Frequency Spectrum Of Oscillations Research Articles

Induction Motor Vibrations Caused by Mechanical and Magnetic Rotor Eccentricity

Vibration reduction of induction motors is a significant problem that requires effective models for the effects of mechanical and electromagnetic unbalanced forces. This article presents a mathematical model of dynamics for induction motors with rotor mass eccentricity and static and dynamic magnetic eccentricity. The model allows for the influence of the gyroscopic torque of the rotor and considers the elastic-damping characteristics of each of the stator supports and their location. The model has eight degrees of freedom, which makes it possible to simulate transverse and axial vibrations of various designs’ rotors and housings of induction motors. The results of modeling the dynamics for a three-phase squirrel cage induction motor with 11 kW capacity agreed with those obtained by other authors. Simultaneously, new results were also obtained within the research. The simulation results showed that the static magnetic eccentricity causes the appearance of additional critical speed of the motor, and its value decreases in proportion to the growth of the number of pole pairs. The change of the moment of inertia of the motor at a mismatch of the main axis of symmetry of the stator and the rotor axis of rotation allowed for obtaining an actual frequency spectrum of free oscillations, including the rotational motion of the stator. Since the actual static magnetic eccentricity can additionally increase at operating frequencies due to the increase of bearing clearance caused by dynamic unbalanced load, it should be considered in the analysis of unbalanced magnetic pull. The angle of static magnetic eccentricity significantly affects the magnitude of radial vibrations. This feature should also be considered when selecting the locations of balancing weights during the rotor balancing procedure.

Vibration spectra of benzene-like models with Hooke’s law interactions

The harmonic oscillations of a spring-ball model of benzene-like nanosystems with Hooke’s law interactions between nearest, second, and third neighbors are explored. We show that in the cylindrical coordinates the dynamics of this cyclic hexagonal system is described by the Lagrange equations similar to those of the one-dimensional two-component crystal model. We demonstrate that the vibration frequencies of the hexagonal model lie on the branches of the dispersion law of the associated lattice model, and their positions are determined by the cyclic Born-Von Karman condition. The hexagonal model is generalized to one describing the benzene molecule and the fully deuterated and halogenated benzenes. The effect of hybridization of vibration modes and pushing apart of spectral branches in the crossover situation is revealed. All the discrete frequency spectrum and normal modes of oscillations and their explicit dependencies on all the constants of elastic interactions are exactly found.

Quasi-periodic oscillation characteristics of a nonlinear energy sink system under harmonic excitation

Quasi-periodic oscillation characteristics of a nonlinear energy sink (NES) system under harmonic excitation are studied in this work. It is found that there exist uniformly distributed sidebands in frequency spectra of quasi-periodic oscillations. The traditional incremental harmonic balance (IHB) method and the IHB method with two time-scales are used to obtain accurate frequency components and amplitudes of periodic responses and two different quasi-periodic oscillations of the system, respectively, with variations of the external excitation frequency and amplitude. The two different quasi-periodic oscillation characteristics are analyzed; energy absorption of the NES system under different excitation frequencies and amplitudes is also analyzed. Stability of quasi-periodic solutions obtained from the IHB method with two time-scales is analyzed by the Floquet theory. Analytical results obtained from the traditional IHB method and the IHB method with two time-scales agree very well with those from numerical integration using the fourth-order Runge–Kutta method. Results show that the efficiency of energy absorption of a strongly quasi-periodic oscillation is greater than those of a periodic response and a weakly quasi-periodic oscillation.

Instability and halo for double-periodic focusing structure

This paper presents a comprehensive investigation into the beam transport issue in the double-period focusing structure of low energy proton/ion cryogenic superconducting linear accelerators (CSLA). The structure, consisting of a large period corresponding to a cryogenic refrigeration module and a small period of focusing solenoid, is modeled with solenoids and drifts to study the impact of higher-order resonances on beam halo in transverse phase spaces without considering the acceleration. Numerical simulation reveals that the double-period structure can cause beam envelope instability even when the small periodic zero-current phase advance (σ0f) is less than 90°, making it more susceptible than the fully periodic structure. The study identifies that 2:1 resonance remains a major factor contributing to the formation of beam halo, particularly in the double-period structure. Furthermore, through exploration of different matching modes, the paper elucidates that not only 2:1 resonance but also higher-order resonances can lead to beam halo formation for space charge dominated beam. The oscillation frequency spectrum of the matched envelope is obtained using fast Fourier transform. It is recommended that particle oscillation frequencies avoid matching the identical fundamental frequency and its multiples of the matched envelope. Overall, the findings of this study can serve as valuable references for the design and optimization of CSLA.

