Vibration analysis of a beam with PCLD Patch

An analytical approach for vibration response analysis of a beam with single passive constrained layer damping (PCLD) patch is presented. The governing equation of motion of the beam is firstly derived on the basis of an energy approach and the Lagrange equation. The noval contribution is that a third admissible function is introduced to represent the longitudinal displacements of the constraining layer in the PCLD patch when the assumed-modes method is applied for discretizing the governing equation. In conventional analytical approaches, only two admissible functions are used together with a longitudinal static equilibrium equation of a section of base beam or constraining layer. Comparison of the computational results from the proposed analytical approach and the conventional analytical approach as well as a commercial FEM code reveals that the proposed analytical approach can describe the vibration responses of the damped beam more accurately for commonly used viscoelastic material (VEM) layer in the PCLD patch while the conventional analytical approach, in general, overestimates the damping effects of the PCLD patch. The advantages and disadvantages of the proposed analytical approach and conventional analytical approach are discussed through some case studies.     

Determination of equivalent salt deposit density using wind velocity for a contaminated insulator

This paper illustrates a new analytical model for determining equivalent salt deposit density (ESDD) on contaminated insulators using wind velocity. The analytical model is derived using the dimensional analysis technique. The values of ESDD from the analytical model are calculated using different values of wind velocity. These results are compared with the experimental results obtained from sites. The analytical results are also compared with the polynomial model output obtained via least-squares analysis of experimental data. It is found that the results obtained by the analytical model are quite consistent with the experimental results for different range of wind velocity.     

Offner成像光谱仪建模及像差分析

利用光线追迹方法得到系统的数值模型,然后运用级数展开方法,建立起系统的3阶解析模型,亦即3阶像差理论.该模型给出系统像差系数和计算系统点列图的解析表达式,可适应于包含变间距凸面光栅的系统,并具有良好的扩展性.通过追迹示例Offner系统中10000条不同波长、不同高度的光线,结果表明运用解析模型可以快速而准确地生成系统...     

Numerical and Analytical Approaches to Modeling Critical Two-Phase Flow with Granular Layer

Based on data obtained in the previous experimental study conducted by the authors, two approaches are proposed for analytical and numerical modeling of a critical two-phase flow in a pipe with a granular layer. An analytical approach is based on a polytrophic model, while a numerical approach was developed using a smoothed particle hydrodynamics method. A model of isenthalpic flow of vapor–water mixture in a fixed bed of solid particles is considered is this study. The mixture expansion process is considered to be polytropic. Similarly to the known problem of gas dynamics of a granular bed, an analytical relationship for calculation of a critical mass velocity was obtained. The results of the calculation based on the analytical and numerical models were compared with the experimental data and agreement between analytical and numerical data and the experiment was observed.     

IR multiple-photon dissociation by a focused uniform beam

An improved analytical method is presented in which the reaction yield in the IR multiple-photon dissociation by a focused uniform beam is expressed in a generalized form as a function of fluence. The analytical solution is derived for a real focusing geometry by assuming the cumulative log-normal distribution (CLND) for the functional form of the dissociation probability vs. fluence. Also presented is a shortcut analytical method with simple and convenient algebraic expressions which approximate the exact analytical solution, thereby speeding up the analysis of experimental data.     

一类非线性微分方程的近似解析解

从理论上研究了一类广义扩散方程的求解问题. 利用相似变换和解析拆分技巧给出了求解该类非线性微分方程近似解的一种有效方法, 方程的解可以表示为一个收敛的幂级数. 近似解结果和数值结果非常符合，证明了所提出的方法的准确性和可靠性, 该方法可以用于解决其他科学和工程技术问题. 关键词： 广义扩散方程 非线性边界值问题 解析拆分 近似解析解     

Analytical solution of transverse oscillation in cyclotron using LP method

We have carried out an approximate analytical solution to precisely consider the influence of magnetic field on the transverse oscillation of particles in a cyclotron.The differential equations of transverse oscillation are solved from the Lindstedt-Poincare method.After careful deduction,accurate first-order analytic solutions are obtained.The analytical solutions are applied to the magnetic field from an isochronous cyclotron with four spiral sectors.The accuracy of these analytical solutions is verified and confirmed from comparison with a numerical method.Finally,we discussed the transverse oscillation at v_0=N/2,using the same analytical solution.     

