Vibrational Motion Research Articles

Experimental and Simulation Research on the Vibration Characteristics of the Traction Motor of Medium and Low Speed Maglev Train under Electromagnetic Excitation

In a medium and low speed maglev train, the linear induction motor (LIM) is employed as the traction motor, during operation its vibration characteristics correlate with the dynamic performance and noise radiation characteristics of the train. This paper conducted tests and established a three-dimensional simulation model of the LIM in a medium and low speed maglev train, to study the motor vibration characteristics by comparative analysis between test and simulation. The analysis results showed that the electromagnetic excitation sources of the train appear in the high-frequency band, with the main characteristic frequencies of 497.33 Hz, 994.33 Hz, 1989.00 Hz, and 3977.67 Hz. The structural modal analysis and vibration harmonic response analysis of the motor showed that the 3rd, 8th, and 18th modal frequencies of the motor structure approximate the frequencies of the electromagnetic excitation sources. As a result, the motor generates resonance at 497.33 Hz and 994.33 Hz under that excitation. The validity of the simulation was confirmed by the corresponding tests. From the perspective of theory, experiment, and simulation, this research can contribute to the optimization of traction systems in the future design of medium and low speed maglev trains.

Investigation on various stator structure towards noise and vibration

<span lang="EN-US">This research analyses the noise and vibration characteristics of permanent magnet motors (PMM) with the electromagnetic characteristics, with an emphasis on high-speed motor segmented closed slot stator. The interaction between the stator, rotor, and magnets can cause a vibration that results in the loud sound due to the high magnetic energy. Even if there aren't many vibrations to contend with, the fluctuation of motor vibrations causes more serious harm. The studies covered slotted stator, closed slot stator, and segmented with closed slot stator. The objective is to analyze the cogging torque relation towards vibration and the effect of natural frequency at steady-state behavior of the structure. ANSYS finite element analysis (FEA) is used to generate electromagnetic analysis performance whilst ANSYS mechanical used to simulate the modal and harmonic analysis at the stator tooth tips surface to define the structure when </span><span lang="EN-US">the steady-state condition under vibrational stimulation. Anticipation on this work shows, the lowest cogging torque produce less radiated sound. Thus, the result indicates the cogging torque profiles had good agreement with the equivalent radiated power level (ERPL) waterfall diagram.</span>

Atomistic analysis of temperature-dependent dislocation dynamics in Ni3Al-based intermetallic alloys

In this study, we investigate the dynamics of superlattice edge dislocations composed of partial dislocations, complex stacking faults, and antiphase boundaries in binary and ternary Ni-based alloys (γ’ phase) with the L12 structure. In the case of Ni3Al, the dislocation velocity decreases with increasing temperature at low applied shear stress, mainly owing to the phonon drag effect. Meanwhile, in the case of ternary alloys constructed by exchanging Ni atoms with Co atoms in Ni3Al, the effects of temperature on dislocation motion are more complex. At low applied shear stress, the dislocation motion is disturbed by solute Co (i.e., solid-solution strengthening). In this case, the temperature promotes dislocation motion because the potential energy barrier dominates the thermally activated dislocation dynamics. In contrast, when the applied shear stress increases, the temperature suppresses dislocation motion owing to the phonon drag effect. The drag effect also increases with increasing Co concentration. The origin of the energy barrier due to solute atoms at low applied shear stress can be explained by the interaction between the partial dislocation and solute Co. Meanwhile, the origin of the drag effect on the superlattice dislocation dynamics is discussed on the basis of atomic vibrational motions and wavy dislocation behaviors. In this study, we propose and construct a map showing the dominant effects on complex superlattice dislocation dynamics. The map has energy-barrier-dominated, phonon-drag-dominated, and sound velocity-dominated regions, suggesting that the dominant factor changes depending on the applied shear stress, temperature, and strength of the solute–dislocation interaction.

