Frequency Of Transverse Vibration Research Articles

Research on Highly Reliable Self-Powered Vibration Sensors for Geological Drilling

Vibration signals at the bottom of the drill string during geological drilling are crucial for lithological identification and drilling parameter optimization. However, existing downhole vibration sensors suffer from limitations in power supply and reliability. This study proposes a self-powered vibration sensor with high redundancy based on the triboelectric nanogenerator principle, which is capable of measuring both axial and transverse vibrations, thereby reducing the dependence on external power sources. The experimental results show that the sensor can measure axial vibration frequencies ranging from 0 to 11 Hz with an error of less than 4% and transverse vibration frequencies ranging from 0 to 5 Hz with an error of less than 5%. It can operate stably in temperatures from 0 to 180 °C and relative humidities from 0 to 95%. The sensor’s axial vibration measurement features six identical measurement structures, providing high redundancy and effectively enhancing its reliability. Furthermore, the sensor exhibits power generation capabilities. When an external load of 1 MΩ is applied to the axial measurement module and 10 MΩ to the transverse measurement module, the sensor achieves its maximum power output for both axial and transverse measurements, reaching 32.4 × 10−9 W and 2.1 × 10−9 W, respectively. Compared to traditional bottom-of-the-hole vibration sensors, this sensor possesses self-powering capabilities and high reliability, which can improve the operational efficiency and hold significant practical value for future applications.

Kink effect on the lattice properties of one-dimensional carbyne nanocrystals under high temperature

Carbyne nanocrystal (CN), as a kind of one-dimensional (1D) sp-hybridized carbon allotrope, has attracted much attention due to its excellent optical and transport properties. However, the lattice properties of 1D CNs under high temperature remain unclear. In our work, we investigate the stability and lattice properties of 1DCNs based on the atomic-bond-relaxation (ABR) approach and first-principles calculations. We find the change of transverse vibration frequencies and bond kinks induced by the thermal effect plays a significant role in the mechanical properties of 1D CNs. We establish a relationship between kink angle and phonon vibration modes, giving a deep inside into high frequency and low-frequency vibration behavior of 1D CNs. Our results indicate the phonon vibration modes modulated by kinks under applied temperatures can lead to a negative thermal expansion behavior in the axial direction of 1D CNs, suggesting an effective way to control the thermal properties of 1D CNs for practical applications.

Текстура рекристалізації та анізотропії пружних властивостей листів сталі DC04

We studied steel sheets DC04 (0.06% C, up to 0.35% Mn, up to 0.40% Si, ~ 0.025% S and P) with a thickness of 0.95 mm as delivered. Sheets of A4 size were annealed in a laboratory oven (6000C in an argon atmosphere, hold for 1 hour). The structure of DC04 steel sheets after recrystallization annealing was studied. The microstructure of the steel sheets under study is presented from the side of the rolling plane and in the section of the sheet perpendicular to the direction. In the plane of the sheets, the grains are elongated; in the cross section, the grains are approximately equiaxed. Pole figures (PF) were constructed based on the results of electron backscatter diffraction (EBSD) on a LEO 1455 VP electron microscope at an accelerating voltage of 20 kV from the plane of the sheets and from the section of the sheet perpendicular to the rolling direction. To improve statistics, PF were constructed by averaging reflex stereographic projections from 20 different representative volumes of material relative to the rolling direction and transverse direction. The texture and anisotropy of Young's modulus in the plane and cross section of steel sheets DC04 after recrystallization annealing was studied using EBSD method. A connection has been obtained between ideal orientations that describe the texture in two mutually perpendicular planes and the corresponding integral characteristics of texture (ICT). Rectangular samples with a length of 100 and a width of 10 mm at different angles to the rolling direction every 150 to measure Young's modulus. Samples were processed in a bag to ensure uniform dimensions. Young's modulus was determined by the dynamic method from the frequency of natural transverse vibrations. Three batches of samples were used to construct Young's modulus anisotropy curves. The anisotropy of the Young's modulus in the plane of steel sheets, calculated from the ICT based on the results of EBSD data, is in good agreement with the results of direct measurements. The value of Young's modulus in the direction normal to the plane of the sheet and in the section plane in the direction normal to the plane of the sheet, calculated from the ICT and the values of the compliance constants of iron, coincide. Keywords: texture, pole figure, anisotropy, integral characteristics of texture, Young's modulus.

