Torsional Vibration Modes Research Articles

Contribution of Torsional Vibration Modes and the Influence on Period Ratios in the Seismic Response of Elastic Plate Bent Frame Structures

The structural characteristics of large-span structures inherently differ from those of conventional multistorey structures, making it challenging to accurately describe the contribution of various vibration modes to the overall response using traditional dynamic response analysis methods. Based on the response spectrum method, this paper investigates the influence of the first torsional mode on the overall effects of large-span structures. It proposes a new metric, called the torsional mode contribution factor, to characterize the contribution of torsional modes. Focusing primarily on single-span frames, the study explores the impact of factors such as eccentricity ratio, aspect ratio, and roof stiffness on the torsional mode contribution factor. Additionally, the relationship between the period ratio and the torsional mode contribution factor is examined to assess the necessity of controlling the period ratio. The findings reveal that the contribution of torsional modes to the overall seismic response varies significantly under different conditions, such as eccentricity ratio, aspect ratio, roof stiffness, and torsional stiffness. The torsional mode’s contribution is minimal for small eccentricity ratios, with the response primarily driven by translational modes. As eccentricity increases, translational-torsional coupling becomes more pronounced, amplifying the influence of torsional modes on the overall dynamic response. The study also highlights that increasing roof stiffness and aspect ratios can mitigate torsional effects to a certain extent. Still, excessive eccentricity ratios and stiffness may result in higher torsional contributions. Additionally, it is found that increasing torsional stiffness reduces the influence of torsional modes but does not eliminate the overall torsional deformation. The proposed torsional mode contribution factor offers an effective way to quantify these effects, demonstrating that traditional control methods, such as period ratio control, may not fully capture the torsional contributions.

Harmonic Vibration Analysis in a Simplified Model for Monitoring Transfemoral Implant Loosening.

A simplified axisymmetric model of a transfemoral osseointegration implant was used to investigate the influence of the contact condition at the bone-implant interface on the vibrational response. The experimental setup allowed the degree of implant tightness to be controlled using a circumferential compression device affixed to the bone. Diametrically placed sensors allowed torsional modes to be distinguished from flexural modes. The results showed that the structural resonant frequencies did not shift significantly with tightness levels. The first torsional mode of vibration was found to be particularly sensitive to interface loosening. Harmonics in the vibrational response became prominent when the amplitude of the applied torque increased beyond a critical level. The torque level at which the third harmonic begins to rise correlated with implant criticality, suggesting a potential strategy for early detection of implant loosening based on monitoring the amplitude of the third harmonic of the torsional mode.

Dynamic characteristics of bridges with short pylons and outwardly inclined cable planes

This study developed a cable-stayed bridge characterised by short pylons and outwardly inclined cable planes. The dynamic characteristics of this bridge were investigated using the Lanczos eigenvalue and finite element methods. The first ten mode shapes and frequencies were analysed to this end. The influences of key parameters, such as the inclination angle of the pylons and the height and stiffness of the cable–pylon anchorage, on the dynamic characteristics of the bridge were examined. The results showed that the transverse bending modes of the main girder occurred first, while modes related to pylons appeared later. The torsional vibrational modes appeared in the 10th order, indicating the bridge had suitable wind resistance. Further, the outwardly inclined cable planes enhanced the lateral seismic resistance of the bridge. Increasing the rigidities of the cable–pylon anchorage and main girder can improve the dynamic characteristics of the bridge. This is accomplished by reducing the height of the cable–pylon anchorage and adding auxiliary piers.

Fluid–acoustic–structure resonance mechanism of a plane cascade via a low-speed wind tunnel test

