Improved Calculation of Vibrational Energy Levels in F2 Molecule using the RKR Method

The potential energy curves of the ground state X2∑＋g of the fluorine molecule have been accurately reconstructed employing the Ryderg-Klein-Rees （RKR） method extrapolated by a Hulburt and Hirschfeler potential function for longer internuclear distances. Solving the corresponding radial one-dimensional Schr？dinger equation of nuclear motion yields 22 bound vibrational levels above v=0. The comparison of these theoretical levels with the experimental data yields a mean absolute deviation of about 7.6 cm^-1 over the 23 levels. The highest vibrational level energy obtained using this method is 13308.16 cm？1 and the relative deviation compared with the experimental datum of 13408.49 cm^-1 is only 0.74%. The value from our method is much closer and more accurate than the value obtained by the quantum mechanical ab initio method by Bytautas. The reported agreement of the vibrational levels and dissociation energy with experiment is contingent upon the potential energy curve of the F2 ground state.

Vibrations induced by tunnel boring machine in urban areas: In situ measurements and methodology of analysis

Excavation with tunnel boring machine(TBM)can generate vibrations,causing damages to neighbouring buildings and disturbing the residents or the equipment.This problem is particularly challenging in urban areas,where TBMs are increasingly large in diameter and shallow in depth.In response to this problem,four experimental campaigns were carried out in different geotechnical contexts in France.The vibration measurements were acquired on the surface and inside the TBMs.These measurements are also complemented by few data in the literature.An original methodology of signal processing is pro-posed to characterize the amplitude of the particle velocities,as well as the frequency content of the signals to highlight the most energetic bands.The levels of vibrations are also compared with the thresholds existing in various European regulations concerning the impact on neighbouring structures and the disturbance to local residents.

Impact of the Foucault Current and Its Vibration Noise Reduction on Bracket Features for AMDT

This manuscript explores the influences of the Foucault current on bracket vibration. Noise measurements are obtained in conditions that the coils are enclosed by the bracket, and exposed to the air for confirming the impact of Foucault current on bracket vibration. The outcomes illustrate that the bracket increases the primary noise to 21 d B. Throughout investigational modal computation, ordinary frequencies of the coils stay afar from the exciting frequency of 100 Hz but the ordinary frequency 72.924 Hz of the bracket stands near to 100 Hz, which similarly explicates the upsurge of the noise level. To do the computations on bracket vibrations instigated by the Foucault current, a finite-element method(FEM) has been utilized for evaluating the eddy current density, electromagnetic forces(EMF), coupled with bracket response in frequency domain. The calculations displayed a proper approval by mean of theoretic investigations, and the simulations analyzed effectively the bracket vibration produced by Eddy current, and the electromagnetic force(EMF). Referring to the simulation, the primary vibration characteristics, and noise level, the method by applying weights(stress) on the top bracket of transformer is proposed to lessen the vibration amplitude, and noise level. To indorse the utility, and application of the suggested technique, the experiment results are obtained, analyzed, and compared with those of simulations, primary vibration characteristics, and noise level.

Weighted Multi-sensor Data Level Fusion Method of Vibration Signal Based on Correlation Function

As the differences of sensor＇s precision and some random factors are difficult to control,the actual measurement signals are far from the target signals that affect the reliability and precision of rotating machinery fault diagnosis.The traditional signal processing methods,such as classical inference and weighted averaging algorithm usually lack dynamic adaptability that is easy for trends to cause the faults to be misjudged or left out.To enhance the measuring veracity and precision of vibration signal in rotary machine multi-sensor vibration signal fault diagnosis,a novel data level fusion approach is presented on the basis of correlation function analysis to fast determine the weighted value of multi-sensor vibration signals.The approach doesn＇t require knowing the prior information about sensors,and the weighted value of sensors can be confirmed depending on the correlation measure of real-time data tested in the data level fusion process.It gives greater weighted value to the greater correlation measure of sensor signals,and vice versa.The approach can effectively suppress large errors and even can still fuse data in the case of sensor failures because it takes full advantage of sensor＇s own-information to determine the weighted value.Moreover,it has good performance of anti-jamming due to the correlation measures between noise and effective signals are usually small.Through the simulation of typical signal collected from multi-sensors,the comparative analysis of dynamic adaptability and fault tolerance between the proposed approach and traditional weighted averaging approach is taken.Finally,the rotor dynamics and integrated fault simulator is taken as an example to verify the feasibility and advantages of the proposed approach,it is shown that the multi-sensor data level fusion based on correlation function weighted approach is better than the traditional weighted average approach with respect to fusion precision and dynamic adaptability.Meantime,the approach is adaptable and easy to use,can be applied to other areas of vibration measurement.