Structural comparison of conventional and chiral auxetic morphed aircraft rib

Abstract Tri-chiral structures are auxetic structures that show negative Poisson’s ratio. This effect is due to their microstructure and geometric sequence. They are used in the development of novel products as they show improved damping and energy absorption properties. While traditional manufacturing methods remain dysfunctional, the development of additive manufacturing technology provides opportunities for new studies in various industries such as aviation, textile, and automotive. In this study, passive airfoil morphing application was applied and a comparative study was carried out. A two-stage study was conducted. First, the tri-chiral pattern was fabricated by an FDM 3D printer with PLA+ and subjected to the in-plane compression test. Stress–strain curves of the tri-chiral structure were generated. Then, it was used in airfoil morphing applications. Morphed airfoil was also manufactured and a compression test was applied. Secondly, the aerostatic loads of the aircraft were calculated. Both conventional and chiral morphed ribs’ behaviors under flight loads were examined using the FEM and results were compared. The weight difference was calculated. In addition, eigenfrequency and eigenvectors of traditional and chiral ribs were computed and transverse vibration frequencies were expressed. Despite being more than 50 % lighter, chiral morphed rib was found to be stiffer than conventional rib.

Modeling the deadwood bearings wear surface by optical scanning

The development of a methodology for modeling the wear surface of deadwood bearings based on optical scanning is considered in the paper. It is noted that the deadwood bearings of the ship’s shaft line wear out unevenly during operation, which affects the stress-strain state of the shaft and the system parameters responsible for the occurrence of resonance of transverse, torsional and longitudinal vibrations. The methodology and results of an experimental study of bearing wear surfaces are presented. The applied optical scanning scheme makes it possible to obtain high-precision digital models of objects due to synchronous shooting of an object with two cameras. The measurement results are obtained by processing with specialized software. The results obtained are an addition to the methodology for determining the elastic force acting on the shaft from the side of a bearing that is unevenly worn along the length with a non-constant gap. Based on the obtained wear values, a solid-state model is constructed and the natural frequencies of transverse, torsional and longitudinal vibrations are determined. For the constructed model, the forms of natural oscillations for practically significant frequencies are obtained. It is noted that bearing wear affects not only the displacement of the natural frequencies values, but also the oscillations shape. The impact of the wear of the aft bearing on the bearing capacity of the shaft line, taking into account the contact interaction, is evaluated. The simulation has shown that the bearing wear surface forms an area of increased contact pressures that arise from the impact of the propeller shaft. Analysis of the propeller shaft tip has revealed the presence of an area of increased concentration of equivalent stresses formed at the place of bearing wear formation. The proposed method of modeling the deadwood bearings wear allows us to evaluate its effect on the magnitude of the displacement of natural frequencies and the change in the bearing capacity of the shaft line. The results obtained in this work are an addition to the existing calculations in the design and evaluation of the ship’s power plant reliability.

Strategies for constructing mathematical models of nonlinear systems based on multiple linear regression models

Abstract Mathematical systems often have nonlinear, time-varying, time-lagged, and uncertain factors, which affect the experimental prediction accuracy. In order to improve the experimental prediction accuracy, this paper inputs the independent and dependent variable data sets as the original samples into a multiple linear regression function performs fitting calculations to obtain the nonlinear factors, and constructs a mathematical model of nonlinear systems based on a multiple linear regression model. In this model, the expected output value is calculated, and the input vector and output vector are continuously controlled for rolling operations to obtain the prediction results. A mathematical experiment of nonlinear system dynamics of vibration of deep water trap-test pipe system is set up to test the prediction ability of the model. The results show that the nonlinear system mathematical model based on the multiple linear regression model has a very high prediction accuracy. In the mathematical experiments of vibration nonlinear system dynamics of deep water trap-test pipe system, the error of the nonlinear system mathematical model based on multiple linear regression model in the transverse flow vibration frequency of the trap pipe column is 2%, which is lower than the single trap pipe calculation model by 4%. The prediction accuracy of the nonlinear system mathematical model based on the multiple linear regression model is higher than that of the single test tube model calculation by 78%. This shows that the nonlinear system mathematical model based on the multiple linear regression model can improve the experimental prediction accuracy.