Acoustic resonance is an important factor that contributes to aeroengine compressor failure. In this study, a plane cascade of compressor blades was designed to reproduce acoustic resonance via a low-speed wind tunnel test. A high-frequency hot-wire, microphone and strain gauge were used to synchronously measure the fluid, acoustic and structural parameters. We analysed the variation in the amplitude and frequency of the multi-field parameters with increasing mean flow velocity and explored the multi-field interaction mechanism that induces the acoustic resonance of the plane cascade. The plane cascade effectively reproduced the acoustic resonance phenomenon. The first-order acoustic-mode frequency of the plane cascade flow duct, second-order torsional vibration mode frequency of the blade and shedding mode frequency of the tip clearance leakage vortex were equal under acoustic resonance. The fluid, acoustic and structural fields showed a strong interaction effect, achieving the maximum blade vibration amplitude and causing fatigue cracks of torsional vibration at the blade root. The frequency lock-in region of the compressor plane cascade was divided into an ‘acoustic–structure’ interaction region, a ‘fluid–acoustic–structure’ interaction region and a first-order acoustic-mode dominant region with increasing mean flow velocity, which demonstrates an interesting phenomenon in which the fluid–acoustic–structure modes compete: acoustic mode > blade vibration mode > vortex shedding mode. The results demonstrate a unique approach to the study of acoustic resonance that provides insight into the acoustic resonance mechanism in a cascade of compressor blades.

Dynamic properties of natural fiber-reinforced polymer composite plates and tubes

Thirty-six flax fibre-reinforced epoxy (FFRE) plates with two, three, and four fabric layers and lengths ranging from 160 mm to 270 mm and nine FFRE tubes with a diameter of 60 mm, a length of six times the tube diameter plus an overly of 50 mm with two, three, and four fabric layers were manufactured. One-hundred-eighty impulse excitation tests were conducted on FFRE plates to determine the dynamic properties of the plates in the bending mode, and 91 impulse excitation tests were conducted on the FFRE tubes to determine the dynamic properties of the tubes in the transverse, torsional, and longitudinal directions. FFRE plates showed up to six times larger specific energy capacities compared to counterpart glass fibre-reinforced polymer plates, showing significant potential for FFRE plates to replace the use of GFRP plates where considerable damping of energy is required. The results showed that the damping ratio of the FFRE plates decreased with the increase in layers and natural frequency. For the FFRE tubes, the highest damping ratio belonged to the transverse vibration mode, followed by the torsional or longitudinal vibration modes.

Measuring Vibrational Modes in Living Human Cells

The question of whether human living cells in physiological conditions exhibit mechanical resonances has remained unresolved for more than 70 years. We here construct a theoretical model to predict how these hypothetical vibration modes of a living cell can modify the stochastic response of a supporting micromechanical resonator. The key signatures that demonstrate the existence of these vibration modes are then searched for experimentally. To this aim, single human breast epithelial cells were attached to the surface of compliant small microcantilevers. Close examination of the frequency spectra of the thermal fluctuations of the microcantilever over a high-frequency range of 1 kHz–1 MHz revealed anomalies that are consistent with our theoretical predictions. We identify the stochastic coupling of the first and third vibration modes of the cell with the torsional and flexural vibration modes of the cantilever, respectively. These mechanical resonances are very broad and are located at 10–30 kHz and 150–180 kHz, respectively. The analysis of the experiments allows us to obtain information on the temporal evolution of several physical properties of the cell, in addition to the resonance frequencies, during the adhesion process—such as the mass, viscoelasticity, and contact area. These results open multiple avenues in our understanding of single cell mechanobiology, vibrational spectrometry of living cells and mechanical destruction of cancerous cells by targeting specific cell frequencies. Published by the American Physical Society 2024

Low-frequency (0-450 cm-1) dynamics of n-alkyl cyanide liquids studied by optical Kerr effect spectroscopy and density functional theory.

This article presents a study of the dynamics of n-alkyl cyanides (CnH2n+1CN with n = 1-5) in the 0-450 cm-1 spectral region as a function of alkyl chain length. The spectra were measured using femtosecond optical Kerr effect (OKE) spectroscopy. The OKE spectra are characterized by a broad band in the 0-150 cm-1 region arising mainly from intermolecular modes and by narrow bands in the 150-450 cm-1 region arising from intramolecular modes. The intramolecular bands in the OKE spectra are in good agreement with the bands in simulated spectra obtained from density functional theory calculations. For cyanide molecules with long alkyl chains (n = 3-5), a low frequency intramolecular band associated with a torsional vibrational mode overlaps with the intermolecular band. Applying multicomponent line-shape analysis to the broad low-frequency band allowed us to obtain the intermolecular component of the band. We find the frequency and amplitude of the intermolecular band decrease with increasing chain length. Based on previous theoretical studies of the OKE spectrum of methyl cyanide and OKE reorientational studies of n-alkyl cyanides, we show that the dependence of the frequency of the intermolecular band on alkyl chain length is consistent with the band being primarily due to the hindered rotational motion of the molecules in the extended configuration about an axis perpendicular to the long axis of the molecule. The dependence of the amplitude of the intermolecular band on alkyl chain length is a mass effect associated with suppression of the collision-induced contribution to the intermolecular band.