Mechanism analysis on wake-induced vibration of parallel hangers near a long-span suspension bridge tower

To reproduce the vibration phenomenon and explore the mechanism of parallel hangers near a suspension bridge tower based on the practical engineering, a pair of hangers in the wake of the bridge tower were taken as the research object. The influences of different wind yaw angles on the flow patterns of the bridge tower and aerodynamic characteristics of parallel hangers were investigated using the computational fluid dynamics (CFD) method. Then, based on the amplitude spectrum results, the relationship between the aerodynamic interference intensities of the tower wake and the displacements of parallel hangers were quantitatively described. Moreover, the coherence between the bridge tower and the parallel hangers were studied. Finally, based on the surface pressure distributions, energy input analysis, and wind speed characteristics, the vibration mechanism of parallel hangers near the bridge tower were explored. The results show that when the wind yaw angle is in the range of 0° ∼ −30°, the tower wake and the vortex shedding from the hangers jointly affect the aerodynamic characteristics of the hangers, which leads to the vibration displacements and movement tracks are observed as a sawtooth shape with multiple frequencies and synchronous skewed ellipses, respectively. The aerodynamic interference intensities of the bridge tower are positively correlated with the displacements of the hangers, and the peak amplitude at the wind yaw angle of −30° with strong aerodynamic interference is 35 mm, which is about 9 times that at the wind yaw angles of ±60° with weak aerodynamic interference. Moreover, at the wind yaw angles with strong aerodynamic interference, the mean wind pressure coefficients of the parallel hangers tend to be negative and their root mean square (RMS) values of wind pressure coefficient exhibit an overall upward trend compared with those at wind yaw angles with weak aerodynamic interference. Based on the analysis of energy input and wind speed characteristics, it is found that the low-frequency vortex shedding from the tower wake is the internal factor that continuously maintain the large vibrations of the parallel hangers.

Molecular Modeling of Supercritical Processes and the Lattice—Gas Model

The existing possibilities for modeling the kinetics of supercritical processes at the molecular level are considered from the point of view that the Second Law of thermodynamics must be fulfilled. The only approach that ensures the fulfillment of the Second Law of thermodynamics is the molecular theory based on the discrete–continuous lattice gas model. Expressions for the rates of the elementary stage on its basis give a self-consistent description of the equilibrium states of the mixtures under consideration. The common usage today of ideal kinetic models in SC processes in modeling industrial chemistry contradicts the non-ideal equation of states. The used molecular theory is the theory of absolute reaction rates for non-ideal reaction systems, which takes into account intermolecular interactions that change the effective activation energies of elementary stages. This allows the theory to describe the rates of elementary stages of chemical transformations and molecular transport at arbitrary temperatures and reagent densities in different phases. The application of this theory in a wide range of state parameters (pressure and temperature) is considered when calculating the rates of elementary bimolecular reactions and dissipative coefficients under supercritical conditions. Generalized dependencies are calculated within the framework of the law of the corresponding states for the coefficients of compressibility, shear viscosity, and thermal conductivity of pure substances, and for the coefficients of compressibility, self- and mutual diffusion, and shear viscosity of binary mixtures. The effect of density and temperature on the rates of elementary stages under supercritical conditions has been demonstrated for a reaction’s effective energies of activation, diffusion and share viscosity coefficients, and equilibrium constants of adsorption. Differences between models with effective parameters and the prospects for developing them by allowing for differences in size and contributions from the vibrational motions of components are described.

Photon Energy-Dependent Ultrafast Exciton Transfer in Chlorosomes of Chlorobium tepidum and the Role of Supramolecular Dynamics.