Investigations on spectroscopic parameters, vibrational levels, classical turning points and inertial rotation and centrifugal distortion constants for the 1 ＋ X^1∑g^＋ state of sodium dimer

The density functional theory （B3LYP, B3P86） and the quadratic configuration-interaction method including single and double substitutions （QCISD（T）, QCISD） presented in Gaussian03 program package are employed to calculate the equilibrium internuclear distance Re, the dissociation energy De and the harmonic frequency We for the XIEg＋ state of sodium dimer in a number of basis sets. The conclusion is gained that the best Re, De and We results can be attained at the QCISD/6-311G（3df,3pd） level of theory. The potential energy curve at this level of theory for this state is obtained over a wide internuclear separation range from 0.16 to 2.0 nm and is fitted to the analytic Murrell-Sorbie function. The spectroscopic parameters De, DO, Re, ωe, ωe Xe, αe and Be are calculated to be 0.7219 eV, 0.7135 eV, 0.31813 nm, 151.63 cm^-1, 0.7288 cm^-1, 0.000729 cm^-1 and 0.1449 cm^-1, respectively, which are in good agreement with the measurements. With the potential obtained at the QCISD/6-311G（3df,3pd） level of theory, a total of 63 vibrational states is found when J = 0 by solving the radial SchrSdinger equation of nuclear motion. The vibrational level, corresponding classical turning point and inertial rotation constant are computed for each vibrational state. The centrifugal distortion constants （Dr Hv, Lv, Mv, Nv and Ov） are reported for the first time for the first 31 vibrational states when J = 0.

New Method to Measure the Fill Level of the Ball Mill Ⅱ-Analysis of the Vibration Signals

The exact measurement of the fill level is the key and basic problem for automatic control and optimized operation of the coal pulverizing system. Because the ball mill pulverizing system is non-linearity, long time delay and time-varying, the reliable and effective method for measuring the fill level was lacked at present. In order to reduce the influence by various factors on measuring the fill level and improve the measuring accuracy of the fill level, a novel characteristic variable is proposed. A set of wireless transmission device was designed to record vibration signals, and an accelerometer with high accuracy and large measuring range was mounted directly on the mill shell to pick up the vibration signals from the mill shell. A series of data acquisition experiments under various ball load and water content of coal conditions were conducted in an industrial mill to investigate the relationship between the fill level and the angular position of the maximum vibration point of the mill shell through the analysis of the vibration signals. The analytical result of test data clearly show that the angular position of the maximum vibration point on the mill shell decreases as the fill level increases. At the same time, comparing with the traditional characteristic variable, the feature variable of the fill level proposed in this paper is not subject to the effect of the ball load and water content of coal, which provides a new solution and reliable basis for the accurate measurement of the fill level.

Distribution of Vibrational Energy Levels of Protein Molecular Chains

The distributions of the quantum vibrational energy levels of the protein molecular chain are found by the discretely nonlinear Schr?dinger equation appropriate to protein obtained from the Davydov theory. The results calculated by this method are basically consistent with the experimental values. Furthermore, the energy spectra at high excited states have also been obtained for the molecular chain which is helpful in researching the properties of infrared absorption and Raman scattering of the protein molecules.

