Calculations of the vibrational frequency and isotopic shift of UF_6 and U_2 F_6

Molecular structure, vibrational frequency and infrared intensity of UF6 are investigated by using the revised Perdew Burke-Enzerhof function with the triple-zeta polarized basis set. The calculation results are in good agreement with the experimental values and indicate the existence of a stable U2F6 molecule with a multiple bonded U2 unit. The calculation results also predict that the D3d symmetry of U2F6 is more stable than D3h. The optimized geometries, vibrational frequencies, and infrared intensities are also reported for U2F6 molecules in D3d symmetry. In addition, the isotopic shift of vibrational frequencies of the two molecules under isotopic substitution of uranium atom are also investigated with the same method. The U2F6 molecule is predicted to be better than UF6 for laser uranic isotope separation.

A critical review of wheel/rail high frequency vibration-induced vibration fatigue of railway bogie in China

Purpose–This review aims to give a critical view of the wheel/rail high frequency vibration-induced vibration fatigue in railway bogie.Design/methodology/approach–Vibration fatigue of railway bogie arising from the wheel/rail high frequency vibration has become the main concern of railway operators.Previous reviews usually focused on the formation mechanism of wheel/rail high frequency vibration.This paper thus gives a critical review of the vibration fatigue of railway bogie owing to the short-pitch irregularities-induced high frequency vibration,including a brief introduction of short-pitch irregularities,associated high frequency vibration in railway bogie,typical vibration fatigue failure cases of railway bogie and methodologies used for the assessment of vibration fatigue and research gaps.Findings–The results showed that the resulting excitation frequencies of short-pitch irregularity vary substantially due to different track types and formation mechanisms.The axle box-mounted components are much more vulnerable to vibration fatigue compared with other components.The wheel polygonal wear and rail corrugation-induced high frequency vibration is the main driving force of fatigue failure,and the fatigue crack usually initiates from the defect of the weld seam.Vibration spectrum for attachments of railway bogie defined in the standard underestimates the vibration level arising from the short-pitch irregularities.The current investigations on vibration fatigue mainly focus on the methods to improve the accuracy of fatigue damage assessment,and a systematical design method for vibration fatigue remains a huge gap to improve the survival probability when the rail vehicle is subjected to vibration fatigue.Originality/value–The research can facilitate the development of a new methodology to improve the fatigue life of railway vehicles when subjected to wheel/rail high frequency vibration.

Vibrational frequency analysis of finite elastic tube filled with compressible viscous fluid

The vibrational frequency analysis of finite elastic tube filled with compressible viscous fluid has received plenty of attention in recent years. To apply frequency analysis to defect detection for example, it is necessary to investigate the vibrational behavior under appropriate boundary conditions. In this paper, we present a detailed theoretical study of the three dimensional modal analysis of compressible fluid within an elastic cylinder. The dispersion equations of flexura], torsional and longitudinal modes are derived by elastodynamic theory and the unsteady Stokes equation. The symbolic software Mathematica is used in order to find the coupled vibration frequencies. The dispersion equation is deduced and analytically solved. The finite element results are compared with the present method for validation and an acceptable match between them are obtained.

A high frequency vibration compensation approach for ultrahigh resolution SAR imaging based on sinusoidal frequency modulation Fourier-Bessel transform

Ultrahigh resolution synthetic aperture radar(SAR)imaging for ship targets is significant in SAR imaging,but it suffers from high frequency vibration of the platform,which will induce defocus into SAR imaging results.In this paper,a novel compensation method based on the sinusoidal frequency modulation Fourier-Bessel transform(SFMFBT)is proposed,it can estimate the vibration errors,and the phase shift ambiguity can be avoided via extracting the time frequency ridge consequently.By constructing the corresponding compensation function and combined with the inverse SAR(ISAR)technique,well-focused imaging results can be obtained.The simulation imaging results of ship targets demonstrate the validity of the proposed approach.