The antenna complex of green sulfur bacteria, the chlorosome, is one of the most efficient supramolecular systems for efficient long-range exciton transfer in nature. Femtosecond transient absorption experiments provide new insight into how vibrationally induced quantum overlap between exciton states supports highly efficient long-range exciton transfer in the chlorosome of Chlorobium tepidum. Our work shows that excitation energy is delocalized over the chlorosome in <1 ps at room temperature. The following exciton transfer to the baseplate occurs in ∼3 to 5 ps, in line with earlier work also performed at room temperature, but significantly faster than at the cryogenic temperatures used in previous studies. This difference can be attributed to the increased vibrational motion at room temperature. We observe a so far unknown impact of the excitation photon energy on the efficiency of this process. This dependency can be assigned to distinct optical domains due to structural disorder, combined with an exciton trapping channel competing with exciton transfer toward the baseplate. An oscillatory transient signal damped in <1 ps has the highest intensity in the case of the most efficient exciton transfer to the baseplate. These results agree well with an earlier computational finding of exciton transfer driven by low-frequency rotational motion of molecules in the chlorosome. Such an exciton transfer process belongs to the quantum coherent regime, for which the Förster theory for intermolecular exciton transfer does not apply. Our work hence strongly indicates that structural flexibility is important for efficient long-range exciton transfer in chlorosomes.

A Frequency-Dependent Dynamic Electric-Mechanical Network for Thin-Wafer Piezoelectric Transducers Polarized in the Thickness Direction: Physical Model and Experimental Confirmation.

This paper is concerned with electric-acoustic/acoustic-electric conversions of thin-wafer piezoelectric transducers polarized in the thickness direction. By introducing two mechanical components with frequency-dependent values, i.e., radiation resistance and radiation mass, into the equivalent circuit of the thin-wafer piezoelectric transducer, we established a frequency-dependent dynamic mechanic-electric equivalent network with four terminals for an arbitrary given frequency, an enhancement from the conventional circuit networks. We derived the analytic expressions of its electric-acoustic and acoustic-electric conversion impulse responses using the four-terminal equivalent circuit to replace the traditional six-terminal equivalent circuit for a thin-wafer transducer with harmonic vibrational motion. For multifrequency electrical/acoustic signals acting on the transducer, we established parallel electric-acoustic/acoustic-electric conversion transmission networks. These two transmission network models have simple structures and clear physical and mathematical descriptions of thin-wafer transducers for electric-acoustic/acoustic-electric conversion when excited by a multifrequency electric/acoustic signal wavelet. The calculated results showed that the transducer's center frequency shift relates to its mechanical load and vibration state. The method reported in this paper can be applied to conventional-sized and small-sized piezoelectric transducers with universal applicability.

Tensile behavior of UHPFRC made by a fiber orientation device with adjustable vibrational frequency

Ultra-High-Performance Fiber Reinforced Concrete (UHPFRC) not only has high compressive and tensile strength, but also exhibits strain-hardening characteristics in tension due to the addition of steel fibers. In this study, a new-style fiber orientation device equipped with a vibration motor of adjustable vibrational frequency was used to prepare UHPFRC. The wall effect and fiber length were considered in the manufacturing process of the device. Uniaxial tensile tests were conducted on fiber-oriented UHPFRC to explore the effects of vibrational frequency and corresponding vibrational force on the tensile behaviors. The test results showed that the elastic ultimate tensile strength, elastic ultimate tensile strain, tensile strength, peak tensile strain, and tensile elastic modulus of UHPFRC specimens cast by fiber orientation process at various vibrational frequencies were different. The fiber orientation parameters were quantitatively evaluated by the image analysis technique to explain the differences in tensile properties of the specimens. The effect of different vibrational frequencies on the tensile strength of UHPFRC matrix and its porosity was also considered. Therefore, this study provides a reference for how to adjust the vibrational frequency of the vibrating platform under the directional channel when pouring relevant components.