Analytical Potential Energy Function,Spectroscopic Constants and Vibrational Levels for A^1E_u^+ State of Dimer ~7Li_2

The symmetry-adapted-duster configuration-interaction method is used to investigate the spectroscopicproperties of ~7Li_2(A^1∑_u^+) over the internuclear distance ranging from 2.4ao to 37ao.The complete potential energycurves are calculated at numbers of basis sets.All the ab initio calculated points are fitted to the analytic MurrellSorbie function and then employed to compute the spectroscopic constants.By comparison,the spectroscopic constantsreproduced by the potential attained at D95(3df,3pd) are found to be very close to the experiments,a^d the values (T_e,D_e,R_e,ω_e,ω_eχ_e,α_e and B_e) are of 1.732 93 eV,1.161 36 eV,0.313 27 nm,251.95 cm^(-1),1.623 cm^(-1),0.005 35 cm^(-1),and0.490 cm^(-1),respectively.With the potential obtained at D95(3df,3pd),the totally 75 vibrational states are found whenJ=0.The vibrational levels,the classical turning points and the inertial rotation constants of the first 68 vibrationalstates are calculated for the first time and compared with the available measurements.Good agreement is obtained.The centrifugal distortion constants of the first 32 vibrational states are also reported for the first time.The reasonabledissociation limit for ~7Li_2(A^1∑_u^+) is deduced using the calculated results at present.

A Strategy for Magnifying Vibration in High-Energy Orbits of a Bistable Oscillator at Low Excitation Levels

This work focuses on how to maintain a high-energy orbit motion of a bistable oscillator when subjected to a low level excitation. An elastic magnifier （EM） positioned between the base and the bistable oscillator is used to magnify the base vibration displacement to significantly enhance the output characteristics of the bistable oscillator. The dimensionless electromechanical equations of the bistable oscillator with an EM are derived, and the effects of the mass and stiffness ratios between the EM and the bistable oscillator on the output displacement are studied. It is shown that the jump phenomenon occurs at a lower excitation level with increasing the mass and stiffness ratios. With the comparison of the displacement trajectories and the phase portraits obtained from experiments, it is vMidated that the bistable oscillator with an EM can effectively oscillate in a high-energy orbit and can generate a superior output vibration at a low excitation level as compared with the bistable oscillator without an EM.

Ab initio calculations on the spectroscopic constants, vibrational levels and classical turning points for the 2^1Пu state of dimer ^7Li2

The accurate dissociation energy and harmonic frequency for the highly excited 2^1Пu state of dimer ^7Li2 have been calculated using a symmetry-adapted-cluster configuration-interaction method in complete active space. The calculated results are in excellent agreement with experimental measurements. The potential energy curves at numerous basis sets for this state are obtained over a wide internuclear separation range from about 2.4a0 to 37.0a0. And the conclusion is gained that the basis set 6-311＋＋G（d,p） is a most suitable one. The calculated spectroscopic constants De, Re, ωe, ωeχe, ae and Be at 6-311＋＋G（d,p） are 0.9670 eV, 0.3125 nm, 238.6 cm^-1, 1.3705 cm^-1, 0.0039 cm^-1 and 0.4921 cm^-1, respectively. The vibrational levels are calculated by solving the radial SchrSdinger equation of nuclear motion. A total of 53 vibrational levels are found and reported for the first time. The classical turning points have been computed. Comparing with the measurements, in which only the first nine vibrational levels have been obtained so far, the present calculations are very encouraging. A careful comparison of the present results of the parameters De and We with those obtained from previous theories clearly shows that the present calculations are much closer to the measurements than previous theoretical results, thus representing an improvement on the accuracy of the ab initio calculations of the potentials for this state.

Investigation of analytical harmonic frequency and potential energy function, vibrational levels for the X^2∑^＋ and A^2Л states of CN radical

This paper calculates the equilibrium structure and the potential energy functions of the ground state （X^2∑^＋） and the low lying excited electronic state （A^2Л） of CN radical are calculated by using CASSCF method. The potential energy curves are obtained by a least square fitting to the modified Murrell-Sorbie function. On the basis of physical theory of potential energy function, harmonic frequency （ωe） and other spectroscopic constants （ωeχe, βe and αe） are calculated by employing the Rydberg-Klei-Rees method. The theoretical calculation results are in excellent agreement with the experimental and other complicated theoretical calculation data. In addition, the eigenvalues of vibrational levels have been calculated by solving the radial one-dimensional SchrSdinger equation of nuclear motion using the algebraic method based on the analytical potential energy function.

