Vibration Model Research Articles

EPR parameters and optical spectrum of α-Al2O3:Ti3+ with dynamic Jahn-Teller effect

The quenching phenomenon of trigonal crystal field (CF), spin–orbit (SO) coupling operators, and orbital operators reflected in electron paramagnetic resonance (EPR) parameters and energy splitting intervals observed in experiments of α-Al2O3:Ti3+ is theoretically investigated by the calculation of EPR g factors and the energy differences of the lowest three levers E3/2, 1E1/2 and 2E1/2 with the formulas derived with high-order perturbation method. In the calculation, the coupling of 2T2g and 2Eg with e vibrational model of dynamic Jahn-Teller effect are considered. The calculated results are in agreement with the experimental values. The local defect structure around Ti3+ ions (bond lengths and angles of [TiO6]9-) and trigonal CF parameters ν and v′ are determinedand the covalence effects on SO coupling parameters ζ, ζ’ and orbital reduction parameters k、k’ are determined also.

Prediction of Vertical Vibrations of a CNC Router Type Geometry

Mechanical vibrations represent an important problem in machining processes performed by machine tools. They affect surface quality, tool life, and productivity. In extreme situations, chattering may appear, which can dramatically reduce the tool life. CNC router machines are particularly sensitive to vibrations, with their structure bearing resemblance to a composition of beams that are uniform in cross-section. These CNC machines are commonly used for different tasks, like engraving, cutting, and 3D printing. This work proposes a modeling methodology for vibration systems that consist of coupled thin beams subjected to vertical vibration. This methodology is used to model vertical vibrations in a CNC router machine. For this, the geometry is decomposed into beams of uniform cross-sections that are coupled at their ends. Each beam is modeled by means of the classical theory of Bernoulli–Euler for thin beams. The boundary conditions are determined by the beam couplings. In the system thus defined, fundamental frequencies are calculated using the bisection method, and then the modes are computed for the corresponding frequencies. The modal amplitudes, being time-dependent, are modeled as a state space system, considering the first m frequencies. In order to provide support to the modeling methodology, simulation experiments are performed for validation, comparing the results provided by models built with the proposed methodology against finite element models and an experimental setting with a real structure. Moreover, an analysis of the vibration model focusing on a specific component of the equipment is presented to illustrate the usefulness and flexibility of the models obtained with the proposed methodology.

Nonlinear combined harmonic resonances of composite cylindrical shells operating in hygro-thermo-electro-magneto-mechanical fields

By considering the effects of the hygro-thermo-electro-magnetic environments, von Karman nonlinear terms, and multi-harmonic excitations, a coupled nonlinear vibration modeling of composite cylindrical shells comprising a carbon nanotube-reinforced composite (CNTRC) core and two piezoelectric/magnetic composite (PEMC) skins is developed, and the nonlinear dynamic behaviors of such cylindrical shells under primary, super/sub-harmonic, and combined resonance states are investigated. In the theoretical modeling process, the effective mechanical properties of the CNTRC core are first determined using the mixing and Schapery laws, and the hygro-thermo-electro-magneto-mechanical constitutive relations of the PEMC skins are then formulated. Within the framework of Reissner-Mindlin shell theory, the Lagrangian of the system containing Green-Lagrange and von Karman nonlinear terms is derived, and solution techniques based on the multiscale method are provided to obtain nonlinear frequencies, dynamic responses, and phases of CNTRC-PEMC cylindrical shells under multi-physics fields. Consequently, comparison studies are conducted to validate the correctness of the proposed model from different aspects. Based on this, various resonance and chaos behaviors of such structures subjected to multiple load components are revealed and compared, and the influences of environmental factors and structure composition on the amplitude-frequency curves, time-history responses, and phase planes are explored, with several recommendations and findings being drawn.