Vibration Frequency in Micro-Vibration Therapy in Nursing Care: A Cross-Sectional Study

This study investigated the vibration frequency in micro-vibration therapy (MVT) performed as a part of nursing care in Japan. We surveyed 31 nurses (25 women and 6 men) who performed MVT with accelerometers attached to the backs of their hands, and the data obtained were analyzed. The mean vibration frequency was 8.3 Hz (standard deviation [SD]: 1.9 Hz) bilaterally, with a left-right difference of 0.8 Hz (SD: 1.1 Hz, right > left). Furthermore, vibration frequency was correlated with duration of MVT use (rs = 0.5, P < 0.01). The vibration frequency was higher in men (9.2 Hz, SD: 2.4 Hz) than in women (8.1 Hz, SD: 1.8 Hz), but this difference was not significant (P = 0.34). The vibrations of MVT are of a lower frequency than those of other vibration therapies.

Research on modeling and self-excited vibration mechanism in magnetic levitation-collision interface coupling system

The modeling and self-excited vibration mechanism in the magnetic levitation-collision interface coupling system are investigated.The effects of the control and interface parameters on the system's stability are analyzed.The frequency range of self-excited vibrations is investigated from the energy point of view.The phenomenon of self-excited vibrations is elaborated with the phase trajectory.The corresponding control strategies are briefly analyzed with respect to the vibration mechanism.The results show that when the levitation objects collide with the mechanical interface,the system's vibration frequency becomes larger with the decrease in the collision gap;when the vibration frequency exceeds the critical frequency,the electromagnetic system continues to provide energy to the system,and the collision interface continuously dissipates energy so that the system enters the self-excited vibration state.

Ab initio potential energy surface and anharmonic vibration spectrum of NF_(3)^(+)

Potential energy surfaces(PESs), vibrational frequencies, and infrared spectra are calculated for NF_(3)^(+) using ab initio calculations, based on UCCSD(T)/cc-p VTZ combined with vibrational configuration interaction(VCI). Based on an iterative algorithm, the surfaces(SURF) program adds automatic points to the lattice representation of the potential function, the one-dimensional and two-dimensional PESs are calculated after reaching a convergence threshold, finally the smooth image of the potential energy surface is fitted. The PESs accurately account for the interaction between the different modes, with the mode q_(6) symmetrical stretching vibrations having the greatest effect on the potential energy change of the whole system throughout the potential energy surface shift. The anharmonic frequencies are obtained when the VCI matrix is diagonalized. Fundamental frequencies, overtones, and combination bands of NF_(3)^(+) are calculated, which generate the degenerate phenomenon between their frequencies. Finally, the calculated anharmonic frequency is used to plot the infrared spectra.Modal antisymmetric stretching ν_(5) and symmetric stretching ν_(6) exhibit a phenomenon of large-intensity borrowing. This study can provide data to support the characterization in the laboratory.

Structures and Vibrational Spectra of C2 and LaC2+ Clusters

C 2 and LaC + 2 were studied using Hartree Fock(HF), B3LYP (Becke 3 paremeter Lee Yang Parr) density functional method, second order Mφller Plesset perturbation(MP2) and coupled cluster singles and doubles with non iterative triples(CCSD(T)) methods. The basis set employed was LANL1DZ. Geometries, vibrational frequencies and other quantities were reported. The results showed that for C 2, all the methods performed well for low spin state(singlet), while only HF and B3LYP remained so for high spin state(triplet). For LaC + 2, four isomers were presented and fully optimized. The results suggested that linear isomers with C ∞v and D ∞h symmetries were predicted to be saddle points on the energy surface for all the methods, while for isomers with C 2v and C s symmetries, they were local minima except C 2v at B3LYP level, and were isoenergetic at HF, MP2 and CCSD(T) levels, near isoenergetic at B3LYP level. From the differences between HOMO and LUMO, it is also known that the isomers with C 2v and C s symmetries offer the largest values and therefore correspond to the most stable structure. For La—C bond lengths, B3LYP gives the shortest, the order is B3LYP<HF<MP2<CCSD(T) for all the methods.