The Ambiguous Origin of Thermochromism in Molecular Crystals of Dichalcogenides: Chalcogen Bonds versus Dynamic Se─Se/Te─Te Bonds.

We report thermochromism in crystals of diphenyl diselenide (dpdSe) and diphenyl ditelluride (dpdTe), which is at variance with the commonly known mechanisms of thermochromism in molecular crystals. Variable temperature neutron diffraction studies indicated no conformational change, tautomerization or phase transition between 100 K and 295 K. High-pressure crystallography studies indicated no associated piezochromism in dpdSe and dpdTe crystals. The evolution of the crystal structures and their electronic band structure with pressure and temperature reveal the contributions of intramolecular and intermolecular factors towards the origin of thermochromism - especially the intermolecular Se⋅⋅⋅Se and Te⋅⋅⋅Te chalcogen bonds and torsional modes of vibrations around the dynamic Se─Se and Te─Te bonds. Further, a co-crystal of dpdSe with iodine (dpdSe-I2) and an alloy crystal of dpdSe and dpdTe implied a predominantly intramolecular origin of the observed thermochromism associated with vibronic coupling.

The Ambiguous Origin of Thermochromism in Molecular Crystals of Dichalcogenides: Chalcogen Bonds versus Dynamic Se−Se/Te−Te Bonds

AbstractWe report thermochromism in crystals of diphenyl diselenide (dpdSe) and diphenyl ditelluride (dpdTe), which is at variance with the commonly known mechanisms of thermochromism in molecular crystals. Variable temperature neutron diffraction studies indicated no conformational change, tautomerization or phase transition between 100 K and 295 K. High‐pressure crystallography studies indicated no associated piezochromism in dpdSe and dpdTe crystals. The evolution of the crystal structures and their electronic band structure with pressure and temperature reveal the contributions of intramolecular and intermolecular factors towards the origin of thermochromism—especially the intermolecular Se⋅⋅⋅Se and Te⋅⋅⋅Te chalcogen bonds and torsional modes of vibrations around the dynamic Se−Se and Te−Te bonds. Further, a co‐crystal of dpdSe with iodine (dpdSe‐I2) and an alloy crystal of dpdSe and dpdTe implied a predominantly intramolecular origin of the observed thermochromism associated with vibronic coupling.

Physics in deformable spacetime: Physical laws emerging from the surface minimality principle and the masses of particles

In this work, the study was focused on how deformable spacetime gives rise to physical laws, particularly quantum and special relativity. It was shown that both the Lorentz factor and quantum mechanics can emerge from the dynamical behavior of minimal surfaces in deformable spacetime, where the Möbius transformations prevail rather than the Lorentz transformations. The motion of deformable surfaces under minimality conditions creates a helicoidal pattern, a minimal surface with a metric designated by AdS (anti-de Sitter) space. Its isometry is a catenoid of which metric belongs to dS (de Sitter) space. When the two ends of the helicoid join it becomes a Möbius strip with multi-twists (i.e. windings), the so-called Möbius helicoid. It represents the most elementary mass with the attributes of charge and spin. It was shown that the number of windings increases with velocity according to the Lorentz factor. In other words, the Lorentz factor emerged from the transformation equations between the helicoid and catenoid, and both of them are isometric minimal surfaces. This fact serves as a means of transforming the metrics of the two isometric surfaces in AdS and dS spaces. There is an intimate relation between helicoidal motion, Möbius helicoid, and the Lorentz transformations. The zitterbewegung behavior of Dirac electron can be explained by the internal dynamics of the Möbius helicoid. Instead of using electromagnetic theory which led to the birth of special relativity, one can use the electrical circuit theory for deformable surface dynamics. A master equation was derived by using the resistive, capacitive, and inductive properties of deformable spacetime. The electromagnetic wave, Schrödinger, Klein–Gordon, Dirac, quantum telegrapher, and quantum torsion equations could be easily obtained from this master equation by making some simplifying assumptions for the parameters involved. The existing torsion due to helicoidal motion modifies the energy/mass equation (i.e.E=mc2) of special relativity. The Higgs potential can be obtained from the dynamic potential term of the master equation. Deformable space–time allows the emergence of a rich number of physical laws and relations. The masses of particles were calculated using the Möbius helicoid model for the very elementary structure of mass. The mass of a particle can be visualized as a three-dimensional network of helicoids with relatively higher stability. The stability is particularly associated with the phase changes of the catenoidal structure of the Möbius helicoid and the torsional vibrational modes of windings. Both the phase (or shape) change and/or the increase of the vibrational energies of windings produce a new configuration that represents a new particle. The masses of 187 particles were determined from this mechanism with an accuracy of ±3 MeV. It turned out that excitation energy states which could be expressed in terms of prime number multiples of a precursor mass play an important role in providing relatively higher stability.