A laterally sensitive quartz vibrating beam accelerometer for inertial navigation application

To improve the sensitivity and stability of a quartz vibrating beam accelerometer (QVBA), a laterally sensitive structure was developed that utilizes the force-frequency characteristics of a quartz double-ended tuning fork (DETF) to realize quasi-digital measurement of acceleration. Two DETFs were purposely designed for the sidewalls of the proof mass, and the hinge of the spring-mass structure was along the proof-mass thickness, which improved the sensitivity. Laterally sensitive structures can also solve the fabrication problems of hinges, including accuracy, deformation, and residual stress. A femtosecond laser was used to release the anchor between the out-of-frame and the proof mass to protect the hinge. The isolation structure was designed to float both the DETFs and hinge to reduce the interference of external stress. Electrodes were deposited on the four surfaces of the vibrating beam in a three-segment configuration to excite the DETF into the antiphase in-plane vibration model. As a result, an accelerometer prototype is fabricated, and the performance characterization results exhibit the sensitivity and stability of 188.61 Hz/g and 7.81 ppm, respectively, and the bias instability (Allan deviation) of 1.26 μg, which proves the design rationality of laterally sensitive QVBA.

Effect of Temperature on the OH-Stretching Bands of the Methanol Dimer.

We present a conceptually simple model for understanding the significant spectral changes that occur with the temperature in the infrared spectra of hydrogen-bound complexes. We have measured room-temperature spectra of the methanol dimer and two deuterated isotopologues in the OH(D)-stretching region. We correctly predict spectral changes observed in the gas phase for the bound OH stretch in the methanol dimer from jet-cooled to room temperature and corroborate this with experimental and theoretical results for deuterated isotopologues. The origin of the observed spectral features is explained based on a reduced-dimensional vibrational model, which includes the two high-frequency OH stretches, the two methyl torsions, and the six intermolecular low-frequency vibrations. Key to the success of the model is a new coordinate definition to describe the intrinsic large-amplitude curvilinear motion of low-frequency vibrations. Despite the deceivingly simple appearance of the room temperature bound OH-stretching fundamental band, it consists of ∼107 vibrational transitions.

Applying Bayesian optimization to predict parameters in a time-domain model for cross-flow vortex-induced vibrations

As the demand for harvesting offshore energy increases worldwide, the need for slender structures, such as marine risers and power cables, will increase. The dominating loads for deep water applications will primarily be caused by current-structure interactions, where vortex-induced vibrations (VIV) are known to be a challenging response type to handle correctly during design. Semi-empirical time-domain models are promising for VIV prediction, but uncertainties related to simplifications in the hydrodynamic load model and empirical parameters lead to over-conservative designs, where the parameters are estimated from model tests within a relatively low Reynolds number range. The aim of this paper is to present an efficient tool to estimate empirical hydrodynamic parameters directly from test data. To illustrate the method, the hydrodynamic parameters were estimated from pure cross-flow VIV model tests in a steady current with Reynolds numbers in the range of 40,000-120,000. The parameters were updated sequentially by using a Bayesian optimization framework, with the aim of minimizing an objective function that incorporates the response errors between time-domain VIV simulations and model test data. It is shown that three empirical parameters can be obtained simultaneously, resulting in small response errors but the optimal parameters were overly sensitive to variations in the flow velocity. The optimal parameters were used to reconstruct the drag amplification related to cross-flow VIV and in forced motion simulations to illustrate how the parameters in the load model would map into the traditional formulation in terms of the added mass and excitation coefficient.

Dynamic behaviors of delaminated nanofilms partly bonded on substrates with sub-nanoscale van der Waals dynamic boundaries