Influence of Laser Wavelength in Simultaneous Patterning of Fluorinated Ethylene Propylene and Copper Electrode Surface Towards Performance Enhancement of Triboelectric Nanogenerator

Triboelectric nanogenerators (TENGs) are promising cost‐effective energy harvesters useful to scavenge vibration or mechanical movements from various domains. Ranging from condition monitoring of machines to motion sensing of humans, its applications are enormous in the internet of things scenario. Enhancing the performance of small‐sized TENGs is of great demand, and pulsed laser‐assisted texturing is an efficient and proven method to enhance the output of energy harvesters. This work studies simultaneous laser patterning of fluorinated ethylene propylene (FEP) dielectric material and the underneath copper electrode with three different wavelengths (355, 532, and 1064 nm) of the Nd3+:YAG laser and the device's electrical performance is analyzed. The maximum enhancement is observed in the case of 355 nm laser‐assisted patterning on FEP and Cu electrode with a laser fluence of 10 J cm−2. The improvement is least in the case of 1064 nm laser‐assisted patterning. Laser patterning on the underlying electrode with this new approach is able to produce an enhancement in the TENG output. However, patterning on the FEP top surface is critical in the process.

Theoretical study of (e,2e) triple differential cross section of 1b3g orbital of ethylene by vibrational multi-center distorted-wave method

The vibrational motions are usually neglected when calculating (e,2e) triple differential cross sections (TDCSs) of molecules. Here, multi-center distorted-wave method (MCDW) has been modified by including molecular vibrations. This vibrational MCDW method is employed to calculate the TDCSs of 1b3g orbital of ethylene at low (100 eV) and medium (250 eV) incident electron energies in coplanar asymmetric kinematic condition. The results show that molecular vibrations significantly influence the angular distributions of the TDCSs, especially in the binary region along momentum transfer near the Bethe ridge.

A Head-Mounted Assistive Device for Visually Impaired People with Warning System from Object Detection and Depth Estimation

People with visual impairment use white cane as their traditional method for perceiving the surroundings. However, the utilization of a cane is limited by its length and orientation. In Thailand, the obstacles on paveway in daily life are not located only on the floor but also above knee level which sometimes could be harmful to pedestrians, especially blind people. A head-mounted assistive device is developed to be an enhancement used with a cane for the visually impaired to comprehend their environment both lower and higher the knee level. The assistive device is designed to be compact and light-weight. It could also send the tactile feedback as a warning from vibration motors mounted on the device. To generate a warning signal, YOLOv4 is used to detect the location of obstacles and depth map from the stereo camera is used to estimate the distance mapping into 4 defined ranges: dangerous, very close, close and fine. The results indicate that the head-mounted assistive device has the ability to perceive obstacles locating farther than 0.9 m. The prediction returned 9.23%, 14.63% and 7.86% error when estimating the depth of obstacles at 1.3 m., 2.8 m. and 4.2 m. respectively. The average execution time for the device to return the command controlling vibration motors is 0.13 second and the maximum estimated time for the motor to send the haptic feedback is 1.05 second.

Ultrasonic-Assisted Extraction of Bioactive Compounds from Elecampagne (Inula helenium, Radix Inulae)

In this study, we had developed a method of ultrasound assisted extraction from Elecampane in order to obtain, identify and the dosing the main bioactive compounds from plant, such as: alantolactone and isoalantolactone, inulin etc. Aqueous/hydroalcoholic extraction assisted by ultrasound, was used in order to obtain plant extracts rich in bioactive compounds, in order to ensure the highest possible extraction yield (exhausting the plant). In the process of extracting bioactive compounds from plant, the acoustic energy of the ultrasound is not absorbed by the molecules and, as such, has an effect of breaking the cell walls and improving the mass transfer. Ultrasound are transmitted in the reaction medium in the form of pressure waves that induce vibrational movements of the molecules, thus the molecular structure of the medium, alternately, it compresses and expands, as a result of a pressure, that varies over time. When the ultrasound intensity is high enough, the expansion cycle can create bubbles or cavities. Cavitation is the process by which bubbles form, grow and undergo implosion. Ultrasound allows the solvent to penetrate the cell walls, and the bubbles produced by the acoustic cavitation favor the breaking of the cell wall and the release of the active compounds, increasing the reaction yield. A high content from these compounds, make the plant to be used in the treatment of different respiratory diseases (asthma, cold, flu), indigestion, intestinal parasites etc. Recent studies had shown that the extracts from dried root of Elecampane have antitumor and antimicrobial effect and also detox and anti-inflammatory action.

