Natural Oscillation Frequency Research Articles

Fault Location Using the Natural Frequency of Oscillation of Current Discharge in MTdc Networks

This paper discusses a novel fault location approach using single ended measurement. The natural dissipation of the circuit parameters are considered for fault location. A relationship between the damped natural frequency of oscillation of the transmission line current and fault location is established in this paper. The hybrid dc circuit breaker (dcCB) interrupts the fault current and the line current attenuates under the absence of any driving voltage source. The line capacitance discharges into the fault at a specific frequency of oscillation and rate of attenuation. Utilizing this information, the fault location in a multi-terminal direct current (MTdc) network can be predicted. A three terminal radial model of a MTdc is used for performance evaluation of the proposed method using Power System Computer Aided Design (PSCAD)/Electromagnetic Transients including dc (EMTdc).

К развитию теории резонансных процессов в обмотках силовых трансформаторов. Ч. 1. Частотные характеристики схемы с двумя П-звеньями

The windings of power transformers are complex oscillatory circuits. Their natural oscillation frequencies range from a few to hundreds of kHz, and under unfavorable conditions they can coincide with the frequencies of transient voltage oscillations in electrical networks caused by switching operations and short circuit faults in cable lines. The development of electrical networks and the technical solutions that have come in wide use in recent years give rise to a situation in which the cases of damage to the insulation of power transformer windings resulting from resonant overvoltages are increasingly more frequently encountered during operation. An attempt is made in the article to develop the theory of resonant processes in the windings of power transformers. The frequency responses of voltages and currents in a simplified equivalent circuit of the power transformer winding are considered. Analytical expressions are obtained for the admittances of individual parts of equivalent circuits and the voltages at intermediate nodes, as well as expressions for the natural frequencies of the equivalent circuits considered. It is shown that the resonant growth of voltage in the transformer windings results from the voltage resonance caused by the presence of the winding’s own inductance and capacitance with respect to ground. By analyzing the frequency dependences of the admittances of equivalent circuit individual parts, the conditions and frequency ranges in which voltage resonance may occur are shown.

Dynamics of bubbles in spherical liquid cavity wrapped by elastic medium

The cavitation effects occur in the ultrasound therapy technology. With the development of ultrasound therapy technology, cavitation effect in biological tissues has attracted more and more attention. The aim of the present study is to discuss the factors affecting cavitation nucleation and dynamics in tissues, and to provide a theoretical reference for the application of cavitation effects to ultrasound therapy. A model is developed for the cavitation inception in a spherical liquid cavity wrapped by an elastic medium. The Blake threshold value and the critical radius of the liquid cavity for the generation of spherical bubbles are obtained by the pressure equilibrium relationship. The effects of the excitation frequency, the volume modulus of the medium and the volume of the liquid in the cavity on the bubble vibration behavior are analyzed by deriving a bubble dynamic equation that consider the elastic effect of the medium outside the cavity using Lagrange equation. It is shown that the volume modulus, initial radius of bubble nucleus and surface tension can affect the Blake threshold pressure and bubble size, and those form a parameter reference for the control conditions that trigger or inhibit cavitation. The gas core can rapidly grow to a new equilibrium radius and oscillate under the action of an acoustic wave, and the bubble equilibrium radius is independent of the external field, but it can affect the bubble dynamic behavior. When the frequency of the ultrasonic signal is equal to the natural oscillation frequency of the bubble, the bubble collapses after several periods of intense vibration, and the pressure fluctuation in the liquid in the cavity is obvious. The response of bubbles under high frequency ultrasonic driving is relatively weak, and the oscillations of bubbles are dominated by free oscillation.