Abstract Dynamic buckling-induced delamination of nanofilms on substrates is a universal and essential phenomenon in nanoelectromechanical systems (NEMS). Van der Waals (vdWs) interactions play an important role in the dynamic buckling-induced delamination of nanofilms on substrates due to the interaction distances at nanoscale or even sub-nanoscale in NEMS. Therefore, it is interesting yet challenging to reveal the effect of intermolecular vdWs interactions on dynamic buckling-induced delamination of nanofilms on substrates. By considering sub-nanoscale dynamic boundary effects induced by intermolecular vdWs interactions, a parametric excitation nonlinear vibration model for dynamic buckling-induced delamination of nanofilms partly bonded on substrates is established. Effects of sub-nanoscale vdWs dynamic boundaries on transient and steady-state responses of dynamically delaminated nanofilms on substrates are analyzed. The sub-nanoscale vdWs dynamic boundaries lead the dynamic responses of delaminated-nanofilm/substrate systems very sensitive to initial conditions. The bending and shifting frequency response results demonstrated that the system nonlinearities can be greatly amplified by the sub-nanoscale vdWs dynamic boundary effect. Moreover, the spontaneous symmetry breaking and violent interfacial tearing/healing phenomena can be also triggered in the systems. Based on spontaneous symmetry breaking, a trans-scale relationship between nanofilm equilibrium positions and intermolecular vdWs interactions is established, which can provide a promising route for trans-scale measurements of molecular scale interfacial interactions. The work can also be helpful for the dynamic design of resonant NEMS devices based on nanofilm/substrate systems.

Characterization and modeling of the internal vibrations of a balanced armature receiver

The balanced armature receiver is a miniature loudspeaker used in hearing aids. When the receiver produces sound, it also exhibits structural vibrations that propagate as both sound and vibrations within the hearing aid structure. These are picked up by the microphones, resulting in feedback. For the first time, a multi-mass lumped element model, representing the mechanical vibrations of the balanced armature receiver, is presented in the literature. The model distinguishes the internal, moving components to capture how their movement propagates to the chassis structure. Component mass is assigned to model their movement, while their mechanical couplings are captured by spring-damper connections. The (ideally) static components (chassis etc.) are lumped into one mass, whose movement represents the structural vibrations that propagate to the hearing aid shell. The model captures the overall behavior of the mechanical system, which means that with physically sound parameter input, we can predict how parameter changes will impact the response. The thorough treatment of the interplay between the components provides a detailed model response that is completed by parameter properties determined through measurements and analytical methods. Validation against the measured electrical and mechanical response, shows that all main features including resonances are explained by the model.

Scalar Auxiliary Variable Techniques for Nonlinear Transverse String Vibration

The simulation of string vibration is of fundamental importance in musical acoustics. If the vibration amplitude is large then nonlinear phenomena, resulting from large deformations, cannot be neglected, and lead to perceptually salient features. Energy-conserving simulation algorithms found in the literature rely on tailored discretisation choices, making them model–specific. Recently, energy quadratisation–based techniques have been developed, under the assumption that the potential energy is single-signed. These methods allow for the solution of a variety of different nonlinear systems with the same time-stepping procedure, requiring only the evaluation of a specific nonlinear potential. Moreover, they possess an exact numerical energy conservation property, and permit efficient operation. Such methods were previously employed for solving nonlinear string models. In this paper, nonlinear models of transverse string vibration are first semi-discretised in space by means of both finite differences and modal methods. The resulting equations are solved through the use of the Scalar Auxiliary Variable (SAV) technique. Results are then compared against those obtained with model – specific numerical integrators in terms of Efficiency and accuracy.

Analysis on the dynamic characteristics of stick-slip vibration in deep well drill string system

In this paper, based on the non-linear mechanics theory of the drill pipe, a mechanical model of stick-slip vibration of the drill pipe has been established by considering the torsional properties of the drill pipe, kinetic energy and the motion law of the bit. The example calculations and sensitivity analysis of the parameters are carried out. The results show that increasing the rotational speed, viscous damping, length of the drill collar and de-creasing the weight of bit have the effect of suppressing the stick-slip vibration.

