Frequency Characteristics Of Vibration Research Articles

Design and Analysis of a Moment of Inertia Adjustment Device

The vibration frequency characteristics of a rotor system are directly related to its moment of inertia. In this paper, a moment of inertia adjustment device is proposed to adjust the frequency characteristics of a rotor system and better reduce vibration by changing the moment of inertia. First, a mathematical model of the moment of inertia and the temperature field are established. A finite element simulation model of the electromagnetic field of the electromagnetic control unit in the device is established. The influence of current and air gap on the electromagnetic forces is discussed. Then, the validity of the finite element simulation for the electromagnetic control unit is verified using experimental results. In addition, the variations in the displacement and force of the moving mass and the moment of inertia of the device with speed are analyzed. The results show that the proposed moment of inertia adjustment device can be used to significantly adjust the moment of inertia, which provides a reference for better controlling vibrations in rotor systems. Finally, a finite element simulation model for an electromagnetic field analysis of the electromagnetic control unit in the device is established. The results show that the maximum temperature of the electromagnetic control device is 332 K in 60 min, which is in accordance with the requirements.

Vibration frequency and mode localization characteristics of strain gradient variable-thickness microplates

Based on the modified strain gradient theory and Kirchhoff–Love assumptions, a free vibration model is established for variable-thickness microplates with three material length scale parameters, and the corresponding Euler–Lagrange equation is derived. Keeping the microplate volume constant, three kinds of thickness variations along the X-direction are considered: linear, parabolic, and cubic variations. Further, a C2-type four-node 36-degree-of-freedom variable-thickness differential quadrature finite element is developed to solve the resulting variable-coefficient boundary value problem by combining the Gauss–Lobatto and differential quadrature rules. Galerkin approximate solution for fully simply supported microplates is provided as a benchmark for numerical method verification. The convergence and accuracy of the model are verified through several examples. Finally, the vibration frequencies of the microplates under different thickness variation types, taper ratios, thickness ratios, material length scale parameters, and boundary conditions are examined through parametric analysis. Also, the influence of each factor on the mode localization of the microplates is quantitatively characterized by the modal assurance criterion (MAC) for the first time. The numerical results show that the thickness variation has a minor effect on the vibration frequency but a significant influence on the mode shape when the volume of the microplate is constant. The strain gradient, taper ratio, and discontinuous boundary have a remarkable effect on the distribution of higher-order mode shape contour lines and the regions where vibration localization occurs.

Mathematical modelling analysis of deep groove ball bearing with misalignment

Deep groove ball bearing is prone to misalignment due to installation and long-term use, which requires research on the frequency characteristics and evolution mechanism excited by misalignment. This article first outlines a mathematical model of a rotor supported at both ends, which is used to describe the multi-body vibration mechanism of bearing-rotor system. The previous investigation on the misalignment dynamics of rolling bearings mainly focuses on the frequency harmonic characteristics of displacement signals. This article explores the acceleration frequency characteristics of misalignment bearings, involving their low-frequency and high-frequency vibrations, and explains the formation mechanism from the perspective of the balls passing through the stiffness change region. This modelling method can clearly describe the periodic impact and frequency modulation characteristics excited by misalignment, with characteristic frequencies including cage frequency [Formula: see text] and its harmonics, inner race relative to cage frequency [Formula: see text] and its harmonics and fault frequency [Formula: see text] and its sideband, thus providing more reasonable reference for design and diagnosis. Furthermore, a mean geometry indicator is developed from square envelope domain to evaluate the vibration frequency characteristics. With the advantages of mean geometry in characterizing nonlinear systems, the stability reliability is investigated to reveal the vibration mechanism and dynamic evolution law of the misalignment. Numerical calculations and experiments have shown that the multi-body vibration model and misalignment mathematical expression proposed in this article can illustrate the multi-frequency characteristics excited by misalignment, and the stability reliability can objectively describe the evolution mechanism of such dynamic system.