Structural, electronic and vibrational properties of indium oxide clusters

Geometric, electronic and vibrational properties of the most stable and energetically favourable configurations of indium oxide clusters InmOn （1 ≤m, n ≤ 4） are investigated using density functional theory. The lowest energy geometries prefer the planar arrangement of the constituent atoms with a trend to maximize the number of ionic In-O bonds. Due to the charge transfer from In to O atoms, the electrostatic repulsion occurs between the atoms with the same kind of charge. The minimization of electrostatic repulsion and the maximization of In O bond number compete between each other and determine the location of the isometric total energy. The most stable linear In-O-In-O structure of In2O2 cluster is attributed to the reduced electrostatic repulsive energy at the expense of In-O bond number, while the lowest energy rhombus-like structure of In2O3 cluster reflects the maximized number of In O bonds. Furthermore, the vibrational frequencies of the lowest energy clusters are calculated and compared with the available experimental results. The energy gap and the charge density distribution for clusters with varying oxygen/indium ratio are also discussed.

Structures,Electron Affinities and Vibrational Frequencies of SF_5OX/SF_5OX^-(X=F,Cl,Br)

The molecular structures,electron affinities,vibrational frequencies and IR intensities of the SF5OX/SF5OX-（X=F,Cl,Br）species have been determined by four different density functional theory（DFT）methods（B3LYP,BHLYP,BP86,BLYP）in conjunction with DZP＋＋ basis set.The BHLYP method predicts the best geometry parameters.The adiabatic electron affinities（EAad）predicted by the B3LYP/DZP＋＋ method are 4.36 eV（SF5OF）,4.13 eV（SF5OCl）,4.12 eV（SF5OBr）,respectively.Large electron affinity implies the corresponding anions are stable.The total intensities in the near IR ＂window＂ of the anions SF5OX-（X=F,Cl,Br）at B3LYP level are 1 602 km/mol（SF5OF-）,1 868 km/mol（SF5OCl-）and 1 916 km/mol（SF5OBr-）,respectively,larger than those of the corresponding neutrals.It suggests that SF5OX/SF5OX-（X=F,Cl,Br）may be used to ＂warm＂ Mars.

Application of coupled analysis methods for prediction of blast-induced dominant vibration frequency

Blast-induced dominant vibration frequency （DVF） involves a complex, nonlinear and small sample system considering rock properties, blasting parameters and topography. In this study, a combination of grey relational analysis and dimensional analysis procedures for prediction of dominant vibration frequency are presented. Six factors are selected from extensive effect factor sequences based on grey relational analysis, and then a novel blast-induced dominant vibration frequency prediction is obtained by dimensional analysis. In addition, the prediction is simplified by sensitivity analysis with 195 experimental blast records. Validation is carried out for the proposed formula based on the site test database of the first- period blasting excavation in the Guangdong Lufeng Nuclear Power Plant （GLNPP）. The results show the proposed approach has a higher fitting degree and smaller mean error when compared with traditional predictions.

Effect of vibration frequency on primary phase and properties of grey cast iron fabricated by lost foam casting

The properties of gray cast iron(GCI)are affected by density of matrix,size of flake graphite and primary austenite.In this paper,the Y-type specimen of GCI was prepared by lost foam casting(LFC)with and without vibration,and the influence of vibration frequency on the density of matrix,size of primary phase,and properties of the GCI was studied.The results show that the length of the flake graphite and the size of the primary austenite in GCI firstly decrease and then increase with the increase of the vibration frequency.With a vibration frequency of 35 Hz,the length of the flake graphite is the shortest,the primary austenite is the finest and the density of the matrix is the highest.In addition,the tensile strength,elongation and hardness of the GCI firstly increase and then decrease with the increase of the vibration frequency,due to the refinement of the primary phase and the increase of the matrix density.In order to analyze the refinement mechanism of the primary phase of the GCI fabricated by the LFC with vibration,the solidification temperature fields of the GCI fabricated by the LFC with the vibration frequency of 0 and 35 Hz were measured.The results show that the vibration reduces the eutectic point of the GCI and increases the supercooling degree during the eutectic transformation.As a result,the length of the flake graphite and the size of the primary austenite in GCI fabricated by LFC with the vibration frequency of 35 Hz decrease.