Natural Oscillations of Underactuated Cable-Driven Parallel Robots

Underactuated Cable-Driven Parallel Robots ( CDPR ) employ a number of cables smaller than the degrees of freedom ( DoFs ) of the end-effector ( EE ) that they control. As a consequence, the EE is underconstrained and preserves some freedoms even when all actuators are locked, which may lead to undesirable oscillations. This paper proposes a methodology for the computation of the EE natural oscillation frequencies, whose knowledge has proven to be convenient for control purposes. This procedure, based on the linearization of the system internal dynamics about equilibrium configurations, can be applied to a generic robot suspended by any number of cables comprised between 2 and 5. The kinematics, dynamics, stability and stiffness of the robot free motion are investigated in detail. The validity of the proposed method is demonstrated by experiments on 6- DoF prototypes actuated by 2, 3, and 4 cables. Additionally, in order to highlight the interest in a robotic context, this modelling strategy is applied to the trajectory planning of a 6- DoF 4-cable CDPR by means of a frequency-based method (multi-mode input shaping), and the latter is experimentally compared with traditional non-frequency-based motion planners.

DYNAMIC ANALYSIS AND FORMULATION OF THE SOLUTION FOR COMPLEX PROBLEM OF DURABILITY INCREASE FOR STRUCTURAL ELEMENTS IN A TURBULENT FLOW OF THE MEDIUM

When designing the structures of modern hydroelastic systems in power engineering, namely heat exchangers for various purposes, effective frequency tuning should be purposefully carried out to prevent intense vibration of individual elements. To do this, it is necessary, in accordance with the specified resource requirements, to provide reasonably defined ratios of various values of the natural oscillation frequencies of the structural elements and the characteristic nearest excitation frequencies in the flow. The optimal choice of the values of the frequency tuning coefficients is realized taking into account the characteristic known factors of hydroelastic systems, such as the effects of attached masses and the significant influence of damping on the intensity of vibrations of the structure in the fluid flow. The article provides a description and a general plan for solving the set complex problem based on the results of numerical and experimental studies known in this direction.

Research of dynamic influence from technological equipment on work of reinforced concrete slabs of overlapping

This article presents full-scale experimental measurements of the parameters of the elements of the load-bearing structures of thebuilding in real time with their subsequent processing and determination of the dynamic characteristics of such elements and the structure as awhole for further modeling and calculation ofbuilding elements.The research is based on an approach based on the hypothesis of considering systems of complex structure, which has a dynamic impact, as a single system with corresponding dynamic characteristics. Within the framework of such a review of the system, it is necessary to identify and assess the impact of various origins.As a dynamic criterion for assessing the condition of load-bearing structures were used the values of natural frequencies of oscillations, their actual measurement on different floors of the existing building.The research was performed by determining the integral dynamic parameters with subsequent analysis and establishment of causal relationships. In the course of the research, records of continuousfixation of dynamic action parameters were used directly on load-bearing structures. The obtained data were processed using ZETLAB SEISMOsoftware using spectral analysis.The obtained spectra were analyzed in order to determine the numerical values of the oscillation frequencies, which correspond to the main peakson the spectrograms and are a consequence of the design response to the sources of dynamic influence.The obtained data will be used to assess the stress state of fiber concrete slabs.

Natural oscillation frequencies in the two lateral prefrontal cortices induced by Transcranial Magnetic Stimulation

Different cortical regions respond with distinct rhythmic patterns of neural oscillations to Transcranial Magnetic Stimulation (TMS). We investigated natural frequencies induced by TMS in left and right homologous dorsolateral prefrontal cortices (DLPFC) and related hemispheric differences. In 12 healthy young adults, single-pulse TMS was delivered in different blocks close to F3 and F4 channels to target left and right DLPFC. An occipital site near PO3 was stimulated as control. TMS-related spectral perturbation analyses were performed on recorded EEG data. A widespread unspecific increase in theta power was observed for all stimulation sites. However, occipital TMS induced greater alpha activity and a 10.58 Hz natural frequency, while TMS over the left and right DLPFC resulted in similar beta band modulations and a natural frequency of 18.77 and 18.5 Hz, respectively. In particular, TMS-related specific increase in beta activity was stronger for the right than the left DLPFC. The right DLPFC is more specifically tuned to its natural beta frequency when it is directly stimulated by TMS than with TMS over the left counterpart (or a posterior region), while the left DLPFC increases its beta activity more similarly irrespective of whether it is directly stimulated or through right homologous stimulation. These results yield important implications for both basic neuroscience research on inter-hemispheric prefrontal interactions and clinical applications.