СПЕКТР ЧАСТОТ СОБСТВЕННЫХ КОЛЕБАНИЙ И АНАЛИТИЧЕСКАЯ ОЦЕНКА ПЕРВОЙ ЧАСТОТЫ ПЛОСКОЙ МОДЕЛИ КОНСОЛЬНОЙ ФЕРМЫ

A formula is derived for the dependence of the lower limit of the main natural frequency of a statically determined cantilever truss on the number of panels. The lattice of the truss is cruciform. The mass of the truss is concentrated in its nodes. Vertical vibrations of nodes are considered. The forces in the bars for calculating the stiffness matrix of the structure according to the Maxwell-Mohr formula are found by cutting out the nodes. Equilibrium equations for nodes are compiled and solved in symbolic form in the Maple computer mathematics system. To determine the lower limit of the first natural frequency of the structure, the Dunkerley method is used. The approximate analytical solution is compared with the lowest frequency of the entire spectrum of oscillation frequencies found numerically. The comparison shows the high accuracy of the resulting formula. As the number of panels increases, the error of the approximate solution decreases. Features of the spectrum of a family of trusses of different orders are revealed. Two spectral constants are found.

Bayesian inference of a spectral graph model for brain oscillations

The relationship between brain functional connectivity and structural connectivity has caught extensive attention of the neuroscience community, commonly inferred using mathematical modeling. Among many modeling approaches, spectral graph model (SGM) is distinctive as it has a closed-form solution of the wide-band frequency spectra of brain oscillations, requiring only global biophysically interpretable parameters. While SGM is parsimonious in parameters, the determination of SGM parameters is non-trivial. Prior works on SGM determine the parameters through a computational intensive annealing algorithm, which only provides a point estimate with no confidence intervals for parameter estimates. To fill this gap, we incorporate the simulation-based inference (SBI) algorithm and develop a Bayesian procedure for inferring the posterior distribution of the SGM parameters. Furthermore, using SBI dramatically reduces the computational burden for inferring the SGM parameters. We evaluate the proposed SBI-SGM framework on the resting-state magnetoencephalography recordings from healthy subjects and show that the proposed procedure has similar performance to the annealing algorithm in recovering power spectra and the spatial distribution of the alpha frequency band. In addition, we also analyze the correlations among the parameters and their uncertainty with the posterior distribution which cannot be done with annealing inference. These analyses provide a richer understanding of the interactions among biophysical parameters of the SGM. In general, the use of simulation-based Bayesian inference enables robust and efficient computations of generative model parameter uncertainties and may pave the way for the use of generative models in clinical translation applications.

Anomalous Hall effect and two-dimensional Fermi surfaces in the charge-density-wave state of kagome metal RbV3Sb5

AV3Sb5 (A = Cs, K, Rb) is a recently discovered superconducting system (–2.5 K) in which the vanadium atoms adopt the kagome structure. Intriguingly, these systems enter a charge-density-wave (CDW) phase (–100 K), and further evidence shows that the time-reversal symmetry is broken in the CDW phase. Concurrently, the anomalous Hall effect (AHE) has been observed in KV3Sb5 and CsV3Sb5 inside the novel CDW phase. Here, we report a comprehensive study of a high-quality RbV3Sb5 single crystal with magnetotransport measurements. Our data demonstrate the emergence of the AHE in RbV3Sb5 when the CDW state develops. The magnitude of the anomalous Hall resistivity in the low temperature limit is comparable to the reported values in KV3Sb5 and CsV3Sb5. The magnetoresistance channel further reveals a rich spectrum of quantum oscillation frequencies, many of which have not been reported before. In particular, a large quantum oscillation frequency (2235 T), which occupies ∼56% of the Brillouin zone area, was recorded. For the quantum oscillation frequencies with sufficient signal-to-noise ratio, we further perform field angle-dependent measurements, and our data indicate two-dimensional Fermi surfaces in RbV3Sb5. Our results provide indispensable information for understanding the AHE and band structure in kagome metal AV3Sb5.