Slab arching degree identification and evaluation based on track dynamic inspection data

Due to structural deterioration and the external environment, the ballastless track is prone to slab arching during high-temperature periods. Arching will weaken the constraints between components, affect the smoothness of the line, and even endanger train safety in severe cases. Therefore, it is necessary to identify the arching in time and clarify the arching severity, which is of great significance for scientifically formulating maintenance plans and ensuring line stability. The existing research has established track geometry-based methods for arching identification, but they are difficult to recognize small arching and cannot quantitatively evaluate arching degree. To this end, this paper proposed a set of arching identification and evaluation methodology based on track dynamic inspection data. Combining the simulated and measured data, the time–frequency characteristics of car body vertical vibration caused by arching were finely extracted, and the arching-induced vibration index was established for identification. Then, a deep learning hybrid model for arching degree evaluation was proposed based on the analysis of the relationship between multiple feature indexes and arching gap height. The results showed that car body vibration could identify the arching defects with gap heights exceeding 1 mm, and the arching degree could be evaluated quantitatively based on multiple feature indexes. In practice, the proposed method can be used to detect arching of different degrees, assist maintenance decision-making, and help avoid the occurrence of serious failures.

The Use of IoT for Determination of Time and Frequency Vibration Characteristics of Industrial Equipment for Condition-Based Maintenance

The subject of study in this article is a method for industrial equipment vibration diagnostics that uses discrete Fourier transform and Allan variance to increase precision and accuracy of industrial equipment vibration diagnostics processes. We propose IoT-oriented solutions based on smart sensors. The primary objectives include validating the practicality of employing platform-oriented technologies for vibro-diagnostics of industrial equipment, creating software and hardware solutions for the IoT platform, and assessing measurement accuracy and precision through the analysis of measurement results in both time and frequency domains. The IoT system architecture for industrial equipment vibration diagnostics consists of three levels. At the autonomous sensor level, vibration acceleration indicators are obtained and transmitted via a BLE digital wireless data transmission channel to the second level, the hub, which is based on a BeagleBone single-board microcomputer. The computing power of BeagleBone is sufficient to work with artificial intelligence algorithms. At the third level of the server platform, the tasks of diagnosing and predicting the state of the equipment are solved, for which the Dictionary Learning algorithm implemented in the Python programming language is used. The verification of the accuracy and precision of the vibration diagnostics system was carried out on the developed stand. A comparison of the expected and measured results in the frequency and time domains confirms the correct operation of the entire system.

Free Vibration Analysis of Isotropic and Orthotropic Cylindrical Shells using Finite Element Method

The understanding of fundamental natural frequencies and mode shapes is crucial for assessing the resonant behavior of structures. Numerous scholars have investigated the free vibration properties of circular cylindrical shells. These cylindrical shell configurations find applications in diverse engineering fields such as aviation, rocketry, missiles, electric motors, and locomotive engines. Within this paper, an analytical solution is derived using the "first order shear deformation theory" to determine the frequency characteristics of free vibrations in symmetric laminated circular cylindrical composite shells. The outcomes are juxtaposed against classical and higher order theories. The central aim of this research is to scrutinize the influence of various parameters on the frequency traits of laminated composite shells. Furthermore, the analysis extends to laminated composite shells employing diverse stiffening methods, with their free vibration behavior explored through the utilization of FEA software ANSYS. Keywords: Cylindrical shell, free vibration, frequencies, mode shapes, laminated composites.

Numerical prediction of ground vibrations induced by LPG boiling liquid expansion vapour explosion (BLEVE) inside a road tunnel

Accidental boiling liquid expansion vapour explosions (BLEVEs) caused by the bursting of liquified petroleum gas (LPG) tank inside a tunnel can induce vibrations of its surrounding geological media and threaten the stability of adjacent tunnels and structures. Therefore, it is essential to understand the characteristics of vibrations induced by LPG BLEVEs inside the tunnel for the safety design of its adjacent structures. Owing to the difficulty in effectively predicting the LPG BLEVE loads, the current practice usually employs equivalent methods, e.g., the TNT-equivalency method, in LPG BLEVE load predictions for structural response analysis, which may lead to inaccurate response predictions. This study compares ground vibrations induced by a BLEVE inside an arched road tunnel with those induced by its equivalent TNT explosion via high-fidelity numerical simulations. The results demonstrate that the frequency of BLEVE-induced vibrations is lower than that induced by the TNT explosion at the same scaled distance. The intensity of LPG BLEVE-induced vibrations at relatively small-scaled distances is lower than that of TNT explosion-induced vibrations at the same scaled distance, but becomes higher after a certain scaled distance because of the relatively low attenuation rate. In addition, parametric analysis is conducted to evaluate the effects of various factors on the characteristics of LPG BLEVE-induced ground vibrations. It is found that the surrounding rock type, the rock porosity, and the cover depth of the tunnel have more significant influences than the concrete grade of the tunnel lining. The recommendation for the tunnel design is also given based on the intensity and frequency characteristics of BLEVE-induced vibrations.

