberg及Levy诸氏之实验,完全吻合。本法亦可适用于一圆板在其它周缘条件及其它荷重情况下之诸问题。     

双模腔场中具有不同耦合常数的两原子多光子辐射谱

研究了与双模腔场具有不同耦合常数的两个二能级原子的多光子辐射谱,给出了双模多光子辐射谱的一般表达式.结果表明,当双模腔场分别处于不同数态时,虽然两原子与双模腔场之间具有不同的耦合常数,但对于任意的N₁和N₂(N_i(i＝1,2,)为模i腔场被每个原子吸收或发射的光子数),辐射谱总是关于共振频率ω₀对称分布;并且,当N₁＝N₂时,对于任意的数态光子数n₁和n₂交换,辐射谱不变.上述特点用解析方法给予了解释.计算了非简并双光子情况下的辐射谱,并得到了一些新结果.双模腔场中单原子及具有相同耦合常数的两原子辐射谱可从本文结果分别做为特例而得到.     

受迫振动的能量共振

通过对受迫振动系统的功能，势能和总能量的分析，推证了受迫振动系统能量共振的频率，并对其结果进行了分析讨论。     

ON THE INELASTICITY OF SUPERHIGH ENERGY COSMIC RAY INTERACTIONS

The inelasticity of p-air and A-air interactions of superhigh energy cosmic rays is analysed and the influence of the nuclear collision geometry is investigated.     

用群论方法确定H2O的振动模式

用群论方法给出Ｈ２Ｏ分子的三种简正振动模式的数学表达式，并对有关计算作进一步分析讨论放补充修正。     

两种类型超导体的能隙

关键词：     

高能带电粒子直接产生电子对

本文叙述利用场强为6200高斯的磁云室,对级联簇射中的能量大于30兆电子伏的电子在铝中直接产生电子对的平均总截面进行了测量。实验上总共找到真正由电子产生的电子三岔8.1个,相应于三岔产生的平均自由路程为672±585厘米或平均总截面为(0.25±0.22)×10^-25厘米²。在数据处理中,对假三岔数目的除去作了应有的适当考虑。此外对Bhabha及Murota等的总截面公式也作了适合于于我们实验具体情况的修正,并算出总截面值,最后将它同实验值作了比较。结果我们认为实验上测得的值和Murota等的总截面值较为接近,但也不与Bhabha的截面值矛盾。     

轴向极化压电陶瓷圆片的自由振动低阶振动方式分析

本文利用解微分方程二点边值问题的伴随法^[6],对应力自由边界条件下的轴向极化压电陶瓷圆片振子的压电运动方程进行了数值积分。求出了厚度与直径比小于0.45的振子在厚度方向运动影响下的低阶径向模的谐振频率及质点位移分布图象。给出了基频的厚度影响修正曲线及与泊松比有关的泛音比曲线。
本文的数值计算全面考虑了压电性的作用,未对振子尺度作任何限制.实验结果与计算结果很好相符。     

A TWO-DIMENSIONAL TCHEBYCHEFF COLLOCATION METHOD FOR THE STUDY OF THE VIBRATION OF A BAFFLED FLUID-LOADED RECTANGULAR PLATE

The vibration and the acoustic radiation of a baffled rectangular plate in contact with a dense fluid is considered. By using Green's representation theorem, the original system of differential equations governing both the displacement and the acoustic sound pressure is transformed into a system of coupled boundary integral equations. The unknown functions (the displacement of the plate, the pressure jump at the surface of the plate and the boundary sources) are expanded as series of Tchebycheff polynomials. The new unknowns (the coefficients of the series) are calculated by using a collocation method. Some results, both theoretical and numerical, are given concerning the resolution properties of the Tchebycheff approximation. The numerical difficulties are presented, and solutions of these are proposed. Numerical examples are given.     

金属和压电陶瓷构成的两层复合薄圆板的强迫振动

本文分析了电压策动或均匀声压策动下的由半径不同的压电陶瓷和金属板构成的两层复合薄圆板的强迫振动。给出了简支边界条件和固定边界条件下的严格解和串联共振频率方程与并联共振频率方程。用Rayleigh-Ritz方法给出了简支边界条件下电压策动的强迫振动的近似解和串联共振频率方程。数字结果给出了能得到较大机电耦合系数的无量纲几何参量的最佳值。本文还讨论了弹性耦合和惯性耦合对共振频率的影响。     

稳定受迫振动中的能量转换

将强迫分解成超前位移π／２和位移相同或反相的两个分量，通过对两分力作功的定量计算，可以方便地讨论受迫振动中的能量转换，并能对共振作出较的物理解释。