Lattice Vibration Frequencies Research Articles

Study on reversal and lateral vibration in the stepped well

The reversal and lateral vibration of the drill string are very complex motion and can affect the normal operation of the drill string. The movement of the drill string in the stepped well is different from the movement of the drill string in the regular well. The vibration of the drill string in the stepped well varies with the size of the wellbore and can be visually reflected by the phase speed. To find out the relationship between reversal and lateral vibration, the natural frequency of lateral vibration of the drill string was solved by using the method of energy conservation. The analysis shows that the phase speed of flexural wave in the stepped well is faster in small size wellbore than in large size wellbore. The reversal and lateral resonance is easy to happen in small size wellbore, and the reversal will excite lateral vibration. When the sum of reversal and rotational angular frequencies approaches the natural angular frequency of lateral vibration, the lateral resonance will occur.

Pressure-induced structural phase transitions in the multiferroic four-layer Aurivillius ceramic Bi5FeTi3O15

The structural stability of the multiferroic four-layer Aurivillius ceramic Bi5FeTi3O15 (BFTO) under hydrostatic pressure was investigated in situ by synchrotron X-ray powder diffraction (SXRPD) and Raman spectroscopy. Measurements performed up to 15 GPa allowed the identification of two well-defined structural phase transitions. The orthorhombic phase (at ambient conditions) transforms into a tetragonal one around 3.2 GPa and a new orthorhombic phase rises around 7.5 GPa. Both phase transitions are evidenced by the pressure dependence of the lattice parameters and vibrational mode frequencies. The analysis of the induced strain indicates that the transitions are of second-order and first-order, respectively. Subtle changes in the Raman spectra and powder patterns suggest the onset of a new phase around 10.5 GPa.

Study on line Vibration Characteristics of Equipment for Electric Multiple Units

The rigid-flexible vibration of high-speed train will cause the violent movement of equipment. This paper first introduced the high-speed EMU equipment and the theory of mass tuning vibration absorption. Then according to the test data, the vibration response of the bogie frame and the vibration response of the equipment, and the vibration response of the equipment under different lines are analyzed. The results show that the lateral vibration frequency of the frame is 4.5 Hz in normal section, and the lateral vibration frequency of the frame is 7.4 Hz in hunting excitation section. During the normal vibration line, the vibration of the equipment is significantly larger than that of the carbody, the vibration characteristics of the frequency domain of the equipment is mainly high-frequency magnetic vibration, the high-frequency vibration of the equipment above 15Hz is not transmitted to the carbody. When the running speed is increased, the vibration of the equipment is enhanced, and the line condition also has an important influence on the vibration of the equipment.

Theoretical and Experimental Study on Dielectric Constant of Cadmium Telluride in Terahertz Band

Abstract The phonon dispersion spectrum, eigenvector and lattice vibration frequency of zincblende cadmium telluride (CdTe) are studied by density functional theory (DFT). The vertical or parallel relationship between the phonon propagating wave vector atomic vibration direction is analyzed, and the frequency of the CdTe transverse (TO)/longitudinal (LO) optical phonon is obtained. The Boltzmann transport equation clearly expresses the phonon scattering process, which is combined with the Huang Kun equation to obtain the three-phonon collision frequency (γ). The terahertz time-domain spectroscopy system is used to measure the reflectivity and dielectric constant of CdTe single crystal. The experimental results verify that the theoretical calculation based on DFT can give the correct terahertz band dielectric constant with frequency dependence characteristics completely independent of the experiment.

Calculating the Lattice Dynamics in the RFe3(BO3)4 Crystals in the Quasi-Harmonic Approximation

The frequencies of lattice vibrations in the RFe3(BO3)4 (R = Pr, Nd, Tb, Dy, or Ho) crystals in the high-temperature R32 phase and their temperature dependence have been calculated using the quasi-harmonic approximation. It has been found that, at the boundary point Λ of the Brillouin zone, the frequency of the unstable vibration mode the structural phase transition R32 → P3121 is related to strong changes with temperature in the TbFe3(BO3)4, DyFe3(BO3)4, and HoFe3(BO3)4 crystals. With increasing temperature, the frequency of the soft mode stabilizes and takes a real value. No significant changes in the phonon spectra, including the boundary point Λ, with increasing temperature for the PrFe3(BO3)4 and NdFe3(BO3)4 crystals have been observed.