Analytical assessment of the frequency of natural vibrations of a truss with an arbitrary number of panels

The aim of the work is to derive a formula for the dependence of the first frequency of the natural oscillations of a planar statically determinate beam truss with parallel belts on the number of panels, sizes and masses concentrated in the nodes of the lower truss belt. Truss has a triangular lattice with vertical racks. The solution uses Maple computer math system operators. Methods. The basis for the upper estimate of the desired oscillation frequency of a regular truss is the energy method. As a form of deflection of the truss taken deflection from the action of a uniformly distributed load. Only vertical mass movements are assumed. The amplitude values of the deflection of the truss is calculated by the Maxwell - Mohrs formula. The forces in the rods are determined in symbolic form by the method of cutting nodes. The dependence of the solution on the number of panels is obtained by an inductive generalization of a series of solutions for trusses with a successively increasing number of panels. For sequences of coefficients of the desired formula, fourth-order homogeneous linear recurrence equations are compiled and solved. Results. The solution is compared with the numerical one, obtained from the analysis of the entire spectrum of natural frequencies of oscillations of the mass system located at the nodes of the truss. The frequency equation is compiled and solved using Eigenvalue search operators in the Maple system. It is shown that the obtained analytical estimate differs from the numerical solution by a fraction of a percent. Moreover, with an increase in the number of panels, the error of the energy method decreases monotonically. A simpler lower bound for the oscillation frequency according to the Dunkerley method is presented. The accuracy of the lower estimate is much lower than the upper estimate, depending on the size and number of panels.

Harnessing Energy from Wind Induced Vibrating Structures

This paper focuses on the harnessing of energy from fluid induced vibrations of bluff bodies due to the phenomenon of vortex shedding. Vortex shedding causes oscillating drag and lift forces due to which the bluff body in question experiences transient forces causing it to vibrate. An experiment has been conducted to investigate the potential of such vibrations and its probable usefulness. Maximum achievable efficiency of the system has been calculated and techniques to convert this mechanical energy into electrical energy have been discussed. In this experiment the bluff body used is a simple circular cylinder. The model developed works on the phenomenon of vortex shedding and resonance. The innovation of the setup is that the natural frequency of the structure can be easily altered by changing the relative distance between two of the mounting springs or by simply using springs of a different stiffness, as a result it can be ensured that the natural frequency of oscillation of the structure is always nearly matched to the frequency of vortex shedding for a wide range of wind velocities thereby ensuring a near resonance condition always.

Dynamic Characteristics of a Rotor with Continuous Friction on a Stator

This paper develops a theory of reverse continuous precession motion (rolling) of a uniformly rotating (with constant angular velocity) balanced unloaded (with constant force) and asymmetric rotor along a rigid stator with slipping. It is shown for the first time that the rotor precession frequency can be accurately calculated not only for the case of rolling without slipping, where it is determined by the rotation frequency and the ratio of the rotor radius at the point of contact with the radial clearance, but also for the case of rolling with slipping. In this case it is determined by a particular frequency of natural oscillations of the rotor resting on the stator and by the coefficients of internal and sliding friction. The theory developed predicts several ranges of true rolling and rolling with slipping of the rotor along the stator. In this case, the friction values determine the precession frequency and the clearance value at the contact point determines the precession amplitude (rotor deflection outside the contact point).

Research into the dynamic loading on the carrying structure of a flat wagon with lower center of gravity when transporting firing equipment

The article presents the study results of the dynamic loading of a flat wagon with a lower gravity center.The authors built a mathematical model that takes into account displacements of a flat wagon loaded with an anti-aircraft installation firing in motion. The solution of the differential equations of motion is carried out by using the Runge-Kutta method. The maximum vertical acceleration was about 5 m/sec2 and almost independent of the fire angle. The horizontal acceleration was about 37 m/sec2. The acceleration values obtained did not exceed the normative ones. The study defined the natural oscillation frequencies for the frame of a flat wagon with lower gravity center. It was established that the critical oscillation frequencies were within the admissible values. The results of the work will contribute to the creation of recommendations on the transportation of military equipment on wagons and the possibility of conducting military operations from them.

Information Length Analysis of Linear Autonomous Stochastic Processes.