Analysis of the characteristics of the direct current discharge in the electrolyte medium at low pressure

The results of experimental studies of direct current electric discharge in the gas-liquid medium of an electrolyte with bubbles for various interelectrode distances (l=50-150 mm) inside a dielectric tube are presented. The presence of a bubble structure with microdischarges affects the nature of the discharge current and voltage ripples. The frequency spectrum of voltage and current oscillations of the discharge was established using the fast Fourier transform. Based on the analysis of experimental data, a mechanism for the development of a direct current electric discharge with a gas-liquid medium with air bubbles and microdischarges has been established.

The Use of Exchange Coupled Atom Qubits as Atomic-Scale Magnetic Field Sensors.

Phosphorus atoms in silicon offer a rich quantum computing platform where both nuclear and electron spins can be used to store and process quantum information. While individual control of electron and nuclear spins has been demonstrated, the interplay between them during qubit operations has been largely unexplored. This study investigates the use of exchange-based operation between donor bound electron spins to probe the local magnetic fields experienced by the qubits with exquisite precision at the atomic scale. To achieve this, coherent exchange oscillations are performed between two electron spin qubits, where the left and right qubits are hosted by three and two phosphorus donors, respectively. The frequency spectrum of exchange oscillations shows quantized changes in the local magnetic fields at the qubit sites, corresponding to the different hyperfine coupling between the electron and each of the qubit-hosting nuclear spins. This ability to sense the hyperfine fields of individual nuclear spins using the exchange interaction constitutes a unique metrology technique, which reveals the exact crystallographic arrangements of the phosphorus atoms in the silicon crystal for each qubit. The detailed knowledge obtained of the local magnetic environment can then be used to engineer hyperfine fields in multi-donor qubits for high-fidelity two-qubitgates.

Research of the Stress-Strain State for Steel Support Structures of Nuclear Power Plant Components under Seismic Loads

Seismic resistance of equipment and piping of nuclear power plant units is determined, particularly, by seismic resistance of their steel support structures. A significant number of these structures are located in the reactor building of nuclear power plants and belong to seismic resistance categories I and II. Therefore, such support structures of nuclear power plant equipment and piping, in general, shall perform their functions under seismic hazards that correspond to the safe shutdown earthquake and design-basis earthquakes, respectively.
 Steel support structures of serial equipment (piping valves, electric and pneumatic drives of piping and pump valves, expansion tanks, etc.) are often designed “on site” in the limited conditions of their actual location. Therefore, it is necessary to design steel support structures of a number of equipment taking into account the fact that it can be connected, in particular, to existing piping with their actual routing. In connection with the above, the research of operation for such support structures under seismic loads is relevant.
 The article presents the research results for the spectrum of natural oscillation frequencies of the equipment support structure, and the stress-strain state of the considered structure under seismic loads is determined. At the same time, the parameters during normal operation and maximum design basis accident at the nuclear power plant power unit are considered. The calculated combination of loads, which simultaneously includes two episodic impacts (maximum design basis accident and an earthquake) is considered.