Analysis on the lateral vibration of drill string by mass effect of drilling fluid

Abstract. It is well known that the influence of the internal and external drilling fluid on the lateral vibration characteristics of drillstring cannot be ignored. In this paper, experiment apparatus for simulating drillstring vibration was established. Hammering method is used to measure drillstring lateral natural vibration frequency when the internal and external drilling fluid is considered. The test results show that the drilling fluid can decrease the natural frequency of the drillstring. Based on the simulation model, considering the influence of the internal and external drilling fluid, an external drilling fluid additional mass coefficient is derived considering the dynamic pressure effect caused by external drilling fluid. Additional mass coefficient can get the result with high precision, which can meet the needs of the project. the simulation results are in good agreement with the test results, and the error is within 2 %. This work provides a useful attempt and lays the foundation for the dynamics of the drill string in the drilling fluid environment.

Mechanisms of Frequency-Dependent Conductivity of Mesoporous Silicon at γ Irradiation with Small Doses

Abstract—The effect of low-dose γ radiation on the mechanisms of low-frequency conductivity of mesoporous silicon has been studied. It has been shown that γ irradiation preserves the hopping character of conductivity at a change of the frequency of phonon lattice vibrations, a decrease in the size of the hop, and a shift of the level of the capture of traps to the Fermi level in the band gap, which makes the structure with mesoporous silicon irradiated by γ radiation promising for the creation of multifunctional resistive and capacitive devices.

Layer breathing and shear modes in multilayer graphene: a DFT-vdW study

In this work, we study structural and vibrational properties of multilayer graphene using density-functional theory with van der Waals (vdW) functionals. Initially, we analyze how different vdW functionals compare by evaluating the lattice parameters, elastic constants and vibrational frequencies of low energy optical modes of graphite. Our results indicate that the vdW-DF1-optB88 functional has the best overall performance on the description of vibrational properties. Next, we use this functional to study the influence of the vdW interactions on the structural and vibrational properties of multilayer graphene. Specifically, we evaluate binding energies, interlayer distances and phonon frequencies of layer breathing and shear modes. We observe excellent agreement between our calculated results and available experimental data, which suggests that this functional has truly predictive power for layer-breathing and shear frequencies that have not been measured yet. This indicates that careful selected vdW functionals can describe interlayer bonding in graphene-related systems with good accuracy.

Механизмы частотно-зависимой проводимости мезопористого кремния при гамма-облучении малыми дозами

Abstract — The effect of low-dose γ radiation on the mechanisms of low-frequency conductivity of mesoporous silicon has been studied. It has been shown that γ irradiation preserves the hopping character of conductivity at a change of the frequency of phonon lattice vibrations, a decrease in the size of the hop, and a shift of the level of the capture of traps to the Fermi level in the band gap, which makes the structure with mesoporous silicon irradiated by γ radiation promising for the creation of multifunctional resistive and capacitive devices.

Theoretical Study of Phonon Dispersion of Lanthanum Aluminate in Terahertz Frequency

The phonon dispersion spectrum, eigenvector and lattice vibration frequency of cubic crystalline lanthanum aluminate (LaAlO3) are studied by density functional theory (DFT). The effects of lattice constant, K-point selection and kinetic-energy cutoff (Ecut) on the calculation accuracy are discussed. The vertical parallel relationship between the phonon propagating wave vector and the atomic vibration direction is analyzed to obtain the frequency of the LaAlO3 transverse (TO)/longitudinal (LO) optical phonon. The comparison results of the first-principles calculation software Materials Studio, the open source component package ABINIT, and he open source component package Quantum Espresso show that the calculation accuracy depends on the convergence analysis and the approximation method adopted in the calculation process.