Machine Learning Solution for Predicting Vibrations while Drilling the Curve Section.

The downhole vibration is one of the most crucial factors that affect downhole equipment performance and failure, besides wellbore instability. Downhole tool failure, hole problems, mechanical energy loss, and ineffective drilling performance are commonly associated with drillstring high vibration levels. The high vibration level will lead to more complications while drilling that might cause nonproductive time and extra cost. Meanwhile, the downhole sensors for detecting the drillstring vibrations add more cost to the operation. Consequently, the new solutions based on technology capabilities provide a powerful tool to integrate and interpret the drilling data for the best use of @@the data for operation performance enhancement. This study provides a successful application for utilizing the surface drilling data to automate drillstring vibration detection during the drilling curve section employing machine learning (ML) techniques. The axial, torsional, and lateral vibration modes are detected through testing four ML techniques named the @@adaptive neuro-fuzzy inference system (ANFIS), radial basis function (RBF), functional networks (FN), and support vector machines (SVMs) with real field data. The models' development was achieved by comprehensive study starting from data gathering, wrangling, statistical analysis, developing the ML models, evaluating the model prediction accuracy, and reporting the high accuracy results. The developed models were evaluated, and results showed that ANFIS and SVM models provided the highest accuracy with a coefficient of correlation (R) ranging from 0.9 to 0.99 followed by the RBF and FN models through model training and testing (R ranging from 0.82 to 0.96). Validating the models over unseen data confirmed the high accuracy prediction for the three vibration modes. Generally, the developed models provided technically accepted accuracy with R higher than 0.93 and AAPE less than 2.8% for SVM and ANFIS models while FN and RBF showed R between 0.82 and 0.95 and AAPE less than 5.7% between actual readings and predictions. Based on these results, the developed ML algorithm might be utilized as an intelligent solution to autodetect downhole vibration while drilling from surface sensor data only, which will save the downhole tool cost.

Longitudinal torsional vibrations of the chain drive system of mine scraper conveyor

To deeply analyse the dynamic characteristics of the scraper conveyor during operation, the mechanical characteristics of the coupled longitudinal and torsional vibrational modes under excitation by cargo loading are studied. Based on the Kelvin‒Voigt model and the point-by-point tension method, a model of the coupled longitudinal and torsional vibrations of the scraper chain drive system is established. Then the functional program is constructed and the numerical simulation is carried out. Finally, the correctness of the model is verified by comparison with experiments. The research results reveal the torsional vibration characteristics of the scraper chain drive system under two different working conditions, light load and medium load, and determine the influence area of the torsional vibration of the scraper. The results of this analysis provide a theoretical basis for the subsequent optimization of the scraper parameters, the prediction of scraper chain drive system failure, and the calculation to give an early warning before failure occurs.