Histologic Examination of Vocal Fold Mucosal Wave and Vibration.

Despite gross anatomic and histologic differences between human and canine vocal folds, similar wave patterns have been described yet not fully characterized. We reconstructed vocal fold (VF) vibration in a canine hemilarynx and performed histologic examination of the same vocal fold. We demonstrate comparable wave patterns while exploring the importance of certain anatomic architectures. An in vivo canine hemilarynx was phonated against a glass prism at low and high muscle activation conditions. Vibration was captured using high-speed video, and trajectories of VF medial surface tattooed landmarks were 3D-reconstructed. The method of empirical eigenfunctions was used to capture the essential dynamics of vibratory movement. Histologic examination of the hemilarynx was performed. Oscillation patterns were highly similar between the in vivo canine and previous reports of ex vivo human models. The two most dominant eigenfunctions comprised over 90% of total variance of movement, representing opening/closing and convergent/divergent movement patterns, respectively. We demonstrate a vertical phase difference during the glottal cycle. The time delay between the inferior and superior VF was greater during opening than closing for both activation conditions. Histological examination of canine VF showed not only a thicker lamina propria layer superiorly but also a distinct pattern of thyroarytenoid muscle fibers and fascicles as described in human studies. Histologic and vibratory examination of the canine vocal fold demonstrated human vocal fold vibratory patterns despite certain microstructural differences. This study suggests that the multilayered lamina propria may not be fundamental to vibratory patterns necessary for human-like voice production. NA (Basic science study) Laryngoscope, 134:264-271, 2024.

Antioxidant Capacity from Ethyl Acetate Fraction of Kenikir (Cosmos Caudatus K)

Antioxidant is an activity that inhibits oxidation reactions due to exposure to free radicals, the search for antioxidant compounds continues to be developed from natural sources. The purpose is to identify new sources of safe and inexpensive agents through antioxidant capacity from ethyl acetate fraction on kenikir leaves was evaluated through enzymatic and non-enzymatic in vitro models. The research began with the method of separating compounds from ethanol extracts and ethyl acetate fractions, quantification of total phenolics and flavonoids, antioxidant capacity tests with DPPH, and tyrosinase enzyme. The results of the study produced isolate E which was observed in a single stain with Rf 0,80. The compound has a typical marker worth 1734.07 cm-1 with an indication of stretching vibration movement on C-O. It has a maximum wavelength of ± 216 nm, with an abundance of 49.75% and a retention time of 27.20 minutes. TPC and TFC test results, the water fraction is the most dominant value with 0.430 mgGAE/g and 0.056 mQE/g. DPPH assay results, isolate E has an IC50 value of 162.03 ppm and a %inhibition of 12.73%. The tyrosinase inhibition test of L-DOPA substrate was resulting an IC50 value of 77.51 ppm compared to kojic acid of 16.48 ppm.

NEXMD v2.0 Software Package for Nonadiabatic Excited State Molecular Dynamics Simulations.