Уточнение результатов численных расчетов частот поперечных колебаний стержня переменного сечения с упругим закреплением экстраполяционным методом

Thearticle describes a numerical experiment with the results of calculating the natural frequencies of transverse vibrations of a rod of variable cross-section with elastic fixation at one of the ends. The possibility of refining by extrapolation the calculated values of natural frequencies obtained by the method of algebraic polynomials of the fifth degree is analyzed. It is shown that ex-trapolation made it possible to increase the accuracy of calculations by the numerical method by 2-3 orders of magnitude

Machine vision-based transverse vibration measurement of diamond wire

Diamond wire sawing is one of the key technologies for wafering in the semiconductor industry. The transverse vibration of the wire during sawing will generate additional displacement that not only reduces the as-cut wafer quality but increases the critical adhesion gap between the wires, which is an important factor limiting the development of diamond wire slicing technology toward narrower kerf loss and thinner as-cut wafer. The vibration measurement of the diamond wire provides an indispensable test basis for its vibration control. Therefore, a machine vision-based transverse vibration measurement method of diamond wire is developed in this paper. The approximate edge position of the wire in the image midline is obtained to crop the region of interest in the image by using the maximum continuous same-directional pixel gradient algorithm and thus reduce the computing time. The wire edges in the image are accurately extracted by an adaptive image segmentation method proposed based on the image histogram. According to the surface topography characteristics of diamond wire, a feature extraction algorithm based on the multiple inward line fitting using the least square method is proposed, which can effectively detect the position of the inner diameter boundary of the diamond wire. Accordingly, the equation of the central axis of the wire in the image is obtained to realize the transverse vibration detection of the diamond wire. To conclude, a diamond wire vibration measurement experiment is conducted and the machine vision detection results are compared with the vibration displacement measured by the accelerometer at the same position of the wire end. The results show that the measurement error of the machine vision vibration inspection is generally small for the different types of diamond wires and the different frequencies of the wire transverse vibration, which means that the measurement method proposed in this paper has good accuracy, and applicability, and robustness.

Measurement of axial motion yarn tension based on transverse vibration frequency

In the process of textile production, the detection of yarn tension is very important to ensure product quality. In order to detect yarn tension efficiently and conveniently, a non-contact detection method based on transverse frequency was established. Firstly, the governing equation of yarn motion was derived by using the Hamilton principle and solved by the Galerkin truncation method. Then, the natural frequencies of yarns with different linear density were calculated according to the yarn characteristic equation. Finally, the fitting formulas of tension, speed, and frequency of yarn axial motion were derived. By measuring the natural frequency of yarn, the yarn tension could be calculated conveniently and quickly. A high-speed camera was used to measure the transverse vibration displacement of yarn and detect the free vibration frequency of yarn. Through experiments, the results of tension sensor and yarn tension detection based on vibration frequency were compared, and the results show that the error was within 5%, which verifies the effectiveness and accuracy of this method.

Metastructure with integrated internal oscillators of constant, linearly and nonlinearly varying natural frequency

This research focuses on the analysis of the model and performance of lightweight metastructures encompassing a distributed array of internal homogenous oscillators, integrated into the host structure to create a single-piece element. This metastructure performs longitudinal vibrations, whose axis is colinear with the direction of the transverse vibration of the internal oscillators. First, the mechanical models of the separate elements of the metastructure and the metastructure as a whole are created and considered. The first modal frequencies of longitudinal vibrations of the metastructure with blocked and free internal oscillators are tuned to the first modal frequency of transverse vibration of one internal oscillator, yielding the optimal number of internal oscillators for this to be achieved, which is a new result for the proposed design. This theoretical result is then checked experimentally with the metastructures produced by 3D printing technology, comprising a different number of internal oscillators, all of which have the same natural frequency. Besides validating the theoretical results, experimental investigations with blocked and freely vibrating internal oscillators of the constant natural frequency are used to explore other performance characteristics, such as the width of the regions where the reduced amplitude is achieved. Finally, based on the theoretical and additional numerical results, the internal oscillators are modified in two ways, which is an original approach: their natural frequency is increased linearly and nonlinearly along the metastructure in accordance with the previous new theoretical results. The benefits of such new redesigns for the multi-modal performance characteristics of the metastructure are discussed.