When studying the behaviour of complex dynamical systems, a statistical formulation can provide useful insights. In particular, information geometry is a promising tool for this purpose. In this paper, we investigate the information length for n-dimensional linear autonomous stochastic processes, providing a basic theoretical framework that can be applied to a large set of problems in engineering and physics. A specific application is made to a harmonically bound particle system with the natural oscillation frequency , subject to a damping and a Gaussian white-noise. We explore how the information length depends on and , elucidating the role of critical damping in information geometry. Furthermore, in the long time limit, we show that the information length reflects the linear geometry associated with the Gaussian statistics in a linear stochastic process.

Determination of the natural oscillation frequency of the structural unit of covering by the action of the shock load

The article presents the results of experimental studies of the wood-metal spatial structural unit-TTMBF-18.6. We should monition, that wood attracts designers both by its resistance to aggressive media, and by its physical properties and strength characteristics. This material has a high deformability and specific viscosity, which allows it to absorb shocks and vibrations, making it an excellent material for use in regions with increased seismic activity. The aim of the work is to obtain the frequencies of natural vibrations for the subsequent study of the dynamic characteristics of the structure. The article describes the advantages of wooden structures. The methodology of the full-scale experiment and the results of research are given. Our data obtained allow us to study the nature of the stress-strain state of structural elements during dynamic loading and in the future to obtain a dynamic design coefficient, which will help to develop a methodology for calculating structures for dynamic effects.

Establishing patterns in the dynamic loading on the body of a semi­wagon with an elastic middle part of the girder beam

To reduce the dynamic loading and prolong the service life of a semi-wagon's girder beam by improving its fatigue strength, it has been proposed to improve its design. A special feature of the girder beam is that its middle part (the distance between the rear supports of auto-couplings) consists of a U-shaped profile, covered with a horizontal sheet above which an I-beam is located. Elastic elements are placed between the horizontal part of the U-shaped profile's shelf and the sheet. Mathematical modeling was performed to substantiate the proposed technical solution. A mathematical model has been constructed describing the fluctuations of the bouncing wagon. It has been established that the maximum vertical acceleration of the body is about 1.8 m/s 2 (0.18 g), and of the bogie ‒ about 9.0 m/s 2 (0.9 g). Based on our calculations, we can conclude that a wagon's movement is assessed as excellent. In this case, the use of the girder beam with elastic links makes it possible to reduce the dynamic load on a wagon, in comparison with the prototype, by almost 35 %. The main indicators of the strength of the improved load-bearing structure of a wagon have been determined. The maximum equivalent strains occur, in this case, in the upper horizontal sheet of the girder beam, and are 136.0 MPa, which are lower, by 20 %, than those of the prototype wagon. The results of the modal analysis of the load-bearing structure of a semi-wagon taking into consideration the improvement measures have demonstrated that their natural frequencies of oscillations are within the permissible limits. Our research could help reduce the dynamic loading on the load-bearing structures of wagons in operation, as well as design the innovative structures of rolling stock

Theory of determining the frequency of natural oscillations of span structures

Theory of determining the frequency of natural oscillations of span structures

Issues of Multi-Motor Electric Drive Dynamics through the Example of Converter Tilting Mechanism

Many heavy machines and mechanisms of mining and metallurgical industry, for example, basic-oxygen converters (BOCs), are equipped with multi-motor electric drive. Reducing the influence of the disadvantages characteristic of a branched multi-connected system is possible by creating control systems based on mathematical models of the considered electromechanical systems (EMS). The full mathematical model takes into account the number of EMS motors, gear backlashes, elasticity of shafting, the effect of dissipative forces, etc. Disadvantage of this approach is complexity of such models, which leads to high computational costs and time expenditure for their implementation. To analyze dynamic processes arising under acceleration and deceleration conditions of the electromechanical system of the converter tilting mechanism, it is proposed to use a simplified equivalent simulation model, which would take into account changing the EMS natural oscillation frequency for any operation conditions based on process and design features. Based on the simulation model analysis, it was concluded that it is necessary to assess mechanical loads in the system by comparing their current and basis values, as well as taking into account the damping properties of the electric drive. To reduce dynamic loads, it is proposed to form a law of changing the control voltage using an intensity generator, which reduces the risks of occurrence of elastic moments, significantly exceeding those permissible for this class of mechanisms. The results of thermal and vibration diagnostics for assessing malfunctions of key units of the converter tilting mechanism, as well as assessing the system behavior based on the Matlab Simulink model with varying shafting elasticity and normalized gear backlashes, showed significant effect of the latters on the dynamic loads.