Theoretical study on the potential energy surface and vibrational energy levels of HXeI

The potential energy surface for the electronic ground state of the HXeI molecule is constructed by using the internally contracted multi-reference configuration interaction with the Davidson correction（icMRCI＋Q）method and large basis sets. The stabilities and dissociation barriers are identified from the potential energy surfaces.The three-body dissociation channel is found to be the dominate dissociation channel for HXeI.Based on the obtained potentials,vibrational energy levels of HXeI are calculated using the Lanczos algorithm.Our theoretical results are in excellent agreement with the available observed values.

An ab initio potential energy surface and vibrational energy levels of HXeBr

A three-dimensional global potential energy surface for the electronic ground state of HXeBr molecule is constructed from more than 4200 ab initio points. These points are generated using an internally contracted multi-reference configuration interaction method with the Davidson correction （icMRCI ＋ Q） and large basis sets. The stabilities and dissociation barriers are identified from the potential energy surfaces. The three-body dissociation channel is found to be the dominate dissociation channel for HXeBr. Based on the obtained potentials, low-lying vibrational energy levels of HXeBr calculated using the Lanczos algorithm is found to be in good agreement with the available experimental band origins.

Theoretical Studies on the Potential Energy Surface and Vibrational Energy Levels of HXeBr

The potential energy surface for the electronic ground state of the HXeBr molecule is constructed from more than 4200 ab initio points calculated using the internally contracted multi-reference configuration interaction method with the Davidson correction （icMRCI ＋ Q）. The stabilities and dissociation barriers are identified from the potential energy surface. The three-body dissociation channel is found to be the dominant dissociation channel for HXeBr. Low-lying vibrational energy levels of HXeBr calculated using the Lanczos algorithm are found to be in good agreement with the available experimental band origins.

Production and Detection of Ultracold Ground State 85Rb133Cs Molecules in the Lowest Vibrational Level by Short-Range Photoassociation

We investigate the production of ultracold ground state x^1∑7＋（u = 0） RbCs molecules in the lowest vibrational level via short-range photoassociation followed by spontaneous emission. The starting point is the laser cooled 85Rb and laa cs atoms in a dual species, forced dark magneto-optical trap. The special intermediate level （5）O＋ （u = 10） correlated to the （2）311 electric state is achieved by the photoassociation process. The formed ground state X1∑＋ （u = 0） molecule is resonantly excited to the 2111 intermediate state by a 651 nm pulse laser and is ionized by a 532nm pulse laser and then detected by the time-of-flight mass spectrum. Saturation of the photoionization spectroscopy at large ionization laser energy is observed and the ionization efficiency is obtained from the fitting. The production of ultracold ground state 85Rblaacs molecules is facilitative for the further research about the manipulation of ultracold molecules in the rovibrational ground state.

Vibrational Spectra of Nonrigid Molecule HCP in an Algebraic Model

An algebraic Harniltonian for the two coupled nonlinear vibrations of highly excited nonrigid molecule HCP was presented. The Hamiltonian reduces to the conventional one in a limit which was expressed in terms of harmonic oscillator operators. It showed that the algebraic model can better reproduce the data than the conventional model by fitting the observed data of HCP.

Safety of engineered structures against blast vibrations： A case study

Blasting used for rock excavation is associated with ground vibrations having potential damage to surrounding structures.The extent of damage produced in a structure depends largely on ground motion characteristics,dynamic characteristics of structure and the type of geological strata on which it is founded.The safety of surrounding structures against blast vibrations is a cause of concern.However,use of a systematic approach to rock blasting helps to complete the excavation safely in time without endangering the safety of surrounding structures.Various steps are commonly adopted at construction sites to ensure safety of engineered structures against blast vibrations,e.g.adopting a suitable safe vibration level,developing site-specific attenuation relation,estimating safe charges for different distances,designing blasting pattern,and monitoring vibrations during actual blasting.The paper describes the details of studies conducted for ensuring safety of an 85 years old masonry dam and green concrete of varying ages during excavation of about 30,000 m;of hard rock in Maharashtra,India.The studies helped to complete the rock excavation safely in time and the safety of the dam was ensured by monitoring blast vibrations during actual rock excavation.