Simulation Analysis of Vibration Characteristics of the Submerged-propeller Shaft Coupling System

The vibration characteristics of the submerged-propeller shaft coupling system are studied in this paper. Firstly, Based on the fluid structure interaction theory on acoustics wave equation, the vibration analysis model of the propeller-shaft system under water is established and computed. And the vibration characteristics of coupling system is analysed by comparing the shaft system and the submerged-propeller system. The results show that the natural vibration of the coupling system presents complicated propeller-shaft strong or weak coupling characteristics. Comparing the natural vibration and frequencies of the shaft system and the submerged-propeller system, all of the coupling system modes are corresponding to the shaft system or the submerged-propeller system in low frequency range. And there is strong transverse coupled vibration of coupling system near the propeller’s 1st-order transverse vibration frequency, which appears as propeller’s 1st-order transverse vibration coupling shaft’s 2nd-order transverse vibration. That indicates the strong transverse coupled natural vibration of the coupling system is easy to be excited near the low order natural frequency of propeller. Which may cause propeller’s transverse excitation force to be easily transmitted to the hull through the bearings under non-uniform flow, resulting in the severe vibration of the hull stern.

Urban bridges studies on dynamic impacts from urban rolling stock

The article is dedicated to the actual dynamic impact study of rolling stock on urban bridges. The requirements for recording the dynamic impact specified in domestic and foreign regulatory documents are considered. Using a mobile measuring complex, the results of which determine the natural frequencies of vertical, horizontal transverse, and horizontal longitudinal vibrations. The technique used in the experiment allows us to obtain initial data for the dynamic calculation of structures, to clarify the real rolling stock dynamics depending on the state of the rail track on the bridge. Urban rolling stock is a relevant and necessary type of public transport that meets modern city requirements. The bridge crossings construction will ensure the connection of the urban areas separated by obstacles into a single network. When designing such structures, it is important to take into account the effects of actual dynamic coercitive forces. The dynamics study allows, on the one hand, to reasonably set the dynamic loads impact on bridges, on the other hand, to diagnose the structures state by dynamic parameters. In this work, using a specialized mobile measuring complex, the authors measured the oscillation parameters on moving vehicles. As a conducted experimental studies result, a methodology for determining the dynamic characteristics of a moving load and directly urban bridges has been demonstrated. As a result of the conducted experimental studies, it can be concluded that the proposed method allows obtaining initial data for the dynamic analysis of structures for the transport load. In addition, fixing the transport load dynamic impact during operation allows you to clarify the real rolling stock dynamics, depending on the state of the rail track on the bridge.

A comprehensive investigation of vortex-induced vibrations and flow-induced rotation of an elliptic cylinder

This work finds its motivation in heat exchanger design and flow control. Flow-induced vibration is studied numerically for combined vortex-induced vibrations and vortex-induced rotations of a horizontally positioned elliptic cylinder. The aspect ratio is taken as 2, and the value of reduced velocities (Ured) considered for the present simulation is between 2 and 12. The body can have to and fro motions in a transverse (y) direction, in-line (x) direction as well as in azimuthal (θ) direction, which provides three degrees of freedom (DOF) to the body. It is found that for one-DOF (y-direction only) and two-DOF (y and x directions) cases, lock-in regions are the same while it is wider for the case of the three-DOF system. With the rotational DOF, y-directional motion is amplified and when it is compared with the one-DOF and two-DOF cases, difference in peak amplitude is about 30%. The rotational response reaches a maximum value within the synchronization regime, and the frequency behavior of rotational and transverse oscillations is showing the same characteristics. The phase difference is plotted to check their synchronization with respective forces and moments. For all DOFs and Ured, synchronized or desynchronized regions, 2S mode of vortex shedding was observed. For one-DOF and two-DOF cases, the transverse vibrational frequency ratio (fy/fn) becomes equal to unity for the range 3.75≤Ured≤5. For three-DOF, fy/fn and rotational frequency ratio (fR/fn) become close to the unity for 3.75≤Ured≤6. The three-DOF system shows smaller wake width and vortex formation length whereas the vortex strength is maximum.