Моделирование и исследование различных типов подвесов инерционной массы в чувствительных элементах микромеханических приборов

In microelectromechanical devices and systems (MEMS), capacitive micromechanical accelerometers (MMA) are used in airbag systems, machine vibration monitoring, navigation, seismology, microgravity measurements, etc. The most important structural elements of the sensing element are suspensions, through which the inertial mass is connected to a fixed frame. To ensure reliable operation and stability of sensor parameters, it is necessary to take into account the results of external factors already at the design stage of the sensor structure, especially its sensitive element, and at subsequent stages of the life cycle. In this work, the characteristic structures of suspension elements, which are made of silicon with different crystallographic orientations, are investigated and the results of modeling their most important parameters are presented. The simulation has been performed using the ANSYS program. The natural frequencies of inertial mass oscillations, residual mechanical stresses in the structural elements of silicon sensitive element with different crystallographic orientations have been calculated upon impact (up to 10 000 g). The natural vibration frequency changes and the dynamics of the change in the residual mechanical stress in the suspension elements with a temperature change in the range from +150 to –150 °C for a short time interval of 10 s, which corresponds to thermal shock, investigated. The results of studies of residual mechanical stresses arising upon impact and natural frequencies of inertial mass oscillations have been made it possible to develop recommendations on the choice of the design of suspension elements made of silicon, providing high sensitivity and stability of MMA parameters. It has been established that the use of folded springs with a rectangular or round cross-sectional shape with a suspension element thickness of 40 μm provides the highest temperature stability of the parameters. The results obtained are useful for developing real designs of MMA and other micromechanical devices

Synchronization of Marangoni waves by temporal modulation of interfacial heat consumption

When a thin film consisting of two layers of different liquids is heated from above, some oscillations of its interfaces can appear spontaneously due to the temperature dependence of interfacial tensions (Marangoni convection). These oscillations have a certain natural frequency. We investigate the possibility of changing that frequency by a periodic modulation of heating or cooling of the interface between the liquid layers. We found that in some intervals of the modulation frequency a synchronization occurs: the natural frequency of oscillations is shifted in such a way that it becomes commensurate to the external modulation frequency.

Gas-Babble Oscillations: Resonance Effects in Nonviscous and Newton Media

A linear mathematical model of forced oscillations of a gas bubble in viscous Newtonian fluid is developed in this paper. The natural frequency of oscillations of the gas bubble is found. A numerical analysis of the resonant effects of gas bubble oscillations within the media is carried out and a comparison of the obtained results with the existing classical ones for non-viscous media is discussed.

Searching for the two­frequency motion modes of a three­mass vibratory machine with a vibration exciter in the form of a passive auto­balancer

The dynamics of a three-mass vibratory machine with the rectilinear translational motion of platforms and a vibration exciter in the form of a ball, roller, or pendulum auto-balancer have been analytically investigated. The existence of steady state motion modes of a vibratory machine that are close to two-frequency regimes has been established. At these motions, the loads in an auto-balancer create constant imbalance, cannot catch up with the rotor, and get stuck at a certain frequency. These loads work as the first vibration exciter, thereby exciting vibrations in resonance with the frequency at which loads get stuck. The second vibration exciter is formed by an unbalanced mass on the body of the auto-balancer. The mass rotates at the rotor's rotation frequency and excites faster vibrations with this frequency. The auto-balancer excites almost ideal two-frequency vibrations. Deviations from the two-frequency law are proportional to the ratio of the mass of the loads to the mass of the platform, which hosts the auto-balancer, and do not exceed 5 %. A three-mass vibratory machine has three resonant (natural) oscillation frequencies, q1, q2, q3 (q1).