Vibration Model Research Articles

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.

Vibration-polynomial-based optimal trajectory planning for mobile concrete pumping equipment with state constraints

To improve the operating stabilities of the flexible hydraulic manipulator in concrete pumping equipment, a trajectory planning method based on optimal vibration energy is presented. First, predefined trajectories are generated by the quintic polynomial method, and kinematic inversions are established by unifying the velocity and angle constraints into the velocity level. Then, relationships between the boom vibration and the vibration energy are solved in modal space. Specifically, hydraulic actuators are regarded as spring-damping systems to calculate generalized forces into the vibration equation. The vibration equation can solve the modal coordinate and vibration model function, such that the elastic potential energy to cause vibration is completely described. Next, floating values are captured by a genetic algorithm to minimize vibration energy, and then introduced to the predefined trajectory to weaken the boom vibration. Last, the proposed trajectory planning method is verified by a concrete pumping spreader with a 13 m hydraulic manipulator.

Research on the tension of steel cord conveyor belts based on transverse vibration modelling

The accurate non-contact tension measurement of steel cord conveyor belt, an important load bearing medium, is critical for long distance belt conveyors. It is necessary to establish the relationship between the conveyor belt transverse vibration and the tension, in order to analyse the conveyor belt tension changes through indirect measurement of transverse vibration. The paper analyses the existing models of transverse vibration in conveyor belts, and finds that these models can hardly directly and accurately calculate the tension of the conveyor belt. Therefore, modifications are needed. Firstly, the paper establishes a dynamic model of the belt conveyor and conducts simulation analysis using RecurDyn software. This allows the authors to obtain the belt tension and transverse vibration displacement of the conveyor belt. Fast Fourier transform is employed to determine the vibration frequency, which is used to evaluate the vibration characteristics of conveyor belts under different operating conditions. Then, the paper conducts simulation analysis on the frequency and tension of the belt conveyor with different idler spacing, and performs nonlinear least squares calculation in MATLAB software to modify the coefficients of the transverse vibration model. This process involves nonlinear fitting, resulting in an improved transverse vibration model. Finally, the modified transverse vibration model is compared with the original model. The modified transverse vibration model can more accurately calculate the tension of the conveyor belt based on its vibration frequency. The validity of the modified model is verified by different types of conveyor belts.

A Convolutional Neural Network Based on Attention Mechanism for Designing Vibration Similarity Models of Converter Transformers

A vibration scale training model for converter transformers is proposed by combining attention modules with convolutional neural networks to solve the nonlinear problem of converter transformers in similar processes. Firstly, according to the structure and operating parameters of the converter transformer, a reliable three-dimensional multi-field coupled finite element model was established considering the influence of the winding and iron core component structure on the overall vibration characteristics. By changing different input parameters such as the size and voltage of the finite element model, corresponding output parameters are obtained, and a dataset is established through data expansion for training and verifying the attention convolution model. By analyzing the prediction processes and results of five prediction models on different operating conditions datasets, it is shown that attention convolution has higher accuracy, faster convergence speed, more stable training process, and better generalization performance in the prediction process of converter transformer recognition. Based on the predictive model, a prototype of the proportional vibration model for the converter transformer with scale factor of 0.2 was designed and manufactured. By analyzing the basic experimental items and vibration characteristics of the prototype, the stability of the prototype and the reliability of the prediction model were verified.

Modeling of absorption spectrum of 2,5-bis(2-benzoxazolyl)hydroquinone

Vibronic structure of the absorption band of 2,5-bis(2-benzoxazolyl)hydroquinone is calculated for the transitions to the first excited state using the Franck-Condon approximation and harmonic model for vibrations. 2,5-bis(2-benzoxazolyl)hydroquinone is an organic compound that undergoes the 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 ωB97X-D3 density functional provides good agreement with the experimental spectrum, overestimating energy of the 0-0 transition by 0.13 eV. The largest intensity of vibronic transitions is demonstrated by deformation vibrations changing the distance between the oxygen and nitrogen atoms of the hydrogen bonds, a deformation vibration of the oxazole rings, deformation and stretching vibrations of the hydroquinone moiety.

Vibrational model for thermal conductivity of Lennard-Jones fluids: Applicability domain and accuracy level.

Exact mechanisms of thermal conductivity in liquids are not well understood, despite a rich research history. A vibrational model of energy transfer in dense simple liquids with soft pairwise interactions seems adequate to partially fill this gap. The purpose of the present paper is to define its applicability domain and to demonstrate how well it works within the identified applicability domain in the important case of the Lennard-Jones model system. The existing results from molecular dynamics simulations are used for this purpose. Additionally, we show that a freezing density scaling approach represents a very powerful tool to estimate the thermal conductivity coefficient across essentially the entire gas-liquid region of the phase diagram, including metastable regions. A simple practical expression serving this purpose is proposed.

Vibration diagnostics of machine friction units: analysis of the current state and prospects

Vibration diagnostics makes it possible to detect defects in the friction parts of the machine at the early stages of their development, which provides for the repair or replacement of parts before they fail. In this work, an analysis of modern research on the use of vibration diagnostics in tribology is carried out, which includes aspects: vibration diagnostics in technology and tribology; vibration during friction and wear; vibration assessment methods; theoretical approaches in the analysis and modeling of vibrations. It is noted that an important aspect is the development and implementation of theoretical approaches in the analysis and modeling of vibrations, which allows a deeper understanding of the dynamics of friction and wear. This approach makes it possible to develop accurate and adaptive strategies for maintenance and optimization of tribotechnical parameters. It is shown that vibration diagnostics is not only a tool for detecting malfunctions, but also a key element for ensuring the long-term and efficient functioning of friction units of machines. The effective use of vibration diagnostics can significantly reduce maintenance costs, increase the reliability and productivity of equipment, which becomes an indispensable condition for the effective functioning of modern technical systems.

FINITE ELEMENT MODELLING AND ANALYSIS OF FREE VIBRATIONS OF AXIALLY FUNCTIONALY GRADED BEAMS WITH NON-UNIFORM CROSS-SECTIONS

The finite element package Abaqus is used for modeling and analysis of free vibrations of axially functional graded beams with non-uniform cross-sections. Considerable attention has been paid to this aspect of the geometry, as it has a significant effect on the behavior of the beam as a structural component. User-defined material model subroutines (UMAT) were developed in a unified way for one- and three-dimensional models of the specified beams to provide numerical implementation of functional material gradients within each finite element. UMAT procedures were programmed in FORTRAN in the MS Visual Studio environment and compiled with the main program package using the Intel Fortran Compiler. In the procedures, material heterogeneity was assigned to each material integration point of appropriate standard one- and three-dimensional finite elements, eliminating the need to design graded finite elements via user-defined element subroutine. Frequencies and mode shapes of free vibrations of one- and three-dimensional axially functional graded beams with non-uniform cross-sections were found using the Lanczos method in Abaqus. An analysis of the accuracy and effectiveness of the proposed modeling approach was carried out, comparing the obtained results with data known in the literature. The presented modeling technique based on user-defined material subroutines provides valuable opportunities for scientists and engineers engaged in the dynamic analysis of structural components made of functionally gradient materials and having variable geometry along the axial direction. Keywords: axially functionally graded beams; non-uniform cross-section beams; free vibrations; graded finite element; Abaqus user defined subroutines

An exact model for free vibration of structures coupled by arbitrarily shaped plates

An exact model for free vibration of structures coupled by arbitrarily shaped plates