Digital technology for spectral analysis of oscillation parameters

Performing the Fourier analysis of the harmonic composition of oscillations is an effective approach to the study of vibration processes in machines and mechanisms. This method of express control remains relevant and highly demanded in the acoustic diagnostics of machines due to its relatively high informativeness. The expansion of its analytical capabilities is implemented by introducing additional means for digital processing of vibration signals, including smart systems. The objective of this work consists in creating a digital method for spectral analysis of vibration signals, the implementation of which would be possible with the use of smart devices. This work presents a method of polyharmonic approximation of the parameters of the signals reflecting oscillatory processes in machines based on the additive combinations of sinusoidal functions. The technology of truncation of the time discretised decomposition of the above signals into a Fourier series is implemented using the Rayleigh theorem and the Lyapunov – Parseval equality. The distortion of the frequency spectrum of oscillations is eliminated by suppressing its side lobes using window filters. To compare the efficiency of different windows, the following special parameters are used: width of the main lobe of the frequency spectrum; coefficient of relative expansion of the main lobes; maximum relative level of side lobes; coefficient of relative attenuation of signal energy. In so doing, the windows of Hanning, Nuttall, Hamming, Barlett were considered, and the parameters of a rectangular window were taken as basic values. The limitations of the digit capacity of analogto-digital signal converters depending on the required accuracy of maintaining the energy balance when truncating the discrete Fourier expansions have been determined. An example of implementation of the digital technology of spectral analysis of the parameters of oscillatory processes is given.

Impact of charge noise on electron exchange interactions in semiconductors

The electron exchange interaction is a promising medium for the entanglement of single-spin qubits in semiconductors as it results in high-speed two-qubit gates. The quality of such entangling gates is reduced by the presence of noise caused by nearby defects acting as two-level fluctuators. To date, the effect of charge noise has been calculated assuming a Gaussian distribution of exchange interaction frequencies between the qubits equivalent to a linear coupling of charge noise with the exchange interaction. In reality the coupling can differ significantly from this linear-coupling approximation depending on the inter-qubit tunnel coupling, detuning of the qubit system, and the magnitude of charge noise. We derive analytical expressions for the frequency spectra of exchange oscillations that encompasses both linear and non-linear coupling to charge-noise. The resulting decoherence times and decay profiles of the exchange oscillations vary considerably. When compared with recent experiments our model shows that non-linear charge-noise coupling is significant and requires consideration to characterise and optimise exchange-based entangling gates.

Determination of natural vibration frequencies of reinforced cylindrical shell

Free vibrations of a reinforced cylindrical shell filled with liquid are investigated. The case of an orthotropic shell is considered when the cord filament is placed symmetrically with respect to the meridian of the shell. The motion of a fluid is potential and is described by a wave equation. The fluid moves without separation from the walls of the cylinders. The fluid pressure is taken into account in the equations of motion of the shells, and the velocities of the fluid and the shell are equalized at the boundaries. Representing a solution in a harmonic form reduces to a system of transcendental equations. Comparison of the solutions of the problems without a liquid and with a liquid shows the dependence of the frequency of the system without a liquid at the frequency of the system with the liquid. An inverse method is proposed for solving the equation. The inverse method for solving the problem has made it possible to construct a more accurate frequency spectrum of free oscillations of the system. For some values of the system parameters, the natural frequencies of the cylinder are determined.

EXPERIMENTAL RESEARCH INTENSITY OF OSCILLATIONS AGRICULTURAL MACHINE-TRACTOR UNITS

Smoothness of movement of agricultural units is one of the important operational indicators of their work which is estimated on influence of fluctuations (translational vertical, cross, angular longitudinal, etc.) The article presents the method and results of experimental assessment of the smoothness of the movement of the bridge agricultural unit, which moves in the footsteps of a constant technological track. Studies of the smoothness of the bridge unit showed that the graphs of normalized correlation functions of vertical oscillations of the bridge agricultural tool developed by us in its motion in the wake of a constant technological track is characterized by a function containing along with random components harmonic, which are expressed by attenuating periodic oscillations. The frequency spectrum of oscillations of the agricultural tool core is concentrated in the range from 0 to 20 s–1, which agrees with the frequency range 0…0.3 cm−1 in which the variances of oscillations of the irregularities of the profile of the traces of the technological track are concentrated. The length of the correlation connection is approximately 0.25 s, which is equal to 0.25 m at the speed of the agricultural tool within 1.0 m / s.The obtained result is explained by the fact that the main spectrum of oscillations of the profile irregularities has a periodicity that corresponds to the step of ground engagement of the tires of the wheels of the agricultural tool. The research confirmed the effectiveness of the method of estimating the intensity of vertical oscillations of an agricultural unit by a measuring and registration complex based on a tablet computer with Android operating system with built-in accelerometer sensors and Accelerometer Meter application.