Closed-loop Control of Biaxial Fatigue Loading of Wind Turbine Blades Based on Visual Inspection

Based on the inertial vibration excitation device, a biaxial fatigue loading system for wind turbine blades is established by using visual inspection technology and virtual spindle decoupling to control the vibration excitation motion of wind turbine blades. The image feature point tracking method is used to detect the blade vibration state. Considering the system vibration frequency characteristics, the phase difference between the exciting force and the vibration displacement is detected based on the phase detector, and the system resonance frequency is adaptively tracked to achieve accurate control of the double-free amplitude of the blade. The fatigue test shows that the control system can maintain the amplitude error of the blade, the adaptive tracking control method is reliable and effective, and the accuracy and reliability of the fatigue test are improved.

Method of normal oscillations and substantiation of the choice of parameters for certain nonlinear systems with two degrees of freedom

On the example of the plane model of wheeled vehicle oscillations with adaptive power characteristic of the suspension system, the methodology for selecting its main parameters that would maximize the movement smoothness is developed. To solve this problem, the mathematical model of relative oscillations of the sprung part is constructed, provided that they are carried out in the vertical plane. The latter represents the system of two nonlinear differential equations describing the relative displacement of the center of mass of the sprung part and the angle of rotation of the latter around the transverse axis passing through the center of mass of the specified part. To construct the approximate analytical solution of this equations system, and thus to describe the main parameters that determine the relative position of the sprung part under reasonable assumptions, the method of normal oscillations of nonlinear systems with concentrated masses is used. This made it possible to obtain the system of ordinary differential equations of the first order that describe the amplitude–frequency characteristics of the sprung part vibrations. Due to the analysis of the latter it is determined that at a certain ratio between the parameters describing the power characteristics of the suspension system, it can perform isochronous vertical and longitudinal–angular oscillations, and thus it is possible to achieve maximum comfort in transporting passengers or dangerous cargo over rough terrain. The main obtained results can be used to create the software product for adaptive suspension, and their validity is confirmed by: a) in passing to the limit, obtaining results known from literary sources; b) generalization, based on the use of periodic Ateb-functions, of widely tested analytical methods for constructing solutions of differential equations with strong nonlinearity.

Vibration velocity and frequency characteristics of surrounding rock of adjacent tunnel under blasting excavation

The aim of this study is to improve the accuracy of response prediction and safety evaluation of blasting vibration of a deeply-buried tunnel group. For this purpose, the expression of frequency-domain and blasting vibration velocity spectra for the equivalent blasting load in multiple holes was derived through theoretical analysis, and propagation and attenuation of the primary frequency of blasting vibration of multiple cutting holes and caving holes in the infinite rock mass were explored. Response characteristics of vibration frequency spectra in rock surrounding of the adjacent tunnel induced by full-section blasting excavation of the tunnel under the high in situ stress were studied using the dynamic finite element method. The research indicates that blasting vibration waves have the greatest influences on the adjacent tunnel at the haunch in the side facing the blasting, where the vibration velocity is inversely proportional to the spacing between tunnels and directly proportional to the tunnel diameter. The centroid frequency increases with the increase of the spacing between tunnels and tunnel diameter. Furthermore, vibration velocity spectra at the most affected location (namely the haunch) in the side facing blasting of the adjacent tunnel under different conditions were derived. The coincidence of the theoretical formula was verified by comparing measured data of blasting of diversion tunnels in Pubugou Hydropower Station (Sichuan Province, China). The research results can provide theoretical guidance and reference for the prediction of blasting vibration response of similar projects in the future.