Asymptotic model of long-wave vibrations of an ultrathin strip-beam taking into account surface effects

The paper is concerned with the derivation of asymptotically consistent equations governing long-wave vibrations of an ultrathin elastic strip-beam taking into account surface effects within the framework of the Gurtin-Murdoch theory of the surface elasticity. Two dimensional equations of motion of an elastic isotropic medium are used as the initial ones. In the general case, the strip-beam is under the action of variable unsteady surface forces. The presence of residual shear stresses is assumed on the face surfaces. The ratio of the strip thickness to the characteristic length of bending deformation is considered as a small parameter. Within the framework of the Gurtin-Murdoch theory, two cases are considered, providing for the presence of large a) residual stresses on the faces, b) effects of surface inertia. Using the method of asymptotic integration over the transverse direction, relations for displacements and stresses in an ultra-thin strip-beam are obtained, and equivalent one dimensional the Timoshenko type equations taking into account surface effects are derived. As an example, free vibrations of a simply supported beam accounting for the surface effects are considered.

Radial sandwich radial-bending composite transducer designed based on acoustic black hole theory

A novel radial sandwich radial bending composite transducer is proposed based on the increasing amplitude of bending waves in the structure of an acoustic black hole (ABH). The transducer consists of a radial sandwich circular ring transducer and an outer acoustic black hole structure. The existence of the ABH structure realizes the conversion between radial vibration and bending vibration of the transducer, and improves the acoustic radiation performance of the transducer. Based on the one-dimensional acoustic black hole bending vibration theory, the bending vibration equation of the circular ABH structure is given. An analytical model of the ABH structure bending vibration is established by using the method of geometrical-acoustics, and the eigen frequency of its bending vibration is given. The relationship between the electromechanical conversion performance and the size of the transducer is discussed by using the finite element method, and the results show that when the eigen frequency of the bending vibration of the ABH structure is close to the resonant frequency of the transducer, the electromechanical coupling coefficient of the transducer reaches a maximum value. The radiation sound pressure field, radiation sound intensity, and radiation directionality of the transducer in the air are also analyzed by the finite element method. The results indicate that the presence of the ABH structure can improve the electromechanical conversion performance of the bending vibration of the transducer, enhance the acoustic radiation performance of the transducer, make the transducer exhibit radiation directionality and the lower order of the bending vibration mode of the ABH structure, the stronger radiation directionality of the transducer towards the left side and the right side. Finally, in order to verify the accuracy of the simulation and theory, we made a prototype transducer and carried out the experimental test of transducer electrical impedance and vibration mode. The measured results are in good agreement with the simulation results. The displacement distribution of the radiation surface of the transducer at resonance frequency is measured, which verifies the bending vibration mode of the ABH structure. This type of transducer is expected to be used as acoustic projector in the air or water.

Spectral analysis and kinetic modeling of radioluminescence in air and nitrogen.

In this article we present a quantitative analysis of the second positive system of molecular nitrogen and the first negative system of the molecular nitrogen cation excited in the presence of ionizing radiation. Optical emission spectra of atmospheric air and nitrogen surrounding 210Po sources were measured from 250 to 400 nm. Multi-Boltzmann and non-Boltzmann vibrational distribution spectral models were used to determine the vibrational temperature and vibrational distribution function of the emitting N2(C3Πu) and N2+(B2Σ+u) states. A zero-dimensional kinetic model, based on the electron energy distribution function (EEDF) and steady-state excitation and de-excitation of N2(X1Σ+g), N2+(B2Σ+u), N2+(X2Σ+g), N4+, O2+, and N2(C3Πu, v), was developed for the prediction of the relative spectral intensity of both the N2+(B2Σ+u → X2Σ+g) emission band and the vibrational bands of N2(C3Πu → B3Πg) for comparison with the experimental data.