On Frequency Sensitivity and Mode Orthogonality of Flexible Robotic Manipulators

This paper presents sensitivity analysis of vibration frequencies of flexible manipulators with respect to variations of systems parameters such as rotational inertia of hub,and mass,moment,and side of tip load.Both Euler-Bernoulli and Timoshenko dynamical models of flexible manipulators are discussed.By using variational method,sensitivity indices are obtained with explicit expressions for measuring the sensitivity of frequencies.Based on variational formulations,a novel method for deriving the orthogonal relations among vibration modal shape functions of flexible manipulators is introduced.With this method,the orthogonal relations can be derived easily without invoking the tedious process of differentiation and integration by part,as commonly used in their derivation.

Structure Optimization of Wheel Force Transducer Based on Natural Frequency and Comprehensive Sensitivity

The current research of wheel force transducer （WFT） mainly focuses on test signal processing and decoupling methods based on signal itself, while the WFT structure optimization research related to decreasing the mass and increase the natural frequency and comprehen- sive sensitivity is not enough. In order to improve the WFT test accuracy, a structure optimization method based on natural frequency and comprehensive sensitivity indicators is put forward. The WPT with 8-beam elastic body is used for the finite element modeling （FEM）, in which the fol- lowing variations are taken into consideration： the con- nection type of elastic body with modified rim, the number of connection holes, and the respects of strain beam including the shape, the cross sectional area and the length, etc.. The test results shows that the natural frequency of the connecting block type is increased by 65.5% compared with the connecting seat type of elastic body ＆ modified rim, and the main channel sensitivity is improved as well. The results show that the connecting block type will achieve the best comprehensive performance when the number of connecting holes between the elastic body and the modified rim is 20. And the thinner and longer strain beam with smaller cross section area is preferable within the scope of elastic body mechanical strength. This research proposes a novel structure optimization method for WFT which contributes to improve the measurement performance of WFT.

Cascaded quasi-zero stiffness nonlinear low-frequency vibration isolator inspired by human spine

Human motion induced vibration has very low frequency,ranging from 2 Hz to 5 Hz.Traditional vibration isolators are not effective in low-frequency regions due to the trade-off between the low natural frequency and the high load capacity.In this paper,inspired by the human spine,we propose a novel bionic human spine inspired quasi-zero stiffness(QZS)vibration isolator which consists of a cascaded multi-stage negative stiffness structure.The force and stiffness characteristics are investigated first,the dynamic model is established by Newton’s second law,and the isolation performance is analyzed by the harmonic balance method(HBM).Numerical results show that the bionic isolator can obtain better low-frequency isolation performance by increasing the number of negative structure stages,and reducing the damping values and external force values can obtain better low-frequency isolation performance.In comparison with the linear structure and existing traditional QZS isolator,the bionic spine isolator has better vibration isolation performance in low-frequency regions.It paves the way for the design of bionic ultra-low-frequency isolators and shows potential in many engineering applications.