Flow-induced vibration of a cantilevered cylinder in oscillatory flow at high KC

Flow-induced vibrations of a cantilevered circular cylinder are measured in sinusoidal, oscillatory, water flows with amplitude of reduced velocity in the range 1.9≤Ur≤4.4 and Keulegan–Carpenter number in the range 120≤KC≤900 respectively. Flow velocities are measured using laser Doppler anemometry, and forces and moments are measured using a 6-axis load cell; the two-degree-of-freedom (2-DOF) cylinder motions are determined from the measured moments. The dominant type of vibration occurring within the flow half-period is shown to depend mainly on Ur, with predominantly in-line vibration occurring for Ur⪅2.7, figure-8 vibration occurring for 2.7⪅Ur⪅4, and transverse vibration occurring for Ur⪆4. In-line vibration frequency, fx, is close to, or slightly higher than the cylinder’s natural frequency in still-water, while transverse vibration frequency, fy, is generally close to the vortex shedding frequency given by Strouhal number St=0.2. Some unsteadiness is seen in the transverse vibration frequency in that accelerating flow fy is consistently higher than decelerating flow fy for the same instantaneous reduced velocity ur. The most notable unsteady effect is seen in the in-line vibration amplitude, Ax, which is much higher during flow deceleration than during flow acceleration; maximum Ax occurs at decelerating ur≈2 for all three vibration types. Transverse vibration amplitude, Ay, increases with increasing ur and shows only slight asymmetry between accelerating and decelerating flow. Experiments with the cylinder placed within a large array of similar cylinders with a spacing between cylinders of six cylinder diameters, show that cylinder vibrations within the array are more variable than those of the isolated cylinder, but exhibit similar average vibration amplitudes and frequencies as the isolated cylinder. An empirical model for unsteady in-line vibration based on theoretical considerations and the experimental data is presented. Model-predicted and measured in-line vibration amplitudes through the flow half-period show good agreement for in-line, figure-8 and transverse vibrations.

Identification of conveyor belt tension with the use of its transverse vibration frequencies

Belt vibration is related to the tension force along the entire length of the conveyor route. The ability to predict belt vibrations can provide information about the correct operation of the conveyor. Vibration analysis is usually based on theoretical models or stationary tests. In this article the vibration frequency of a working conveyor was measured, in the absence of the material and with the belt loaded. The tests were carried out in motion using a specially made device placed onto the conveyor belt. The distribution of the frequency of transverse vibration of the belt along the entire length of the conveyor route was identified. Using the phenomenon of belt vibration, the increase in belt tension in the top belt strand was determined. The comparison of the measured increases in the tensile force with the values obtained by computer simulation showed the high accuracy of the method.

ВЗАИМОСВЯЗЬ ПРОГИБОВ И ЧАСТОТ СОБСТВЕННЫХ ПОПЕРЕЧНЫХ КОЛЕБАНИЙ КРУГЛЫХ ИЗОТРОПНЫХ ПЛАСТИН ПЕРЕМЕННОЙ ТОЛЩИНЫ ПО ЗАКОНУ КВАДРАТНОЙ ПАРАБОЛЫ С УТОЛЩЕНИЕМ К ЦЕНТРУ

The relationship between the maximum deflections W0 from a static uniformly distributed load q and the fundamental frequency of natural transverse vibrations ω of a round isotropic plate of variable thickness according to the law of a square parabola with a thickening in the center under homogeneous conditions of support along the outer contour, depending on the ratio of the thickness of the plate in the center to the thickness along the edge, is considered.According to the results of the study, graphs of the dependence of the maximum deflection and the frequency of natural vibrations of the plate on the ratio t2/ t1 are constructed. It is shown that for round plates of linearly variable thickness at t2/t1≤1.1, the coefficient K with an accuracy of 5.29% coincides with the analytical coefficient for round plates of constant thickness.

