Frequencies Of Bending Vibrations Research Articles

Multiphoton-induced fluorescence spectrum of sulfur dioxide

The laser-induced fluorescence spectrum of sulfur dioxide (SO2) in the range of 200–460 nm has been obtained with the dyer laser (579 nm) pulsed by an Nd:YAG laser as the excitation source. The transition process, both X1A1→C1B2, excited by three photons and X1A1→A1A2, excited by two photons, has been evaluated. The relaxation kinetics of the excited molecules in the states of C1B2 and A1A2 have been analyzed on the basis of the excitation spectrum in the range of 560–580 nm. The spectral sequence rules are assigned, and it can be calculated that the symmetric stretching vibration and the bending vibration frequencies of the C1B2 state are ω1=942.9 cm−1, ω2=369.8 cm−1, and the bending vibration frequencies of the A1A2 state are ω2=493.4 cm−1. The analysis of the time-resolved spectrum proved that the relaxation process, C1B2→A1A2→X1A1, and the phosphorescent process, a3B1→X1A1, exist simultaneously.

Photoabsorption Assignments for the C̃1B2 ← X̃1A1 Vibronic Transitions of SO2, Using New Ab Initio Potential Energy and Transition Dipole Surfaces.

The high resolution spectroscopy of the SO2 molecule is of great topical interest, in a wide variety of contexts ranging from origins of higher life, to astrophysics of the interstellar medium, to environmental chemistry. In particular, the C̃1B2 ← X̃1A1 UV photoabsorption spectrum has received considerable attention. This spectrum exhibits a highly regular progression of ∼20 or so strong peaks, spaced roughly 350 cm-1 apart, which is comparable to the C̃1B2 bending vibrational frequency. Accordingly, they have for decades been largely attributed to the (1, v2', 2) ← (0, 0, 0) bend progression. Using a highly accurate new ab initio potential energy surface (PES) for the C̃1B2 state, we compute vibrational energy levels and wave functions, and compare with a photoabsorption calculation obtained using the same PES and corresponding C̃1B2 ← X̃1A1 transition dipole surface (TDS). We find that the above putative assignment is incorrect, contradicting even general qualitative trends-thus necessitating a very different dynamical picture for this highly unusual molecule.

The impact of root flexibility on the fundamental frequency of a restrained cantilever beam

This study presents the theoretical and experimental studies of the impact of root flexibility on the fundamental frequency of the free bending vibration of a uniform Euler–Bernoulli cantilever beam elastically restrained at the root. The dispersion relation between the natural frequency and modal number has been derived and solved numerically and approximately using the series method of the expansion in terms of the modal number. It is shown that the approximate solution is reduced to the empirical Dunkerley rule, which is sound not universally true. A commercial force sensor is used for the experimental detection of the effect of root flexibility on the fundamental frequency of bending vibrations of a cantilevered beam. The strip-shape specimen attached to the force sensor forms a cantilever beam restrained at the root against rotation and translation and it fundamental frequency is identified. The results of measurements for a series of industrial materials are compared with exact calculations and those predicted by Dunkerley’s formula and an excellent agreement is observed.

Effect of train carbody’s parameters on vertical bending stiffness performance

Finite element analysis(FEA) and modal test are main methods to give the first-order vertical bending vibration frequency of train carbody at present, but they are inefficiency and waste plenty of time. Based on Timoshenko beam theory, the bending deformation, moment of inertia and shear deformation are considered. Carbody is divided into some parts with the same length, and it’s stiffness is calculated with series principle, it’s cross section area, moment of inertia and shear shape coefficient is equivalent by segment length, and the fimal corrected first-order vertical bending vibration frequency analytical formula is deduced. There are 6 simple carbodies and 1 real carbody as examples to test the formula, all analysis frequencies are very close to their FEA frequencies, and especially for the real carbody, the error between analysis and experiment frequency is 0.75%. Based on the analytic formula, sensitivity analysis of the real carbody’s design parameters is done, and some main parameters are found. The series principle of carbody stiffness is introduced into Timoshenko beam theory to deduce a formula, which can estimate the first-order vertical bending vibration frequency of carbody quickly without traditional FEA method and provide a reference to design engineers.