Исследование вибрационных и механических свойств обандаженных направляющих лопаток с предварительным натяжением

The article considers the effect of the stator blade tension of an axial compressor on blade vibration and mechanical properties. Attention is paid to modeling the stress-strain state of a pre-tensioned blade and calculating the strength of the developed model as well as modal analysis. A method of stator blade pre-tensioning is proposed: the blade root is fixed in the groove of the body, and fitting into the shroud ring is made with a gap providing the blades with the necessary space for stretching. The tension is adjusted by changing the position of the tightening nut. Nuts are tightened evenly around the circumference. The proposed method allows increasing the rigidity of the stator blades and, consequently, reducing their thickness in order to improve aerodynamic performance while maintaining vibration-frequency characteristics. The pre-tension has the greatest influence on bending shapes. The ability to regulate the natural vibration frequencies of the stator blade in a wide range allows avoiding resonance.

Study on Dominant Frequency Attenuation of Blasting Vibration for Ultra-Small-Spacing Tunnel

The middle rock pillar in ultra-small-spacing tunnels is significantly narrow, and the stability of the primary support and lining are easily influenced by the blasting vibration wave from an adjacent tunnel. Therefore, understanding the vibration frequency characteristics is essential for the blasting vibration control. Based on the blasting works on a double-track roadway tunnel (Jiuwuji tunnel in Guizhou, China), this study investigates the dominant frequency attenuation in the preceding tunnel with the middle rock pillar spacing ranging from 4.0 m to 9.4 m. The results show that the ranges of the dominant frequency distributions on the primary support and lining are widely within 200 Hz, but there are varieties in their propagation laws. The distribution of the dominant frequencies on the primary support is broader than that on the lining; and the dominant frequencies are concentrated on a specific range when the lining is far from the blast face beside a particular value, which is not present on the primary support. As the presence of cavity and changing medium between the lining and the primary support, it made a significant contribution to the filtering the vibration waves. Furthermore, on the primary support, the high-frequency part of the vibration waves attenuates rapidly with distance, and then, the practical prediction equations describing dominant frequency attenuation were proposed. The comparison on frequency characteristics per delay for the millisecond delay blasting shows that multiple delay sequences blast contributes to a multi-structured amplitude spectrum of blast vibration waves; and the varies of the equivalent explosion sources dimensions and numbers of free surfaces in each blast delay resulting in diverse vibration waveforms. Finally, the dominant frequencies determined by different methods were compared, and the results show a nonlinear relationship between the ZCFs and DFs. The above research conclusion expands the understanding of blasting vibration in tunnel engineering, particularly in the frequency distribution.

Research on the Approximate Calculation Method of the Fundamental Frequency and Its Characteristics on a Tensioned String Bridge

As a new type of composite bridge, the dynamic structural characteristics of a tensioned string bridge need to be deeply studied. In this paper, based on the structural characteristics of a tensioned string bridge, the Rayleigh method is used to derive formulas for calculating the frequencies of vertical, antisymmetric and lateral bending vibrations. The characteristics of the vertical and lateral bending vibration frequencies are summarized. The fundamental frequencies of the antisymmetric vertical bending and lateral bending of the tensioned string bridge are the same as that of the single-span beam under the corresponding constraint conditions. The shape and physical characteristics of the main cable have no effect on the frequency. The vertical bending symmetrical vibration frequency of the tensioned string bridge is greater than the corresponding symmetrical vibration frequency of the simply supported beam. The shape and physical characteristics of the main cable have a greater impact on the vertical bending symmetrical vibration frequency than the lateral bending frequency, and the vertical bending symmetrical vibration frequency increases with an increasing rise-to-span ratio. The tension force of the main cable has no influence on the frequency of tensioned string bridges. The first-order frequency of the tensioned string bridge is generally the vertical bending symmetrical vibration frequency. By adopting a tensioned string bridge structure, the fundamental frequency of a structure can be greatly increased, thereby increasing the overall rigidity of the structure. Finally, an engineering example is applied with the finite element parameter analysis method to study the vibration frequency characteristics of the tensioned string bridge, which verifies the correctness of the formula derived in this paper. The finite element analysis results show that the errors between the derived formula in this paper and the finite element calculation results are less than 2%, indicating that the formula derived in this paper has high calculation accuracy and can meet the calculation accuracy requirements of engineering applications.