Vibrational thermal pool multi-level theoretical model and design simulation of HBr-filled hollow-core fiber gas laser

The hollow-core fiber gas laser (HCFGL) has developed into a significant mid-infrared laser source, but the development of theoretical model still lags behind experimental progress. In this work, we propose a multi-level vibrational thermal pool (VTP) model of HBr-filled HCFs, which comprehensively considers the rovibrational relaxation effects on laser gain in reasonable approximations of transition coefficients, and studies the laser characteristics on multi-line lasing, bottleneck effect, line competition, etc. The VTP model shows more precise results of laser slope efficiency, and threshold than previous models while fitting the experimental data very well, and successfully predicts an output bottleneck at 1 W pump. The P-branch laser is relatively advantageous over the R-branch laser for its larger Einstein <inline-formula><tex-math id="M1">\begin{document}$A$\end{document}</tex-math><alternatives><graphic specific-use="online" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="15-20240428_M1.jpg"/><graphic specific-use="print" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="15-20240428_M1.png"/></alternatives></inline-formula> coefficient and emission cross section, and the seed injection can intensify the line competition and reach the highest P4 power proportion of 80%. The VTP model reveals that the output of various pump lines has a pattern similar to the Boltzmann distribution, suggesting that the distribution of ground rotational levels limits the laser gain of pump lines. Moreover, we discuss the photon leakage in high-energy pulsed pumping conditions. With the introduction of the leaking coefficient, this model shows relaxation oscillations and laser slope efficiencies close to experimental values and greater than the results in the CW condition, and solves the overpump problem in pulsed pump simulation. Finally, we confirm that the photon leakage is intensified at high repetition rate and the leaking coefficient should relate to the pulse repetition rate. This work develops a comprehensive modeling method for MIR laser simulation and this model is also applicable to various gas-filled HCFGLs.

CO2 ultrathin film growth on a monolayer of CO2 adsorbed on the NaCl(100) surface: sticking coefficient and IR-optical signatures in the ν3 region.

CO2 ultrathin molecular films were grown onto a preadsorbed monolayer NaCl(100)/p(2 × 1)-CO2 at 40 K. Polarization infrared spectroscopy (PIRS) reveals that so-prepared films have better quality than directly grown films. A sticking probability of 0.74 ± 0.1 was deduced from the integrated IR absorption. The presence of the monolayer doublet in the film spectra suggests a Stranski-Krastanov film growth with locally varying film thicknesses on the surface. In the region of the ν3(12C16O2) band, fine structure was observed between the well-known transverse-optical (TO) and longitudinal optical (LO) bands. Two independent computational models were applied to analyze the nature of the observed fine structure. Both pair potential calculations in combination with a vibrational exciton model as well as plane-wave density functional theory (DFT) in combination with phonon calculations of IR intensities at the Γ-point reveal that a weak mode visible in s-polarization and p-polarization originates from a vibrational film excitation located near the substrate interface. A series of p-polarized weak bands appearing and partly disappearing upon film-growth is assigned to film stacks of unique local thickness.

An estimation of mechanical stresses in the stator of the NB-514 motor of an electric locomotive

The aim of the research is to determine the causes of cracks in stators of traction electric motors of the NB-514 series. The application of mathematical modeling using the finite element method, which allows one to evaluate the mechanical stresses arising in the stator under the influence of thermal and vibration loads, is considered. The results of thermal modeling are presented for uneven heating of the electric motor frame to temperatures typical for the hourly operation of a traction motor. The results of vibration modeling, including the study of natural vibration modes and frequencies, are also presented. Based on the results of the studies, it was concluded that the cause of the formation of cracks in the area of ventilation hatches is a complex of cyclically repeating temperature and vibration effects, creating points of mechanical stress with a large value in the area of crack formation. Vulnerabilities in the design of the electric motor frame have been identified. Options have been proposed for improving the design of the ventilation hatches of the frame, allowing reducing mechanical stresses with a constant area of the ventilation and inspection hatches.