Study of vertical bending vibration behavior of continuous prestressed concrete box girders with corrugated steel webs

Prestressed concrete girders with corrugated steel webs have received considerable attention in the past two decades due to their light self-weight and high prestressing efficiency. Most previous studies were focused on the static behavior of corrugated steel webs and simple beams with corrugated steel webs. The natural frequencies are very important characteristics when evaluating the dynamic responses of a bridge under external loads; however, very few studies have been conducted to investigate the dynamic behavior of full prestressed concrete girders or bridges with corrugated steel webs, and no simple formulas are available for estimating the natural frequencies of prestressed concrete girder bridges with corrugated steel webs. In addition, experimental work on full-scale bridges or scale bridge models is very limited. In this article, formulas for predicting the vertical bending vibration frequencies of prestressed concrete box girders with corrugated steel webs are proposed based on Hamilton’s energy variational principle. A one-tenth scale model is developed for an existing prestressed concrete box-girder bridge with corrugated steel webs. The frequencies predicted by the proposed formulas are compared to the finite element analysis results and also the experimental results from the scale bridge model. Good agreement is achieved between these results, indicating that the proposed formulas can provide a reliable and efficient tool to predict the vertical bending vibration frequencies of prestressed concrete box-girder bridges with corrugated steel webs.

Dynamic characteristics analysis of partial-interaction composite continuous beams

The dynamic characteristics of continuous steel-concrete composite beams considering the effect of interlayer slip were investigated based on Euler Bernoulli\'s beam theory. A simplified calculation model was presented, in which the Mode Stiffness Matrix (MSM) was developed. The natural frequencies and modes of partialinteraction composite continuous beams can be calculated accurately and easily by the use of MSM. Proceeding from the present method, the natural frequencies of two-span steel-concrete composite continuous beams with different span-ratios (0.53, 0.73, 0.85, 1) and different shear connection stiffnesses on the interface are calculated. The influence pattern of interfacial stiffness on bending vibration frequency was found. With the decrease of shear connection stiffness on the interface, the flexural vibration frequencies decrease obviously. And the influence on low order modes is more obvious while the reduction degree of high order is more sizeable. The real natural frequencies of partial-interaction continuous beams commonly used could have a 20% to 40% reduction compared with the fully-interaction ones. Furthermore, the reduction-ratios of natural frequencies for different span-ratios two-span composite beams with uniform shear connection stiffnesses are totally the same. The span-ratio mainly impacts on the mode shape. Four kinds of shear connection stiffnesses of steel-concrete composite continuous beams are calculated and compared with the experimental data and the FEM results. The calculated results using the proposed method agree well with the experimental and FEM ones on the low order modes which mainly determine the vibration properties.

Nonlinear analyses of functionally graded microplates based on a general four-variable refined plate model and the modified couple stress theory

In this paper, a general nonlinear four-variable refined plate model is developed to investigate the bending and free vibration behavior of a functionally graded (FG) microplate resting on an elastic foundation. In this model, a shape function is defined to describe the effect of the transverse shear deformation, and the size effects of the microplate are captured by using the modified couple stress theory. Firstly, the equations of motion and boundary conditions are derived from the Hamilton’s principle. Then the equations of motion are reduced to ordinary differential equations by applying the Galerkin method, and via solving the ordinary differential equations, closed-form solutions for the nonlinear bending deflection and vibration frequency are obtained. It is found that the solutions for the general refined plate model are identical to those for a size-dependent Kirchhoff plate model and a refined first-order plate model respectively when the shape function of the transverse shear deformation is chosen to be certain forms. In addition, numerical studies are carried out to compare a special nonlinear size-dependent refined higher-order plate model with its linear counterpart as well as the nonlinear refined first-order plate model.