SPECTRUM OF OWN FREQUENCIES OF A SPATIAL SURFACING GIRDER

Statement of the problem. The scheme of a statically definable girder of a spatial rectangular surfacing is discussed. The problem is to identify the formula for the dependence of the lower estimate of the first frequency of the natural oscillations of the structure by means of the Donkerley method on the number of panels. The truss has supports on the sides and consists of separate rod cells connected in pyramids. Results. Based on the analysis of the sequence of analytical solutions for the first frequency of girders with a different number of panels by induction, the coefficients in the desired formula are derived. The common members of the sequences of coefficients are found as solutions of homogeneous recurrent equations formed according to the results of the calculations using Maple operators. The resulting dependences are obtained in the form of polynomials by the number of panels. A comparison of the analytical solution with the numerical one is provided.Conclusions. An algorithm for deriving an analytical estimate of the fundamental frequency of oscillations of a spatial structure depending on the number of panels, mass, size, and elastic properties of the material is shown. The spectrum of oscillation frequencies of the structure is analyzed. The resulting dependences can be employed in seismic and structural optimization problems.

An Approach to Identify Circulating Tumor Cell Using Ring Resonator Type of Electrode Using Oscillation Technique at Centimeter Frequency Bands

A ring-resonator type of electrode (RRTE) has been proposed to detect the circulating tumor cell (CTC) for evaluation of the current cancer progression and malignancy in clinical applications. Main emphasis is placed on the identification sensitivity for the lossy materials that can be found in biomedical fields. At first, the possibility of the CTC detection was numerically considered to calculate the resonant frequency of the RRTE catching the CTC, and it was evident that the RRTE with the cell has the resonant frequency inherent in the cell featured by its complex permittivity. To confirm the numerical consideration, the BaTiO3 particle, whose size was similar to that of the CTC, was inserted in the RRTE instead of the CTC as a preliminary experiment. Next, the resonant frequencies of the RRTE with internal organs of the beef cattle such as liver, lung, and kidney were measured for evaluation of the lossy materials such as the CTC, and degraded Q curves were observed because the Q-factors inherent in the internal organs were usually low due to the poor loss tangents. To overcome such difficulty, the RRTE, the oscillator circuit consisting of the FET being added, was proposed to improve the identification sensitivity. Comparing the identification sensitivity of the conventional RRTE, it has been improved because the oscillation frequency spectrum inherent in an internal organ could be easily observed thanks to the oscillation condition with negative resistance. Thus, the validity of the proposed technique has been confirmed.

Oscillations of {B}_s^0 Mesons as a Probe of Decays with Unreconstructed Particles

A new experimental technique to study the decays of {B}_s^0 mesons into final states involving unreconstructable particles is proposed. The method uses a characteristic feature of fast flavour oscillations of {B}_s^0 mesons. Analysis of the oscillation-frequency spectrum of partially reconstructed flavour-tagged {B}_s^0 decays provides information about the mass spectrum of unreconstructed decay products and suppresses any background that does not come from the decays of {B}_s^0 mesons.