Analytical solution to LIDAR return signals from clouds with regard to multiple scattering

An analytical approach to LIDAR return signal calculation with regard to multiple scattering is suggested. Two versions of the method are developed. The first one is completely analytical and undispensible for qualitative studies. The second semianalytical approach provides a sufficient accuracy up to a sounding optical depth about 5. Being somewhat more tedious than the proposed analytical solution, the second approach appears to be time saving in comparison with known methods.     

An approximate analytic solution of the steady state Brillouin scattering in single mode optical fiber without neglecting the attenuation coefficient

The analysis of steady state Brillouin scattering in a long single mode optical fiber is presented. Meanwhile, an approximate analytical functions of distributed Brillouin scattering and pump wave along the fiber with the fiber attenuation coefficient are obtained for the first time. A comparison is made among the analytical solutions with the attenuation coefficient, the analytical solutions without the attenuation coefficient and the exact numerical solutions. The results show that the analytical solutions with fiber attenuation coefficient are more close to the numerical solutions, which can be used to describe the power distribution of the pump wave and the Stokes wave along the long distance single mode optical fiber accurately.     

An analytical model for the determination of the cup-burner minimum extinguishing concentration of inert fire suppression agents

An analytical model based on the perfectly stirred reactor (PSR) concept is developed and utilized in the prediction of the minimum extinguishing concentration (MEC) of inert fire suppression agents that is established in the standard cup-burner test. In the PSR-based approach, both thermal (heat absorption) and chemical mechanisms of fire suppression can be captured. The assumed perfect mixing, on the other hand, prevents the ability to capture transport related mechanisms. In past work, the PSR approach using detailed chemistry was demonstrated to be effective in reproducing the MEC albeit with the need of single point calibration. The closed form solution presented herein becomes possible when the detailed chemistry is simplified to a single step, mole preserving chemical reaction. At the core of the model is an analytical expression for the extinction temperature which is transcendental and thus requires a numerical iterative solution. The analytical model is first verified using a traditional computational PSR (CHEMKIN package) that employs the same reduced kinetics as the analytical model. Subsequently, results from the analytical model are contrasted to those from a traditional PSR with detailed chemistry, from a semi-analytical approach that assumes heat absorption by the agent is the primary extinguishing mechanism, and from experimental data of various research groups. Good agreement is achieved validating the analytical model as a simple and accurate approach to determine the MEC. The analytical model is also used in a parametric assessment of the impact of geographic altitude (i.e. effect of ambient pressure) on the MEC and results are in good agreement with those of a traditional PSR with detailed chemistry.     

Wigner distribution function of Gaussian beam through an apertured and misaligned ABCD optical system

By expanding the hard aperture function into a finite sum of complex Gaussian functions, approximate analytical expressions of Wigner distribution function for fundamental mode Gaussian beam through an apertured and misaligned ABCD optical system are derived. Compared with the aligned case, results show that the misaligned optical system will introduce in the output Wigner distribution function a coordinate shift in space-frequency plane. To examine the analytical results, some numerical simulations are carried out and the absolute errors between analytical results and numerical integral ones are presented. It is shown that the approximate analytical results are proper and ascendant.     

Analytical second derivatives for excited electronic states using the single excitation configuration interaction method: theory and application to benzo[a]pyrene and chalcone

A compact formulation and a semi-direct implementation are described of analytical second derivatives of the single excitation configuration interaction (CIS) energy. CPU time, memory usage and disc storage all scale with the same power of system size as the ground state Hartree—Fock (HF) method, with a coefficient only 2 to 3 times larger. Thus usually analytical excited state CIS frequencies are feasible when HF frequencies are feasible. As a computational example, analytical CIS/3-21G frequencies for benzo[a]pyrene are calculated more efficiently than with finite differences. As a chemical application, analytical CIS/6-31G^* frequencies are used to investigate non-planarity in the lowest π → π excited state of transchalcone.     

Evaluation of the generalized Goodwin-Staton integral using binomial expansion theorem

A new analytical technique for evaluating the generalized Goodwin-Staton integral (GGS) is described. A closed-form evaluation is presented. The GGS integral are expressed in terms of linear combinations of binomial coefficients and incomplete gamma function. A further comparison of analytical results with numerical models demonstrates a high accuracy of the developed analytical solution. The convergence of the results is shown.     