Calculating bending vibrations of main axial mine fan rotor shaft

The article presents a calculation procedure for critical rotary speed of an axial main mine fan rotor. The calculations are made for fan model VO-21. The suppositions that make the calculations simpler without considerable errors of the results are evaluated. The calculations use the finite element method and ANSYS software. The critical rotary speeds are determined from the Campbell diagrams plotted for the estimates with and without regard for the stiffness of the bearing assemblies of the rotor. The effect exerted by the rotor bearing assembly stiffness and by the gyroscopic moment of the fan impeller on the frequency of free bending vibrations of the rotor shaft under direct and back precession is illustrated. The estimated critical rotary speeds are compared with the analytical data obtained based on discrete two-mass models. For the preliminary engineering estimation, it is possible to use a discrete two-mass model of the fan rotor without regard for the yielding of the bearing assemblies and for the influence of the gyroscopic model; in the design model, it is required to replace the transmission shaft by the point mass. The calculation error will not exceed 7%.

The Possibility of Increasing Emission Intensity of a Counter-current Hydrodynamic Generator

The article considers the possibility of increasing operation efficiency of a counter-current hydrodynamic generator, used for the intensification of chemical technology processes. To increase the intensity of the emission it is suggested to use rod resonance system, where the frequency of bending vibrations is in agreement with the frequency of flow shell vibrations. The dependence of the frequency of the generated signal on geometric and hydrodynamic oscillator parameters is experimentally proven. It is also found out that the dependence of the pressure differential, produced by a resonator, on the liquid consumption, will look like a resonance curve. To keep maximum values of the generated vibrations amplitudes, it is suggested to use extremal system of the automated control.

Water Adsorption on Free Cobalt Cluster Cations.

Cationic cobalt clusters complexed with water Con(+)-H2O (n = 6-20) are produced through laser ablation and investigated via infrared multiple photon dissociation (IR-MPD) spectroscopy in the 200-1700 cm(-1) spectral range. All spectra exhibit a resonance close to the 1595 cm(-1) frequency of the free water bending vibration, indicating that the water molecule remains intact upon adsorption. For n = 6, the frequency of this band is blue-shifted, but it gradually converges to the free water value with increasing cluster size. In the lower-frequency range (200-650 cm(-1)) the spectra contain several bands which show a very regular frequency evolution, suggesting that the exact cluster geometry has little effect on the water-surface interaction. Density functional theory (DFT) calculations are carried out at the OPBE/TZP level for three representative sizes (n = 6, 9, 13) and indicate that the vibrations responsible for the resonances correspond to bending and torsional modes between the cluster and water moieties. The potential energy surfaces describing these interactions are very shallow, making the calculated harmonic frequencies and IR intensities very sensitive to small geometrical perturbations. We conclude that harmonic frequency calculations on (local) minima structures provide insufficient information for these types of cluster complexes and need to be complemented with calculations that provide a more extensive sampling of the potential energy surface.

Hydrogen bond dynamics in liquid water: Ab initio molecular dynamics simulation

The effect of intermolecular interaction on the distribution of the harmonic vibrational frequencies of water molecules was investigated through ab initio molecular dynamics simulations based on the Born-Oppenheimer approach. For single water, the effect of the dynamics of the oxygen atom in single water and the simulation time step on the frequency distribution were examined. The distributions of the OH stretching and HOH bending vibrational frequencies of liquid water were compared to those of single water. The probability distributions of the change in OH bond length and the lifetime of the dangling OH bond were also obtained. The distribution of the frequencies was strongly affected by the long lifetime of the dangling OH bond, resulting in the formation of hydrogen bonds between water molecules.