Dynamics of a Pedestrian’s Walking Motion Based on the Inverted Pendulum Model

In this paper, the inverted pendulum model is proposed to describe a pedestrian’s walking motion by considering that the pivot point vibrates periodically up and down. The stability, periodic solutions and oscillations of the inverted pendulum are theoretically investigated, the correctness of which is illustrated by numerical simulations. According to frequency spectrum analysis, the inverted pendulum can exhibit periodically or quasi-periodically stable oscillations. However, we demonstrate that the inverted pendulum will maintain the ratio between the lateral and vertical vibration frequencies near [Formula: see text] as an optimizing selection of stability. The theoretical result agrees with the measurement result for a normal pedestrian such that the lateral step frequency is always half the vertical step frequency, which means that it is feasible and reasonable to describe a pedestrian’s walking motion using the inverted pendulum with the pivot vibrating harmonically in the vertical direction. The inverted pendulum model suggested in this paper could contribute to the study of pedestrian–footbridge interaction, which overcomes the difficulty of directly determining the expression of the lateral force induced by pedestrians.

Competing radiative and nonradiative decay of embedded ions states in dielectric crystals: theory, and application to Co2+:AgCl0.5Br0.5.

We present a generally applicable theoretical model describing excited-state decay lifetime analysis of metal ions in a host crystal matrix. In contrast to common practice, we include multi-phonon non-radiative transitions competitively to the radiative one. We have applied our theory to Co2+ ions in a mixed AgCl0.5Br0.5 crystal, and as opposed to a previous analysis, find excellent agreement between theory and experiment over the entire measured temperature range. The fit predicts a zero absolute temperature radiative lifetime τrad(0) = 5.5 ms, more than three times longer than the measured effective low-temperature one τeff(0) = 1.48 ms. Furthermore, the fit configuration potential dissociation energy has been estimated as D = 2500 cm-1 and the lattice vibrational cutoff frequency as ħωco = 180 cm-1. We have experimentally verified the latter by optical reflection measurement in the far-IR.

Lattice response to the relaxation of electronic pressure of ultrafast laser-irradiated copper and nickel nanofilms

The impact of electronic pressure and electronic pressure gradient induced by laser excitation on the dynamic response of metals (Cu and Ni) has been numerically investigated using two complementary approaches. In the framework of DFPT, for electronic temperatures up to 6 eV, we demonstrate that electronic pressure results in a higher lattice stability. In other words, the electronic pressure has a negative influence on the phonon entropy and induces an increase in the shear modulus, which improves the melting temperature and lattice vibration frequency. Given the relaxation of electronic pressure during an extreme non-equilibrium state, we adopt a modified 2T-MD model to identify the contribution of the electronic pressure gradient to the atomic dynamics during fs laser excitation. Our results indicate the presence of rapid destabilization of the structure of Cu and Ni nano-films along the electronic pressure gradients. Specifically, the nucleation of the voids and heterogeneous nucleation occur at the surface layer, at a depth of several nanometers, for Cu and Ni, respectively. With the coexistence of a-thermal and thermal effects on scales, two different ultrafast destructuring processes of Cu and Ni both interrelate a hot electronic blast force and classical electron–ion dynamics.

Invariant eigen-operator calculated vibration mode of lattice in the case of absorbing an atom onto crystal surface

The influence of diffusion and defects of crystal surface on the crystal vibration mode are an important and basic subject in surface physics research. The frequency of lattice vibration corresponds to the energy band of the system. Since the vibrations of the atoms in the crystal lattice are not isolated from each other, and the crystal lattice is periodic, thereby forming a lattice wave in the crystal. The lattice wave represents that all the atoms in the crystal vibrate at an identical frequency, which is often called a vibration mode. The lattice chain model has been studied as the vibrating mode of phonon and the energy-band in solid state physics. The vibrating modes of the lattice chain model have been analyzed with the Newton equation and the Born-von-Karman boundary condition in the literaure. In general, it is difficult to solve this problem due to the complex nonlinear characteristic of the interactions between the matter particles and the environment. Noting the complicacy in directly diagonalizing quantum Hamiltonian operator of a long chain, we introduce the invariant eigenoperator method (IEO) for deriving the energy gap of a given crystal lattice without solving its eigenstates in the Heisenberg picture. The Heisenberg equation is as important as the Schrödinger equation. However, it has been seldom used for directly deriving the energy-gap in previous studies. Following the Heisenberg's original idea that most observable physical quantity in quantum mechanics is energy spectrum, Hong-yi Fan, one of the authors of the present paper, developed the IEO method. This method provides a natural result of combining both the Schrödinger operator and the Heisenberg equation. Using the IEO method, we study the vibration modes of crystal lattice, which are affected by absorbing an atom with mass m0, which is different from the mass of atom in the crystal. Moreover, the attractive potential constantβ0 of the lattice surface differs from the inner constantβ. With the help of invariant eigen-operator method, we deduce the vibration mode ω=√(2β(1-cosh α))/ħm, where α=ln[-(mβ0+m0(-2β+β0)+√β0√-4 mm0β+(m+m0)2β0)/2m0β]. Our numerical results show that vibration mode ω depends not only on the absorption potential and the mass of the absorbed atom, but also on the mass of the lattice atom and the inner potential. In general, by discussing the vibration modes via some numerical solutions or approximate methods, we show the relations between the system vibration modes with different parameters which describe the environment influences. These results can deepen our understanding of quantum Brownian motion and demonstrate the applicability of the IEO method.