We present NEXMD version 2.0, the second release of the NEXMD (Nonadiabatic EXcited-state Molecular Dynamics) software package. Across a variety of new features, NEXMD v2.0 incorporates new implementations of two hybrid quantum-classical dynamics methods, namely, Ehrenfest dynamics (EHR) and the Ab-Initio Multiple Cloning sampling technique for Multiconfigurational Ehrenfest quantum dynamics (MCE-AIMC or simply AIMC), which are alternative options to the previously implemented trajectory surface hopping (TSH) method. To illustrate these methodologies, we outline a direct comparison of these three hybrid quantum-classical dynamics methods as implemented in the same NEXMD framework, discussing their weaknesses and strengths, using the modeled photodynamics of a polyphenylene ethylene dendrimer building block as a representative example. We also describe the expanded normal-mode analysis and constraints for both the ground and excited states, newly implemented in the NEXMD v2.0 framework, which allow for a deeper analysis of the main vibrational motions involved in vibronic dynamics. Overall, NEXMD v2.0 expands the range of applications of NEXMD to a larger variety of multichromophore organic molecules and photophysical processes involving quantum coherences and persistent couplings between electronic excited states and nuclear velocity.

Nonlinear vibration of SMA hybrid composite beams actuated by embedded pre-stretched SMA wires with tension-bending coupling effect

Theoretical and numerical analyses for nonlinear vibrations of the shape memory alloy hybrid composite(SMAHC) beam actuated by the pre-stretched shape memory alloy(SMA) fibers with tension-bending coupling effect are presented in this paper. Under the sudden action of thermal temperature, a recovery force and moment are caused in the SMAHC beam due to the phase transition in the SMA fibers, exciting the nonlinear vibration of the SMAHC beam. The one-dimensional Brison constitutive model was adopted to express the influence of the phase transition temperature, initial volume fraction of martensite, and pre-strain on the phase transition in the shape memory alloy. On this basis, the constitutive law of the SMAHC beam is built by considering the tension-bending coupling effect and the phase transition in the SMAHC beam. The equation of motion for nonlinear vibration of the SMAHC beam with geometric nonlinearity and material nonlinearity is derived from the Hamilton principle and is discretized into matrix form using the Galerkin method. According to the algorithm of the NewMark-β method, numerical solutions are computed by developing Matlab program and are compared with the results from ABAQUS analysis. It shows that the frequencies and amplitudes of the theoretical calculations are very consistent with those obtained from ABAQUS analysis. In addition, both the theoretical study and ABAQUS simulation indicates that the high frequency for longitudinal vibration is not observed in the spectrum diagram of transverse vibration, while the low frequencies for transverse vibration are captured in the longitudinal vibration. With the established Matlab program, parametric study is carried out to investigate the effect of the temperature and the location of the SMA fibers on the vibration responses of the SMAHC beam. The results from this study indicate that the transverse vibration of SMAHC beams is characterized as one of low frequency, while the longitudinal vibration has the characteristics of high frequency. Especially in the case of nonlinear vibration, not only the vibration of high frequency but also the vibration of low frequency observed in the transverse vibration will occur in the longitudinal direction of the SMAHC beam. Furthermore, the double and triple fundamental frequencies of the transverse vibration are excited in the nonlinear vibration of the SMAHC beam. The results of this paper can provide a theoretical basis for the evaluation of the safety and stability of smart composite structures.

A Sage-Husa Prediction Algorithm-Based Approach for Correcting the Hall Sensor Position in DC Brushless Motors.

Accurate knowledge of the rotor position is essential for the control of brushless DC motors (BLDCM). Any deviation in this identification can cause fluctuations in motor current and torque, increase noise, and lead to reduced motor efficiency. This paper focused on a BLDCM equipped with a three-phase binary Hall sensor. Based on the principle of minimum deviation, this paper estimated the relative installation offset between the Hall sensors. It also provided a clear method for ideal phase commutation position recognition and eliminated the Hall sensor installation position deviation. The proposed pre-calibration method identified and eliminated the offset of the permanent magnet poles, the delay time caused by the Hall signal conditioning circuit, and the offset of the sensor signal identification due to armature response under different loads. Based on the pre-calibration results, a correction strategy for correcting the rotor position information of BLDCMs was proposed. This paper presented a self-adaptive position information prediction algorithm based on the Sage-Husa method. This filters out rotor position information deviations that are not eliminated in pre-calibration. Experimental results on a hydrogen circulation pump motor showed that, after the pre-calibration method was adopted, the Mean Square Error (MSE) of motor speed fluctuations decreased by 92.0%, motor vibration was significantly reduced, average phase current decreased by 62.8%, and the efficiency of the hydrogen circulation pump system was significantly improved. Compared to the traditional KF prediction algorithm, the Sage-Husa adaptive position information prediction algorithm reduced the speed fluctuation during the uniform speed operation stage and speed adjustment stage, the speed curve overshoot, and the commutation time deviation throughout the process by 44.8%, 56.0%, 54.9%, and 14.7%, respectively. This indicates a higher disturbance rejection ability and a more accurate and stable prediction of the commutation moment.