Quantum chemical study on surface complex structures of phosphate on gibbsite

Quantum mechanics calculations based on the density functional theory (DFT) were used to identify phosphate surface complexes on gibbsite at low and high pH. The different phosphate species were represented using the Al6(OH)18(H2O)6 cluster model considering four different geometries: monodentate mononuclear (Pmm), monodentate binuclear (Pmb), bidentate mononuclear (Pbm) and bidentate binuclear (Pbb). The corresponding adsorption reactions were modelled via ligand exchange between phosphate species and surface functional groups (hydroxyls and protonated hydroxyls at high and low pH, respectively). The theoretical results indicate that phosphate surface complexes are thermodynamically more favored at acid pH, in agreement with experimental evidences. The first step in these reactions, i.e., the generation of required aluminum vacant sites, was predicted to be particularly favorable when singly coordinated aquo groups are released. Stretching and bending vibrational frequencies associated with the different surface structures were calculated at both pH conditions. The corresponding values at low pH were found to be shifted to higher frequencies with respect to those ones at high pH. ATR-FTIR studies were also carried out. The resulting spectra are dominated by a strong band within the 800–840cm−1 interval due to P–OH stretching modes. The corresponding peak appearing around 820cm−1 at high pH is shifted to lower frequencies with respect to the position at low pH, a tendency well predicted by DFT calculations.

Adsorption Properties of Ni(II) by D301R Anion Exchange Resin

The adsorption of Ni(II) with D301R resin was investigated in this paper. The results showed that the saturated extent of adsorption Ni(II) by the resin was 84.3 mg/g. The equilibrium data of Ni(II) sorption was better described by Langmuir isotherm model (r2=0.994) while that of Ni(II) sorption also fitted in Freundlich isotherm model within the experimental concentration range. The amount of the constant (q0) of Ni(II) under 298 K in Langmuir model was 76.92 mg/g, which was close to the experimental results. The constant n was within 2–10 in Freundlich model; it was shown that adsorption of Ni(II) by the resin was easy to take place. The uptake kinetics followed the Lagergren pseudo-first-order rate equation (r2=0.9813). The particle diffusion controlled the adsorption process of Ni(II). The coefficient of the intraparticle diffusion increased with the increase of the pH values and the concentration of Ni(II) in aqueous solution. There was a drop of 20.1 cm−1for the bending vibration frequency of N–H bond. Results showed that the adsorption of Ni(II) by D301R anion exchange resin was the surface complexation through the infrared spectrum analysis.

Spontaneous Symmetry Breaking of a Hinged Flapping Filament Generates Lift

Elastic filamentous structures found on swimming and flying organisms are versatile in function, rendering their precise contribution to locomotion difficult to assess. We show in this Letter that a single passive filament hinged on the rear of a bluff body placed in a stream can generate a net lift force without increasing the mean drag force on the body. This is a consequence of spontaneous symmetry breaking in the filament's flapping dynamics. The phenomenon is related to a resonance between the frequency associated with the von Kármán vortex street developing behind the bluff body and the natural frequency of the free bending vibrations of the filament.

Bending vibrations of rotating nonuniform nanocantilevers using the Eringen nonlocal elasticity theory

The natural frequencies of the flapwise bending vibrations of a nonuniform rotating nanocantilever has been calculated, considering the true spatial variation of the axial force due to the rotation. The area of the nanobeam cross-section is assumed to change linearly. The problem has been formulated using the nonlocal Eringen elasticity theory and it was solved by a pseudo-spectral collocation method based on Chebyshev polynomials. The effect of the nonlocal small-scale, angular speed, nonuniformity of the section and hub radius on the vibration behavior of the nanocantilever is discussed.

Identification of longitudinal incisions of the beam from its own frequencies

The natural frequencies of bending vibrations of a prismatic beam with symmetrical bilateral longitudinal incisions are considered. A method is proposed that makes it possible to calculate the parameters of the incisions with by two frequencies taken from different spectra. These spectra belong to bending vibrations in two mutually perpendicular planes, which are chosen in such a way that in both cases the neutral cross-section line is parallel to the sides. The dependence of the natural frequency on the depth of the defect is also studied. It is proved that the values of the frequencies for the beam under consideration and the identical beam without cuts do not coincide for any value of the defects.