Influence of torsional stick-slip vibration on whirl behavior in drill string system

Torsional and lateral vibrations, which are important causes of drill string failure, are harmful vibration modes that can occur during drilling. As its form of expression, stick-slip and whirl significantly limit the drilling efficiency and the bottom hole assembly (BHA) performance. Prediction of the correlation between these vibration modes has an important significance in adjusting basic parameters to avoid the effects of stick-slip and whirl vibration in the drilling process. In this work, in order to provide a general understanding of the vibration mechanism, a coupled torsional stick-slip and whirl model with 6 degrees of freedom (6-DOF) was proposed, and numerical simulations were conducted. The Lagrange method was used to derive the model, and the stabilizer-borehole wall interaction, drill collar-borehole wall interaction, and bit-rock interaction were additionally considered. Torsional vibrations were modeled with respect to the entire drill string system, while the lateral vibration was restricted to the BHA part. The results showed a correlation between torsional and lateral vibration modes when stick-slip vibration occurs and disappears. These correlations were performed by analyzing the time domain, frequency domain, and correlation coefficients. The relationship between torsional and lateral vibration modes was verified by performing a qualitative comparison with field experiments.

Impedance-frequency characteristic analysis of bypass damping filter in suppressing AC–DC system’s subsynchronous resonance

Recently, subsynchronous resonance (SSR) in HVDC transmission is considered to be related to electronic converter equipment and complex control systems. Aiming at the subsynchronous resonance problem caused by frequent topology changes of AC–DC systems, this paper firstly proposes an impedance-frequency characteristic analysis method based on Thevenin Equivalent and Fast Fourier Transform (FFT) algorithm. This method is used to analyze the impedance frequency characteristics of AC–DC systems after the bypass damping filter (BDF) is configured. Firstly, based on the IEEE first benchmark model, the mechanism of BDF in suppressing subsynchronous resonance is explained by quantitative analysis, and the BDF parameter setting method is proposed. Then, the time domain simulation model of a single-machine HVDC system with BDF is established in PSCAD/EMTDC. Finally, according to Thevenin’s theorem, the equivalent structure of each subsystem is simplified, and the FFT algorithm is used to solve the harmonic equivalent impedance of each subsystem. After BDF is configured, the mechanical resonance frequency ”transfers” from 16Hz to 10Hz, and the minimum electrical damping changes from -0.9637 to -0.4581. The results show that the BDF configuration can change the impedance-frequency characteristics of the system, thereby improving the electrical damping in the torsional vibration mode in a targeted manner, and has a certain effect on suppressing the subsynchronous resonance of AC–DC systems.

Transfer of Energy from Flexural to Torsional Modes for the Fish-Bone Suspension Bridge Model

We consider a conservative coupled oscillators system which arises as a simplified model of the interaction of flexural and torsional modes of vibration along the deck of the so-called fish-bone (Berchio and Gazzola in Nonlinear Anal 121:54–72, 2015) model of suspension bridges. The elastic response of the cables is supposed to be asymptotically linear under traction, and asymptotically constant when compressed (a generalization of the slackening regime). We show that for vibrations of sufficiently large amplitude, transfer of energy from flexural modes to torsional modes may occur provided a certain condition on the parameters is satisfied. The main result is a non-trivial extension of a theorem in Marchionna and Panizzi (Nonlinear Anal 140:12–28, 2016) to the case when the frequencies of the normal modes are no more supposed to be the same. Several numerical computations of instability diagrams for various slackening models respecting our assumptions are presented.

Integral resonant control preserving the rigid body mode of torsional vibration systems*

Integral resonant control (IRC) is an effective vibration control technique for flexible structures including multiple vibration modes, even though the controller is a simple first-order system. However, IRC can not be directly applied to flexible structures with rigid body modes. This paper proposes a new method to apply IRC by choosing an angle difference output in which the rigid body modes are unobservable but only elastic modes observable. The proposed method is effective for applying IRC to torsional vibration systems where the control objective is to reduce only torsional vibration modes while leaving the rigid body mode preserved. However, side effects such as an inverse response and a brake effect occur depending on the choice of the controller parameter. This paper clarifies the condition for the inverse response and the magnitude of the brake effect on the rigid body motion analytically. A new design method for the IRC controller is then presented based on the trade-off between the brake effect and the vibration suppression performance.