A Theory Treatment of Pedestrian-Induced Lateral Vibration of Structure

The lateral excessive sway motion caused by pedestrian traffic has attracted great public attention in the past decades years. However, the theories about exploring the effect of pedestrian on the lateral dynamic properties of structure are scarce. The new contribution of this paper is that a new pedestrian-structure system is proposed for exploring the effect of human on structural dynamic properties based on a sway assumption. Study shows that pedestrian deteriorates the natural frequency of structure and improves structural damping. The influence tendencies of pedestrian on structure can be supported by measurements. The further parametric study shows that the changes of human dynamic parameters have some evident impacts on structural dynamic performances. For example, the increase of leg damping can trigger an improvement of structural damping capacity. In addition, the walking step frequency closing structural harmonic natural frequency can incur the worst response. The increase of step width deteriorates lateral vibration and structural frequency but can slightly improve structural damping. One of essential reasons influencing structural lateral dynamic properties is the dynamic human system including body mass, damping, stiffness, and its motion behavior such as step frequency. This theory is proposed to analyze how pedestrian alters the lateral dynamic performances on those sensitive structures such as the footbridges or stadium bleachers. For example, how the variation of step width influences the change of natural frequency of structure?

The Motor Active Flexible Suspension and Its Dynamic Effect on the High-Speed Train Bogie

We put forward the motor active flexible suspension and investigate its dynamic effects on the high-speed train bogie. The linear and nonlinear hunting stability are analyzed using a simplified eight degrees-of-freedom bogie dynamics with partial state feedback control. The active control can improve the function of dynamic vibration absorber of the motor flexible suspension in a wide frequency range, thus increasing the hunting stability of the bogie at high speed. Three different feedback state configurations are compared and the corresponding optimal motor suspension parameters are analyzed with the multi-objective optimal method. In addition, the existence of the time delay in the control system and its impact on the bogie hunting stability are also investigated. The results show that the three control cases can effectively improve the system stability, and the optimal motor suspension parameters in different cases are different. The direct state feedback control can reduce corresponding feed state's vibration amplitude. Suppressing the frame's vibration can significantly improve the running stability of bogie. However, suppressing the motor's displacement and velocity feedback are equivalent to increasing the motor lateral natural vibration frequency and damping, separately. The time delay over 10 ms in control system reduces significantly the system stability. At last, the effect of preset value for getting control gains on the system linear and nonlinear critical speed is studied.

Optical phonon modes and polaron related parameters in GaxIn1−xP

Based on a pseudopotential approach under the virtual crystal approximation that includes the effect of compositional disorder, the optical lattice vibration frequencies and polaron related parameters in zinc-blende GaxIn1−xP have been studied. Our findings showed generally reasonably good accord with data in the literature. Other case, our results are predictions. The composition dependence of longitudinal optical (LO) and transverse optical (TO) phonon modes, LO-TO splittings, Frӧhlich coupling parameter, Debye temperature of LO phonon frequency, and polaron effective mass has been analyzed and discussed. While a non-monotonic behavior has been noticed for the LO and TO phonon frequencies versus Ga concentration x, a monotonic behavior has been observed for the rest of the features of interest. The information derived from this investigation may be useful for optoelectronic technological applications.