Usefulness of inclined circular cylinders for designing ultra-wide bandwidth piezoelectric energy harvesters: Experiments and computational investigations

This study proposes to change the inclination angle (α) of a circular cylinder with respect to oncoming flow in order to broaden the effective wind speed bandwidth of the piezoelectric energy harvester. Comprehensive wind tunnel experiments are conducted to investigate the energy harvesting characteristics of the system under different inclination angles. The experimental results demonstrate that compared to the conventional vortex-induced vibration piezoelectric energy harvester (VIVPEH), an appropriate inclined cylinder can broaden the effective wind speed range for the VIVPEH. It is experimentally shown that the inclined cylinder at α = 60° can reduce the threshold wind speed and broaden the effective wind speed bandwidth by more than 229%. In addition, inclined circular cylinders at α = 25°, 30°, 35°, 40°, and 45° can produce torsional vibration and high voltage output under high wind speed. Through frequency analysis and computational fluid dynamics (CFD) simulations, the influence mechanism and causes of torsional vibration are explored in detail. The results show that the axial flow will prevent the free shear layer from falling off and cause the force imbalance at the top and bottom of the inclined cylinder, resulting in a torsional vibration and a series of other phenomena. The appearance of the torsional vibration rapidly reduces the frequency of the conventional transverse vortex-induced vibration (VIV). The superposition of the transverse bending vibration and the torsional vibration within a certain wind speed range results in a high voltage output.

Decoupling the effects of material thickness and size scale on the transverse free vibration of BNNTs based on beam models

Here we establish a new model to decouple the material thickness and elastic property of single-walled boron nitride nanotubes, and thus we can evaluate natural frequencies of transverse free vibration by directly using the Timoshenko beam and Euler-Bernoulli beam models. Full atomic simulations regarding on the vibration behaviors are also presented for comparison. The determination procedure of thickness and the physical meaning of scale parameter for one-atomic thick material are clearly defined. In order to comprehensively unfold the influence of the selection of tubular thickness on natural frequencies, a series of assumed tubular thickness is also adopted to analyze the sources of error and its trend, and finally confirms the accuracy of our proposed result. The accuracy of the beam models is also found to be dependent on the type of boundary constraints. The precision of the beam theory improves for weaker boundary constraints due to the release of shear stresses. The paper heals the rift between atomic simulations and continuum theories.

THE METHOD OF VARIATION OF ARBITRARY CONSTANTS IN THE CASE OF A SYSTEM OF LINEAR DIFFERENTIAL EQUATIONS OF DIFFERENT ORDERS

The paper considers structures consisting of rods connected in one node.Longitudinal and transverse vibrations of such a structure are described by systems of linear differential equations on star graphs.The noted system of equations consists of three linear differential equations of different orders.Two equations correspond to two transverse vibrations, and the third equation describes the longitudinal vibrations of the bar.Moreover, the system of three linear differential equations in the general case does not decompose. In this work, a fundamental system of solutions of a homogeneous system is constructed when the conjugation conditions are satisfied at the point of connection of the rods. Also, by the method of variation of arbitrary constants, a particular solution of an inhomogeneous system is constructed, which is subject to the conjugation conditions at the point of connection of the rods. In subsequent works, the authors intend to investigate the natural frequencies of longitudinal and transverse vibrations of a structure consisting of many rods

Models of Transverse Vibration in Conveyor Belt—Investigation and Analysis

The transverse vibration frequency of conveyor belts is an important parameter describing the dynamic characteristics of a belt conveyor. This parameter is most often identified from theoretical relationships, which are derived on the basis of an assumption that the belt is a stationary elastic string. Belt vibrations have a number of analogies to other tension member systems, such as, for example, power transmission belts. Some research findings suggest that in the case of a limited length of the belt section, a more accurate description of its vibration can be obtained with a beam model rather than with a string model. Experimental research has so far mostly revolved around measurements of stationary belts. This article presents the results of vibration measurements performed for a moving belt and obtained for various operating parameters of the conveyor, as well as for several configurations of the distance between idler supports. The analysis was conducted on a moving steel-cord belt. Belts of this type are commonly used in the majority of mines and industrial plants. The measurement results were compared with the model of a string and with the model of a beam in tension. Both of the theoretical models allowed for the belt speed, whose influence was demonstrated in both theoretical calculations and experimental tests to be negligible. On the other hand, the tensile force in the belt was observed to have a significant impact on the vibration frequency. Depending on the idler spacing, the measurement results are approximate to those of the beam model or of the string model. For spacing smaller than 1.6 m, the belt shows properties approximate to an elastic beam, while for spacing greater than 1.6 m, the belt behaviour can be better represented through a string model. A beam model is, therefore, more applicable in analyses of vibrations in the upper strand of the belt, while a string model is more useful in analyses of vibrations in the lower strand.