DESIGN AND ANALYSIS OF NOVEL ACTIVE ACTUATOR TO CONTROL LOW FREQUENCY VIBRATIONS OF SHAFT SYSTEM

Aiming at providing with high-load capability in active vibration control of large-scale rotor system, a new type of active actuator to simultaneously reduce the dangers of low frequency flexural and torsional vibrations is designed. The actuator employs electro-hydraulic system and can provide a high and circumferential load. To initialize new research, the characteristics of various kinds of active actuators to control rotor shaft vibration are briefly introduced. The purpose of this paper is to introduce the preliminary results via presenting the structure, functions and operating principles, in particular, the working process of the electro-hydraulic system of the new actuator which includes a set of high speed electromagnetic valves and a series of sloping cone-shaped openings, and presenting the transmission relationships among the control parameters from control signals into the valves to active load onto shaft. The course of the work is dynamic, and a series of spatial forces and moments are put on the shaft to get an external resultant force to reduce excitations that induce vibration of shafts. By checking states of vibration, the actuator can control the impulse width and the interval of injection time for applying different control force to a vibration shaft in two circumference directions through the regulating action of a set of combination directional control valves. The results from simulating analysis and experiment show evidence of that this design can satisfy the case of active process of decreasing of flexural and torsional vibrations.

Geometrical structures, vibrational frequencies, force constants and dissociation energies of isotopic water molecules (H_2O, HDO, D_2O, HTO, DTO, and T_2O) under dipole electric field

The dissociation limits of isotopic water molecules are derived for the ground state. The equilibrium geometries, the vibrational frequencies, the force constants and the dissociation energies for the ground states of all isotopic water molecules under the dipole electric fields from -0.05 a.u. to 0.05 a.u. are calculated using B3P86/6-311＋＋G（3df,3pf）. The results show that when the dipole electric fields change from -0.05 a.u. to 0.05 a.u., the bond length of H-O increases whereas the bond angle of H-O H decreases because of the charge transfer induced by the applied dipole electric field. The vibrational frequencies and the force constants of isotopic water molecules change under the influence of the strong external torque. The dissociation energies increase when the dipole electric fields change from -0.05 a.u. to 0.05 a.u. and the increased dissociation energies are in the order of H2O, HDO, HTO, D2O, DTO, and T2O under the same external electric fields.

Changes in the natural frequency of a ferromagnetic rod in a magnetic field due to magnetoelastic interaction

Based on the magnetoelastic generalized variational principle and Hamilton＇s principle, a dynamic theoretical model characterizing the magnetoelastic interaction of a soft ferromagnetic medium in an applied magnetic field is developed in this paper. From the variational manipulation of magnetic scale potential and elastic displacement, all the fundamental equations for the magnetic field and mechanical deformation, as well as the magnetic body force and magnetic traction for describing magnetoelastic interaction are derived. The theoretical model is applied to a ferromagnetic rod vibrating in an applied magnetic field using a perturbation technique and the Galerkin method. The results show that the magnetic field will change the natural frequencies of the ferromagnetic rod by causing a decrease with the bending motion along the applied magnetic field where the magnetoelastic buckling will take place, and by causing an increase when the bending motion of the rod is perpendicular to the field. The prediction by the mode presented in this paper qualitatively agrees with the natural frequency changes of the ferromagnetic rod observed in the experiment.

DESIGN AND DYNAMICAL SIMULATION TO NEW VIBRATING CENTRIFUGE WITH WIDER FREQUENCY RANGE

A new type of vibrating centrifuge with wider frequency range is designed instead of the traditional one with a single frequency to improve the vibrating effect. With the aid of a new dynamical model, one simulation without considering the visco-elasticity of basis is presented, then the dynamical responses of time and frequency in different scheme are given. The computational results show that the improved vibrating centrifuge possesses a remarkably widened frequency range.

Ab Initio Studies of Radicals HBX(X=H, F, Cl, Br): Molecular Structure,Vibrational Frequencies and Potential Energy

We describe high-level ab initio calculations on the BH_2, HBF, HBCl and HBBr radicals. Molecular structure,vibrational frequencies and potential energy curves of the ground state and the first excited state, which are two Renner-Teller components for a^2Π state at linearity, are studied using the basis sets aug-cc-pVTZ and icMRCI＋Q technique. On the basis of the potential energy curves, a reliable potential energy barrier to dissociation HB＋X（X=F, Cl, Br） fragments and to linearity are given. The ab initio results will add some understanding on the spectrum and the photo-dissociation dynamics of the series of radicals.