Robust Preview Control for Half‐Vehicle Active Suspension System of Hub‐Driven Electric Vehicles with Coupling Effects

The mechanical‐electrical‐magnetic coupling effects caused by the air gap deformation in in‐wheel motors exacerbate motor magnetic force oscillation, deteriorating the in‐wheel motor operation and ride comfort. In order to enhance vehicle performances, it is imperative to mitigate these coupling effects during the design of hub‐driven electric vehicle suspensions. In this paper, the analytical investigation is conducted on the coupling effects between electromagnetic excitation and transient dynamics in EVs based on the half‐vehicle model. The dynamic responses of hub‐driven EVs considering coupling effects are explored under both open‐loop and closed‐loop systems at various speeds and road conditions. Numerical simulations demonstrate that the closed‐loop system with wheelbase preview robust control exhibits superior comprehensive performance in suppressing coupling effects of the rear wheel hub motor and enhancing ride comfort compared to the system without preview control. Furthermore, as vehicle speed increases, robust preview control effectively reduces fluctuations in pitch angle acceleration, pitch angle, and rear wheel rotor eccentricity. In addition, robust preview control yields better performance in reducing vehicle body centroid acceleration and rear wheel rotor eccentricity and enhancing motor and vehicle performance with increasing road roughness. This work provides a practical vibration model and control reference for studying the dynamic characteristics of hub‐driven EVs.

Fast simulation of the Kirchhoff-Carrier string with an energy-storing boundary condition using a Scalar Auxiliary Variable approach

Various string vibration models exist; linear models are common in musical acoustics but lack accuracy for complex phenomena. Nonlinear terms are necessary for pitch glides and modal couplings at higher amplitudes. Realistic boundary conditions are vital, often overlooked for simplicity. This study proposes an efficient time-stepping routine for nonlinear strings with energy-storing boundaries, derived from the Scalar Auxiliary Variable method, allowing fast inversion using the Sherman-Morisson formula.

Model analysis of flow-induced vibration (LIV) in submarine oil and gas pipeline

Abstract In order to realistically simulate the flow-induced vibration of submarine oil and gas pipelines, this paper assembles a gas-liquid two-phase flow vibration device, develops a detailed and comprehensive experimental procedure, and sets the flow aperture, flow pressure, flow depth, flow direction, and gas-liquid phase apparent flow rate and other variables. According to the different types of pipelines, the multiphase flow-induced vibration of submarine oil and gas pipelines can be categorized into straight pipe vibration and elbow pipe vibration, and combined with the theoretical knowledge of fluid dynamics and the equations of motion to construct a multiphase flow-induced vibration model of submarine oil and gas pipelines and discuss the vibration mechanism of submarine oil and gas pipelines in two-phase liquid flow. Combined with the corresponding experimental parameters, the vibration phenomenon induced by gas-liquid two-phase flow in submarine oil and gas pipelines is experimentally analyzed. It is analyzed that the first-order intrinsic frequency of the submarine oil and gas pipeline is kept at 23.2 Hz when the value of the Reynolds number of the in-pipe flow ranges from 2.53 × 104 to 1.08 × 107. The first-order intrinsic frequency of the submarine oil and gas pipeline monotonically decreases with the increase of the Reynolds number of the in-pipe flow. In addition, when Ul=0.4m/s, the average standard deviation of the data is only 1.114m/s² with the rise of Ug, indicating that the vibration intensity of the fluid on the subsea oil and gas pipeline increases gradually with the increase of the apparent flow velocity of the liquid phase. By analyzing the multiphase flow problem of oil and gas pipelines, this study is of great significance in improving the efficiency of oil and gas transportation.

Vibronic structure of absorption spectrum of 2,5-di-(2-benzoxazolyl)phenol

Vibronic structure of the absorption spectrum of 2,5-di-(2-benzoxazolyl)phenol is calculated using the Franck-Condon approximation and harmonic model for vibrations. 2,5-di-(2-benzoxazolyl)phenol is an organic compound that exhibits excited-state intramolecular proton transfer. It is found that the use of normal modes and values of energy of the electronic states calculated with the B3LYP density functional provides good agreement with the experimental spectrum in terms of the position of intense bands. The largest intensity of vibronic transitions is found for deformation vibrations changing the distance between the oxygen and nitrogen atoms of the hydrogen bond, a deformation vibration of the phenol ring, stretching vibrations of the benzoxazole moieties.