激光诱导击穿光谱在材料表面分析领域中的应用进展

激光诱导击穿光谱作为表面分析工具是近十年发展起来的,对表面分析基础理论、仪器装置及其在材料科学领域中的应用进行详细的综述。重点阐述了激光诱导击穿光谱在国内外冶金、半导体、电子等材料科学领域中的元素分布分析及镀层分析应用进展,指出激光束单个脉冲能量、环境气体及气压、激光束能量分布等参数对分辨率的影响,同时指出在兼顾灵敏度的前提下提高分辨率的途径。与传统经典表面分析工具相比较具有扫描面积大、分析速度快及样品导电与否均可分析等优点,成为传统表面分析工具的有力补充。     

基于二阶矢量位的矩形截面回折线圈阻抗和脉冲磁场的解析建模与计算

本文基于二阶矢量位建立了回折线圈的阻抗和磁场计算的解析模型,并提出了计算磁场脉冲响应的方法.根据回折线圈用于涡流检测和电磁超声检测时的通用模型,将回折线圈的阻抗和磁场计算问题转化为多个单匝矩形线圈阻抗和磁场的叠加问题.基于二阶矢量位和时谐电磁场方程,推导了回折线圈的频域标势表达式;利用标势与矢量磁位和磁通密度间的关系,推导了计算区域的磁通密度和式样表面涡流的频域解析计算公式;通过计算线圈的感应电势和阻抗变化表达式,得到了线圈阻抗的频域解析表达式;采用FFT-IFFT方法计算了脉冲磁场的时域响应.以一双层双 关键词： 无损检测 回折线圈 二阶矢量位 解析建模     

A UNIVERSAL MODULATION FUNCTION AND A GENERALIZED ANALYTICAL SOLUTION FOR PHOTOREFRACTIVE TWO-WAVE COUPLING

We proposed a universal form of the modulation function,and derived a generalized analytical solution of the two wave coupled equation in transmission geometry in photorefractive crystal corresponding to the universal modulation function. The generalized analytical solution can be transformed into different analytical solutions reported in previous works on different conditions.In addition, other new analytical solutions can be obtained from the generalized analytical so lution,and an example is given in the present paper.     

A UNIVERSAL MODULATION FUNCTION AND A GENERALIZED ANALYTICAL SOLUTION FOR PHOTOREFRACTIVE TWO WAVE COUPLING

We proposed a universal form of the modulation function,and derived a generalized analytical solution of the two wave coupled equation in transmission geometry in photorefractive crystal corresponding to the universal modulation function. The generalized analytical solution can be transformed into different analytical solutions reported in previous works on different conditions.In addition, other new analytical solutions can be obtained from the generalized analytical so lution,and an example is given in the present paper.     

Studies of beam propagation characteristics on apertured fractional Fourier transforming systems

Based on the principle that a rectangular function can be expanded into a sum of complex Gaussian functions with finite numbers, propagation characteristics of a Gaussian beam or a plane wave passing through apertured fractional Fourier transforming systems are analyzed and corresponding analytical formulae are obtained. Analytical formulae in different fractional orders are numerically simulated and compared with the diffraction integral formulae, the applicable range and exactness of analytical formulae are confirmed.It is shown that the calculating speed of using the obtained approximate analytical formulae, is several hundred times faster than that of using diffraction integral directly. Meanwhile, by using analytical formulae the effect of different aperture sizes on Gaussian beam propagation characteristics is numerically simulated, it is shown that the diffraction effect can be neglected when the aperture size is 5 times larger than the beam waist size.     

Unsteady analytical solutions of the spherical shallow water equations

A new class of unsteady analytical solutions of the spherical shallow water equations (SSWE) is presented. Analytical solutions of the SSWE are fundamental for the validation of barotropic atmospheric models. To date, only steady-state analytical solutions are known from the literature. The unsteady analytical solutions of the SSWE are derived by applying the transformation method to the transition from a fixed cartesian to a rotating coordinate system. Fundamental examples of the new unsteady analytical solutions are presented for specific wind profiles. With the presented unsteady analytical solutions one can provide a measure of the numerical convergence in the case of a temporally evolving system. An application to the atmospheric model PLASMA shows the benefit of unsteady analytical solutions for the quantification of convergence properties.     

光电直读光谱法测定纯金属中的痕量元素

光电直读光谱法评价分析低含量元素的重要依据是：检测限、精密度、稳定性。通过对光电直读光谱法测量纯金属中痕量元素分析条件的研究,发现被测元素的检出限主要取决于所选择的分析谱线及放电类型,与参比线基本无关;被测元素的测量精密度及稳定性主要取决于分析线对（分析谱线／参比线）及放电类型。这个规律可用于选择最佳测量条件,快速准确地测定纯金属中痕量元素。