ІДЕНТИФІКАЦІЯ ОБ’ЄКТІВ МАШИНОБУДУВАННЯ ЗА КІЛЬКОМА КІЛЬКІСНИМИ ОЗНАКАМИ ОДНОЧАСНО

Показано, що діагностика об'єктів машинобудування передбачає обґрунтування розширення застосовуваних фізичних ефектів, орієнтованих, в першу чергу, на неруйнівного контролю параметрів продукції машинобудування. На підставі досліджень, які показують перспективність експериментальних і теоретичних доказів, доведена доцільність пошуку підтвердження інформативності частотних спектрів резонансних акустичних сигналів досліджуваних об'єктів, порушених широкосмуговими резонаторами рівній амплітуди в акустичному діапазоні. Надані прикладі застосування широкосмугових випромінювачів наноамплітудних впливів на досліджувані об'єкти з метою акустичної спектроскопії для створення їх ідентифікаційних моделей. Для практичного використання експериментальних результатів для ідентифікації розмірних і фізико-механічних характеристик станів діагностованих об'єктів авторами застосовані нейромережні моделі. Такі моделі служать практичним цілям діагностики станів об'єктів на основі частотних спектрів власних резонансних коливань. Доведено, якщо діагностика об'єкта проводиться щодо опорного сигналу у вигляді широкосмугового впливу постійної амплітуди, то такий підхід дозволяє нормувати вихідні діагностичні сигнали щодо опорного сигналу. представлені ідентифікаційні моделі, побудовані на нейромережному базисі, показали реальну можливість їх використання для створення системи діагностики об'єктів за кількома кількісними ознаками. Причому, кількість таких ознак, які можна контролювати одночасно, практично, не обмежена. Авторами роботи проведені додаткові дослідження, які показали можливість одночасного контролю не тільки геометричних характеристик об'єктів, а й їх фізико-механічних характеристик, включаючи показники напруженого стану, твердості і т.ін..

ДИНАМІКА КОЛИВАННЯ СИСТЕМИ "РІДКА ВАННА - ФУРМА" ПРИ ІНЖЕКЦІЙНІЙ ОБРОБЦІ РОЗПЛАВУ В КОВШІ

The aim of the study was to evaluate the influence of key waveform factors on the dynamics of the process during injection molding of cast iron with granular magnesium in ladles, their significance and relationship between them. Based on the theories of wave motion of liquid layers, a mathematical model has been developed that allows to investigate the oscillatory processes in the ladle during the processing of cast iron melt with granular magnesium. The model involved the processing of cast iron by injection of granular magnesium through the tuyeres of devices that are immersed in the melt. The oscillating system "Liquid bath - lance" is considered on the example of the bath of a heavy - duty filling bucket with its own frequency - 0.47 Hz. The influence of the most probable oscillation sources (natural frequency of the lance oscillation and the frequency of the conditional source) on the amplitude-frequency oscillations of the system elements is calculated. It is established that in addition to the natural frequencies of these elements, the system has two more natural oscillations. Given that the mass of the melt is much greater than the mass of the lance, it practically determines the behavior of the system during its excitation. That is, the system responds only to those excitations in which the frequency is close to the natural frequency of the liquid bath. In turn, it is shown that the natural frequency of the bath is largely determined by its diameter at the top. In practice, it is necessary to know the resonant frequencies of the liquid bath, the tuyere device, as well as all other sources of oscillations (gas jet decay, and oscillations of pop-up bubbles). Accordingly, it is necessary to try to dampen the amplitude with this dangerous resonant frequency. To reduce the oscillation amplitude of the bath surface when treating cast iron with granular magnesium, it is recommended to first estimate the natural resonant frequency of the liquid bath, and then select design solutions and processing parameters, avoiding dangerous frequencies close to the natural frequency of the bath. However, it should be noted that the spectrum of oscillation frequencies in the purl zone is quite wide and, of course, contains dangerous low frequencies.

Numerical simulation of flow-induced acoustic oscillations around circular cylinders

Questions of numerical simulation of acoustic oscillations generation modes in the liquid flow around the groups of two and three circular cylinders are considered. In mining industry the processes of hydrodynamic impact on gas-saturated porous media produce significant acoustic emission both at the injection stage and at the liquid discharge stage. Simulation of such kind of acoustic processes is one of the actual problems of theoretical and applied fluid mechanics and under certain assumptions could be reduced to the flow around a group of bodies. Two approaches for numerical simulation of the acoustic oscillations generation induced by the flow around circular cylinders based on numerical solution of the Navier-Stokes equations for compressible and incompressible flows closed by differential model of turbulence and complemented by acoustic analogy equations have been developed. For laminar flows, eight different modes that fundamentally differ both in the flow structure and in the frequency spectrum of parameter oscillations have been identified. For turbulent flows, the classification criteria for the three main frequency modes are presented. Acoustic data are obtained using the Direct Noise Computation technology and acoustic analogies as well.