Aggregation‐induced narrowband isomeric fluorophores for ultraviolet nondoped OLEDs by engineering multiple nonbonding interactions

AbstractTraditional donor‐acceptor type organic luminescent materials usually suffer from unfavorable spectral broadening and fluorescence quenching problems arising from strong inter/intra‐chromophore interactions in aggregation state. Here, two ultraviolet carbazole‐pyrimidine isomers (named o‐DCz‐Pm and m‐DCz‐Pm) with novel aggregation‐induced narrowband phenomenon are constructed and systematic investigated by experiments and theoretical simulations. Benefitting from strengthened steric hindrance and multiple noncovalent interactions, the nonradiative decay, vibrational motion, and structural relaxation of singlet state can be effectively suppressed in aggregation state. Consequently, the electroluminescence peak of 397 nm, full width at half maximum of 21 nm and external quantum efficiency of 3.4% are achieved simultaneously in nondoped o‐DCz‐Pm‐based device. This work paves an avenue toward the development of high‐performance narrowband nondoped ultraviolet materials and organic light‐emitting diodes.

Structural, Spectroscopic, and Dynamic Properties of Li2+(X2∑g+) in Interaction with Krypton Atom.

We report a computational study of the potential energy surface (PES) and vibrational bound states for the ground electronic state of Li2+Kr. The PES was calculated in Jacobi coordinates at the Restricted Coupled Cluster method RCCSD(T) level of calculation and using aug-cc-pVnZ (n = 4 and 5) basis sets. Afterward, this PES is extrapolated to the complete basis set (CBS) limit for correction. The obtained interaction energies were, then, interpolated numerically using the reproducing kernel Hilbert space polynomial (RKHS) approach to produce analytic expressions for the 2D-PES. The analytical PES is used to solve the nuclear Schrodinger equation to determine the bound states' eigenvalues of Li2+Kr for a J = 0 total angular momentum configuration and to understand the effects of orientational anisotropy of the forces and the interplay between the repulsive and attractive interaction within the potential surface. In addition, the radial and angular distributions of some selected bound state levels, which lie below, around, and above the T-shaped 90° barrier well, are calculated and discussed. We note that the radial distributions clearly acquire a more complicated nodal structure and correspond to bending and stretching vibrational motions "mode" of the Kr atom along the radial coordinate, and the situation becomes very different at the highest bound states levels with energies higher than the T-shaped 90° barrier well. The shape of the distributions becomes even more complicated, with extended angular distributions and prominent differences between even and odd states.

Influence of high‐order electromagnetic force on vibration characteristics of induction motor

AbstractThe exploration of electromagnetic vibration sources is very important for the vibroacoustic reduction of a squirrel‐cage induction motor. However, the influence of high‐order electromagnetic force on the electromagnetic vibration of induction motor has not been studied before. The influence of high‐order electromagnetic force on motor vibration is investigated in detail. Firstly, the Maxwell stress tensor method is applied to calculate the electromagnetic force. Next, the force transfer function is introduced to describe the phenomenon that the high‐order electromagnetic force induces the low‐mode motor vibration. Then, the high‐order forces in the air gap of the induction motor are analysed in detail and their effects on motor vibration are simulated. Finally, an experiment is conducted to verify the correctness of the analytical scheme.