Analysis of Inherent Characteristics of Two‐Speed Planetary Gear Transmission System

In the helicopter transmission system, because the two‐speed gear planetary transmission system without power interruption adopts the design of a double planetary gear system, the complexity of the structure leads to the time‐varying meshing stiffness, tooth surface friction and the interaction between components and other nonlinear factors are uncontrollable, and causes the helicopter transmission system vibration noise, unstable operation, and other problems. To solve the above problems, the inherent characteristics of the two‐speed planetary gear transmission system without power interruption were studied and analyzed to find out the influence law of its inherent characteristics. The inherent characteristics of a planetary gear drive system are mainly related to the integrated stiffness such as component mass, support stiffness, and meshing stiffness in the system. Based on the centralized mass method, the translation‐torsional coupling dynamics model of the double planetary gear drive system was established. According to the displacement coordination relationship between the components of the system, the dynamics equation of the double planetary gear drive system was constructed. The mass matrix and stiffness matrix were obtained using MATLAB, and the system’s natural frequency was obtained by solving the dynamics equation. The results show that the low‐order natural frequency is mainly the torsional vibration mode of the center component and the torsional vibration mode of the center component. The influence of the mass of the component on the natural frequency is more complex and has a certain influence on both the high‐ and low‐order natural frequency. The support stiffness in the system mainly affects the low‐order natural frequency and the meshing stiffness in the system mainly affects the high‐order natural frequency.

Wheel Vibration Analysis for Indirect Tyre Pressure Monitoring Systems

It is evident that tyre pressure has an important impact on driving safety, fuel consumption and driving dynamics. Both direct and indirect tyre pressure monitoring systems have evolved recently, but the direct systems are far more expensive. The most advanced version of the indirect system is based on the eigenfrequency analysis of the angular velocity of the wheels, therefore the understanding of the tyre vibration is an important issue. In this paper we develop a simulation methodology to study the pressure-dependent tyre vibration behaviour. The aim is to better understand the tyre-rim-axle vibration system, with particular emphasis on the torsional vibration modes of the wheel. The focus is on the pressure-dependent correlation between the natural frequency and amplitude of the wheel vibration and the angular velocity and the longitudinal acceleration of the rim. Thus, we describe the oscillatory behaviour relevant for indirect tyre pressure monitoring systems on a theoretical level.

Nonlinear ensemble gray and black-box system identification of friction induced vibrations in slender rotating structures

Due to the nonlinear bit-rock and drill–string–borehole interactions, the modeling and analysis of drill string dynamics are a challenging work. These slender structures are subjected to torsional, lateral, and axial vibration modes, which are generally prejudicial to the drilling process. For this reason, proper modeling of the system dynamics is necessary to optimize drilling performance. In the present paper, we focus on the torsional dynamics and model of an experimental system subjected to friction torque. An ensemble approach, combining gray and black-box modeling techniques, is used to calibrate some of the dynamical system parameters, particularly those related to friction. This combination is chosen with the aim of improving the prediction accuracy of a pure gray-box approach while retaining interpretability in the dynamic responses. The present paper compares four well-known friction models with increasing levels of complexity using experimental data. It is shown that the ensemble model proposed can improve the gray-box by up to 92.68% in terms of prediction errors, by adding a non-physical layer to it. The present analysis demonstrates that better results can be obtained by using an ensemble of gray and black-box identification techniques for friction modeling and simulation, aiming at improving data-driven model construction of complex torsional dynamics in slender structures.

Effect of ribs on vibration characteristics of cantilever plate

Analytical solution for the vibration response results of the ribbed rectangular cantilever plate using the Kirchhoff plate theory is presented in this paper. The validity of the analytical solution is verified by comparison with the results of finite element analysis. The analytical model is then used to study the effect of the single rib, periodic ribs and orthogonal ribs on the modal vibration of the cantilever plate. According to the minimum inertia axis and torsion center line of the cantilever plate, the modal vibration shapes generated by the cantilever plate are divided into flexural and torsional vibration mode. The effect of the insertion of single rib on the modal vibration of the cantilever plate and the curvature of the insertion position are analyzed. It can be found that the effect of single rib on modal vibration of cantilever plate depends on the vibration mode and the location of the rib insertion, where a rib can be used as a mass loading, a stiffness attachment, or a combination of both. And the effect of periodic ribs on the vibration characteristics of the cantilever plate is further investigated. When periodically ribbed, the effect of the periodic ribs on the modal vibration of the cantilever plate depends on the dominant of the total of the mass loading or the stiffness enhancement played by each of these ribs. However, when another rib is added to the torsion center line of the periodic ribbed cantilever plate, it shows stiffness enhancement in both flexural and torsional vibration.