Investigations on analytic potential energy function, spectroscopic parameters and vibrational manifolds (J = 0) of the SD + (X^3 Σ^- ) ion

This paper investigates the spectroscopic properties of the SD^＋（X^3∑^-） ion by employing the coupled-cluster singles-doubles-approximate-triples [CCSD（T）] theory combining with the quintuple correlation-consistent basis set augmented with diffuse functions （aug-cc-pV5Z） of Dunning and co-workers. The accurate adiabatic potential energy function is obtained by the least-squares fitting method with the 100 ab initio points, which are calculated at the unrestricted CCSD（T）/aug-cc-pV5Z level of theory over the internuclear separation range from 0.09 to 2.46 nm. Using the potential, it accurately determines the spectroscopic parameters （De, ωeХe, αe and Be）. The present De, Re, We, ωeХe, αe and Be results are of 3.69119 eV, 0.13644 nm, 1834.949 cm^-1, 25.6208 cm^-1, 0.1068 cm^-1 and 4.7778 cm^-1, respectively, which are in remarkably good agreement with the experimental findings. A total of 29 vibrational states has been predicted by numerically solving the radial Schrodinger equation of nuclear motion when the rotational quantum number J equals zero. The complete vibrational levels, classical turning points, inertial rotation and centrifugal distortion constants are reported when J = 0 for the first time, which are in good accord with the measurements wherever available.

颗粒阻尼在浮筏隔振系统中的减振特性研究

在船载和舰载机械设备的隔振工程实践中,浮筏系统作为一种高效被动振动控制措施得到广泛应用。为进一步提高浮筏隔振系统的减振效果,以一低内阻浮筏隔振系统为研究对象,采用子结构导纳法建立其动力学方程。设计由厚壁铝壳和不同粒径钢珠构成的颗粒阻尼器,将其安装于浮筏隔振系统的上平台或下平台。使用激振器对浮筏隔振系统进行扫频激励,通过对比安装有等质量的颗粒阻尼器和配重的隔振系统振级落差,定义颗粒阻尼器的替代损失和平均替代损失,通过该指标研究颗粒阻尼安装位置、粒径、填充率、表面粗糙度等对隔振性能的影响,并对颗粒阻尼器减振效果进行评估。研究表明,在浮筏隔振系统中颗粒阻尼器在较宽频段上都能起到良好减振效果,颗粒阻尼器平均替代损失大约能够达到4dB。

地下水位变化对砂土地层地铁隧道沉降影响试验研究

为考察地铁运营后列车载荷和地下水对隧道造成的影响,对某砂性土地层城市中某一地铁盾构隧道区段运营6年间的沉降变形进行实测观察;根据实测所得沉降规律,设计并开展缩尺模型试验,研究车致振动条件下因地下水位变化产生的隧道沉降规律。结果表明:随着时间推移,隧道各测点所得数据呈现一定的周期性上升与下降变化趋势,前2年隧道总体上浮,之后略有沉降,第3年后虽有波动但基本未发生进一步沉降,第6年后隧道最大沉降不超过3 mm;砂性土地层中,地下水位变化会造成重塑土层内部应力变化,且振动荷载会导致土体颗粒结构重新调整至密实,易导致隧道发生沉降,因此不能忽视地铁周围施工降水给隧道带来的不利影响;土体振密及因地下水产生的浮力共同作用,导致隧道的上浮及沉降。相比于软土地层,砂性土地层中盾构隧道的沉降速率明显更低且沉降基本稳定时间更短,2种地层下的沉降规律、影响因素完全不同,各地层下的沉降分析理论亦无法相互适用。