Mathematical modeling of forced oscillations of manometric tubular springs

Difficult working conditions, as well as vibrations of technological process units and unstable load intensity impose high demands on overpressure monitoring devices that ensure the required measurement accuracy and trouble-free operation of equipment. The use of pressure gauges today is a mandatory requirement for monitoring overpressure. The main type of pressure gauges uses manometric tubular springs (MTP) as elastic sensing elements. Therefore, the issue of calculating the motion of the MTP under the influence of external variable loads, in particular variable internal pressure, is relevant. Issues related to the influence of internal pressure pulsations and external periodically changing external forces remain unexplored. For successful operation, the strength and frequency characteristics of vibrations of tubular springs were previously investigated, the effects of cross-sectional shapes and basic geometric dimensions on their vibration characteristics were considered, and the process of vibration damping by liquid was analyzed. The paper presents a mathematical model of forced oscillations of the MTP based on Lagrange equations of the second kind. The MTP is considered as a mechanical system with two degrees of freedom, that is, defined by two generalized coordinates. They are a relative change in the main angle of the tube and an increase in the small semi-axis of the cross section. The model allows us to determine the nature of the movement of the MTP under the influence of periodically changing internal pressure. To implement it, a program has been developed in MATLAB, which makes it possible to determine the required characteristics of pressure monitoring devices that exclude the possibility of resonance. With the help of the developed program, the influence of geometric characteristics and internal pressure pulsations on the movements of the free end of the MTP is estimated. The presented model can be successfully used for dynamic calculations of manometric tubes, since it is a classical approach to solving problems of vibrations of mechanical systems. In addition, it will allow you to calculate the parameters of tubular elastic elements used in various mechanisms as power elements.

PPV and Frequency Characteristics of Tunnel Blast-Induced Vibrations on Tunnel Surfaces and Tunnel Entrance Slope Faces

Tunnel blast-induced vibration probably causes damage to the rock mass surrounding the tunnel surface and also to the rock mass of the slope at the tunnel entrance. It is important to simultaneously monitor the vibration on the tunnel surface and on the tunnel entrance slope face, especially when the blasting work face is close to tunnel entrance. During blasting excavation of the traffic tunnel at Baihetan hydropower station, vibration monitors were installed both on the tunnel surface and on the tunnel entrance slope face. Based on the monitoring data, a comparative study is conducted on the peak particle velocity (PPV) and frequency characteristics of the vibrations at these two locations. A three-dimensional FEM simulation of the tunnel blast is then performed to verify the field test results. The field monitoring and the numerical simulation show that there is significant difference between the vibration on the tunnel surface and that on the tunnel entrance slope face. The vibration on the tunnel surface has greater PPV and faster attenuation, while the tunnel entrance slope face has higher frequency and faster reduction rate in the center frequency. These differences are attributed to the different wave types and wave propagation paths. The tunnel surface is mainly surface waves transmitted through the damaged rock mass around the tunnel profile, while the tunnel entrance slope face originates mainly from the body waves transmitted via the undamaged rock mass inside the mountain. The comparisons of the monitored vibrations with the velocity limits specified in the Chinese standard show that the most dangerous vibration that may exceed the limit occurs on the tunnel surface. Therefore, the maximum charge weight used in the tunnel blast is determined by the vibration on the tunnel surface. Under different control standards, the allowable maximum charge weight per delay is further discussed.

Auxiliary Piers on Long-Span Specially Shaped Mixed Steel Structure Main Tower Cable-Stayed Bridge: Research on the Impact on the Dynamic Performance

This study investigates the influence of auxiliary piers on the natural frequency, deformation characteristics, displacements of the related parts, and internal forces of a long-span heterogeneous steel-structured main tower cable-stayed bridge. Taking the Guohe Third Bridge in Anhui Province as an example, the software ANSYS was used to establish a three-dimensional finite element model of a cable-stayed bridge, and the dynamic characteristics of a long-span specially shaped hybrid steel structure main tower cable-stayed bridge with auxiliary piers added to single span and double spans were analysed. The results show that when one or three pairs of auxiliary piers are added to a single span, the changes in the natural frequency and deformation characteristics are smaller than those when there are no auxiliary piers. When one or three pairs of auxiliary piers are added to each of the two spans, the natural frequency and deformation characteristics are relatively low. Auxiliary piers induce relatively large changes; the changes with 3 pairs of auxiliary piers for a single span is compared with those with 1 pair for a single span, and 3 pairs and 1 pair of auxiliary piers are added to both spans for comparison. The natural vibration frequency and deformation characteristics exhibit relatively small changes; the presence or absence of auxiliary piers and the number of auxiliary piers have a greater influence on the vertical displacement of the main girder and less influence on the vertical displacement of the main tower. An appropriate number of auxiliary piers are beneficial to the seismic resistance of a cable-stayed bridge, and if the number of auxiliary piers is too large, the seismic capacity of the bridge is reduced; it is recommended that a pair of auxiliary piers be added to both spans to optimize the overall dynamic performance of a cable-stayed bridge. This research method can be used on similar cable-stayed bridges to optimize their dynamic characteristics by setting a certain number of auxiliary piers.