Microstructured hydroxyl environments and Raman spectroscopy in selected basic transition-metal halides

Raman vibrational spectra of the selected basic (hydroxyl OH and deuteroxyl OD) transition-metal halides, geometrically frustrated material series α-, β-, γ-Cu2(OH)3Cl, α-Cu2(OH)3Br, β-Ni2(OH)3Cl, β-Co2(OH)3Cl, β-Co2(OH)3Br, γ-Cu2(OD)3Cl, and β-Co2(OD)3Cl are measured at room temperature and analysed to investigate the relationship between the microstructured OH environments and their respective Raman spectra. Among these selected samples, the last two are used to determine the OH stretching vibration region (3600 cm−1−3300 cm−1) and OH bending vibration region (1000 cm−1−600 cm−1) of OH systems in the spectra. Through the comparative analysis of the distances d(metal—O), d(O—halogen), and d(OH), the strong metal—O interaction and trimeric hydrogen bond (C3v, Cs or C1 symmetry) are found in every material, but both determine simultaneously an ultimate d(OH), and therefore an OH stretching vibration frequency. According to the approximately linear relationship between the OH stretching vibration frequency and d(OH), some unavailable d(OH) are guessed and some doubtful d(OH) are suggested to be corrected. In addition, it is demonstrated in brief that the OH bending vibration frequency is also of importance to check the more detailed crystal microstructure relating to the OH group.

Research on Axisymmetric Vibration of Gear with Stepped Variable Thickness

Ultrasonic gear honing is a kind of precision processing technology with great application prospect. The gear is a special kind of load in ultrasonic machining, and its vibration characteristic and natural frequency has great influence on processing frequency of the system. According to the structure characteristic of the gear with stepped variable thickness, its equations of axisymmetric bending vibration frequency were derived on the basis of the thick plate theory in this paper, and then the gear’s natural frequency is obtained which is in accordance with the results of FEM computation. Besides, the main factors affecting the calculation accuracy are analyzed with some examples in this paper The analysis shows that within the application range of Mindlin’s plate theory, the gears’ frequency obtained by the suggested method is accurate.

Theoretical investigation of vibronic and spin-orbit effects in the ground X 2Πu electronic state of the dicyanoacetylene cation

The aim of the present study is to predict by means of ab initio calculations the vibronic and spin-orbit structure in the X (2)Π(u) electronic state of NC(4)N(+) and to elucidate some details in an observed laser-induced fluorescence spectrum of this species, particularly those interpreted in terms of the bending overtones and the spin-orbit splitting. The ground electronic state of NC(4)N(+) was investigated by density functional (B3LYP) and complete active space self-consistent field-multi-reference configuration interaction (CASSCF-MRCI) methods. The bending vibrational frequencies ω(T1) = 558 cm(-1), ω(T2) = 266 cm(-1), ω(C1) = 459 cm(-1), and ω(C2) = 113 cm(-1) were obtained. The spin-orbit coupling constant was calculated using state-average CASSCF wave functions in the framework of the MRCI method, and the value of A(SO) = -44 cm(-1) was determined. This quantity and the data for the bending frequencies and Renner parameters were employed for handling a combined effect of the vibronic and spin-orbit coupling, according to a model developed in our earlier studies.

Free vibrations of thick layered cylindrical shells

Two approaches to the calculation of closed thick layered cylindrical shells are developed. They are based on division of the cylindrical shell across its thickness by concentric circumferential surfaces into a series of constituent cylindrical shells. Satisfying the contact conditions on the surfaces between constituent shells, it is possible to determine the frequency of free bending vibrations of the initial shell with a sufficient accuracy. In the first approach, the distribution of unknown functions across the shell thickness is sought on the basis of an analytical solution to the corresponding system of differential equations; in the second one, the distribution is assigned by polynomial approximation functions.