An Analysis of Common Drill Stem Vibration Models

Excessive drill stem (DS) vibration while rotary drilling of oil and gas wells causes damages to drill bits and bottom hole assemblies (BHAs). In an attempt to mitigate DS vibrations, theoretical modeling of DS dynamics is used to predict severe vibration conditions. To construct the model, decisions have to be made on which beam theory to be used, how to implement forces acting on the DS, and the geometry of the DS. The objective of this paper is to emphasize the effect of these assumptions on DS vibration behavior under different, yet realistic, drilling conditions. The nonlinear equations of motion were obtained using Hamilton's principle and discretized using the finite element method. The finite element formulations were verified with uncoupled analytical models. A parametric study showed that increasing the weight on bit (WOB) and the drill pipe (DP) length clearly decreases the DS frequencies. However, extending the drill collar length does not reveal a clear trend in the resulting lateral vibration frequency behavior. At normal operating conditions with a low operating rotational speed, less than 80 RPM, the nonlinear Euler–Bernoulli and Timoshenko models give comparable results. At higher rotational speeds, the models deliver different outcomes. Considering only the BHA overestimates the DS critical operating speed; thus, the entire DS has to be considered to determine the critical RPM values to be avoided.

Investigations on bending-torsional vibrations of rotor during rotor-stator rub using Lagrange multiplier method

The ever-increasing need of highly efficient rotating machinery causes reduction in the clearance between rotating and non-rotating parts and increase in the chances of interaction between these parts. The rotor-stator contact, known as rub, has always been recognized as one of the potential causes of rotor system malfunctions and a source of secondary failures. It is one of few causes that influence both lateral and torsional vibrations. In this paper, the rotor stator interaction phenomenon is investigated in the finite element framework using Lagrange multiplier based contact mechanics approach. The stator is modelled as a beam that can respond to axial penetration and lateral friction force during the contact with the rotor. It ensures dynamic stator contact boundary and more realistic contact conditions in contrast to most of the earlier approaches. The rotor bending-torsional mode coupling during contact is considered and the vibration response in bending and torsion are analysed. The effect of parameters such as clearance, friction coefficient and stator stiffness are studied at various operating speeds and it has been found that certain parameter values generate peculiar rub related features. Presence of sub-harmonics in the lateral vibration frequency spectra are prominently observed when the rotor operates near the integer multiple of its lateral critical speed. The spectrum cascade of torsional vibration shows the presence of bending critical speed along with the larger amplitudes of frequencies close to torsional natural frequency of the rotor. When m×1nX frequency component of rotational frequency comes closer to the torsional natural frequency, stronger torsional vibration amplitude is noticed in the spectrum cascade. The combined information from the stator vibration and rotor lateral-torsional vibration spectral features is proposed for robust rub identification.

A theoretical model study on interplay between Coulomb potential and lattice energy in graphene-on-substrate

The graphene-on-substrates breaks the sub-lattice symmetry leading to the opening of a small gap. The small band gaps can be enhanced by electron–phonon interactions by keeping strongly polarized superstrate on graphene. To describe the band gap opening in graphene, we propose a tight-binding model Hamiltonian taking into account of third-nearest-neighbor electron-hoppings. We introduce repulsive Coulomb interaction at two sub-lattices of graphene. Further, we consider phonon coupling to the electron densities centered at two sub-lattices in the presence of phonon vibration with a single frequency. For high frequency phonons, the present interaction represents the Holstein interaction. Applying Lang–Firsov canonical transformation in the high phonon-frequency limit, we calculate the modified Coulomb interaction and the effective hopping integral which are functions of electron–phonon coupling, phonon-frequency and nearest-neighbor electron-hopping integral. The electron Green’s functions are calculated by Zubarevs technique. The electron occupancies at two sub-lattices for up and down spins are calculated and computed self-consistently. Finally, we calculate the modulated substrate induced gap of graphene-on-substrate, which is computed numerically for [Formula: see text] grid points for electron momentum. We have studied the interplay of Coulomb interaction, electron–phonon interaction in high phonon-frequency limit. The maximum band gap achieved due to the interplay is nearly 67% more than the substrate induced gap. To achieve this condition, one requires low Coulomb energy for low frequency phonon, while one needs high Coulomb interaction and high electron–phonon interaction of a given lattice vibration frequency. For given electron–phonon interaction and phonon-frequency, the modified gap is enhanced throughout the temperature range with increase of Coulomb interaction.