Experimental and Numerical Study of the Dynamic Response of XCC Pile–Raft Foundation under High-Speed Train Loads

A series of dynamic large-scale model tests and three-dimensional finite element analyses were conducted to investigate the dynamic response of track embankment and XCC pile-raft composite foundation in soft soil for a ballastless high-speed railway under moving train loads. The results indicate that the vibration velocity obtained from the FE numerical simulation agrees well with that from the model test in vibration waveform, amplitude, and frequency characteristics. The peak values corresponding to the passing frequency of train carriage geometry (lc = 25 m), bogie (lab = 7.5 m), and axle distance (lwb = 2.5 m) respectively reflect the characteristic frequencies of the train compartment, adjacent bogie, and wheel load passing through. The peak velocity significantly depends on the distance from the track center in the horizontal direction, of which the attenuation follows the exponential curve distribution. The vibration velocities decrease rapidly within embankment, show a vibration enhancement region from raft to the 1 m depth of foundation soil, then decreases gradually along the subsoil foundation, to a very low level at the bottom of the subsoil, which is much lower than that at the track slab and roadbed. The pile-raft composite foundation can reduce the vibration level effectively and improve the safety of trains running in soft soil areas.

Multi-parametric Dynamic Analysis of a Rolling Bearings System

A method for calculating amplitudes and constructing frequency characteristics of forced and self-excited vibrations of a rotor-fluid-foundation system on rolling bearings with a non-linear characteristic based on the method of complex amplitudes and harmonic balance has been developed. Non-linear equations of motion of the rotor-fluid-foundation system are derived, and analytical methods of their solution are presented. Frequencies of fundamental and ultra-harmonic resonances are determined. The intervals between self-oscillation frequencies are estimated. The dependence of amplitudes on the amount of fluid in the rotor cavity, the mass of the foundation, linear imbalance, the value of the stiffness coefficient, and the damping coefficient is shown.

A detection method of gear micro-cracks based on tuned resonance

Detection of micro-cracks before assembling has always been a challenge in gear defect detection. A mature detection method of micro-cracks is not available. Due to the complex detection environment and large production of gears, it’s urgent to develop a rapid and accurate detection method of gear micro-cracks. It’s the key to separate and extract weak vibration signals accurately under complex disturbances in gear defect detection. In this study, vibration characteristics of gear defects under resonance conditions were firstly explored and a detection method of gear micro-cracks was proposed based on tuned resonance. Based on the amplification effect of tuned resonance on the peak frequency spectrum of gear vibration, meshing frequency and sideband frequency characteristics of the gear defect signal spectrum were experimentally investigated. The amplitudes of gear meshing frequency and its harmonic meshing frequency in the signal frequency domain diagram were higher and the surrounding sideband frequency components were clearer.

Health monitoring and safety evaluation of bridge dynamic load with a ground-based real aperture radar

Through a series of experiments of dynamic deformation and destruction under time series loading on an indoor real model bridge, Ground-based real-aperture radar interferometry (GB-InRAR) discovered that before the structure of the bridge was damaged, its amplitude and acceleration increased with the increase of load; After its structure was damaged or cracked, such dynamic characteristics as natural frequency, damping ratio, stiffness and bearing capacity decreased obviously. Moreover, GB-InRAR dynamic load monitoring of Xiangtan Railway Bridge and Inter-city Railway Bridge. In the process of vehicle dynamic load, such important parameters as bridge deflection, natural frequency and damping ratio conform to the bridge loading procedures and dynamic characteristics. The results show that the GB-InRAR can accurately measure the deflection changes, natural vibration frequency and spectrum characteristics of bridges, and it can be used as effective means of the dynamic characteristics analysis in the safety detection and health evaluation of bridges.