Free Oscillations Research Articles

INCREASING THE RADIATION SAFETY OF NUCLEAR POWER PLANTS USING THE METHOD OF CONTROLLING THE TIGHTNESS OF FUEL ELEMENTS

The problem of monitoring the tightness of fuel elements at the stage of their manufacture to improve the radiation safety of nuclear power plants is considered. A vibration method is proposed for non-destructive testing of the tightness of cylindrical fuel rods. The method makes it possible to perform accelerated testing of a batch of fuel rods and remove samples with gross leakage under conditions of mass production. A description of the method is given, a mathematical model of free vibrations of a fuel element is developed. The time dependences of the pressure and the period of free oscillations of the fuel element were obtained by calculation. The assessment of the influence of the inhomogeneity of the fuel element structure on the test result is carried out. Inhomogeneity causes an error in measuring the oscillation period up to 1%, which can lead to a false result. Three-dimensional plots were constructed, reflecting the main form of free vibrations of a homogeneous and inhomogeneous section of a fuel element. On the basis of the performed assessment, recommendations were given for conducting fuel rod tightness control, excluding a false result.

Time‐ and frequency‐domain analyses of the hydraulic system using a discrete numerical scheme based on equivalent circuit modelling

Mathematical modeling is widely used for the time-and frequency-domain analysis of hydraulic systems. To explore the complicated hydraulic transients of the piping system under various operating conditions, different formulations of the equivalent circuit model (ECM) are systematically discussed in this study. In particular, comparative studies are performed regarding the restrictions on the tempo-spatial discretization of the time-domain ECM and the state-of-the-art numerical schemes. In addition, the eigenanalysis of the free oscillation response and frequency features of the forced oscillation response were discussed in detail, respectively. Furthermore, the influence of spatial discretization on the frequency response precision for ECM is also quantified. Analytical results indicate that the ECM can achieve satisfactory performances in both numerical simulation and frequency analysis with affordable computational effort and relatively loose tempo-spatial discretization restriction.

Free Core Nutation and Its Relation to the Spin-over Mode

The time-varying response of Earth’s and other planets’ rotation to external gravitational torques depends strongly on their internal structure. In particular, the existence of the mode known as the free core nutation in the fluid core is known to amplify the forced nutations in the near-diurnal retrograde frequency band (as measured in the planetary frame of reference). Due to their proximity in shape and frequency, this mode is sometimes equated with the so-called spin-over mode, which denotes the free oscillation of a steadily rotating ellipsoidal fluid core. Through a careful study of the freely rotating two-layer planetary model with a rigid mantle and an inviscid fluid core, we show that the spin-over mode frequency corresponds to that where the sum of the external and internal torques on the mantle is balanced, causing it to rotate steadily. The presence of dissipation at the core−mantle boundary causes the free core nutation to become damped and slightly offsets its resonance frequency. We show that this offset, which is ≈−1 day for Earth, can be interpreted as the result of the proximity of the free core nutation frequency to that of the spin-over mode, which now corresponds to a minimum in the magnitude of the transfer function for nutations. We also show how this proximity leads to a slightly lower quality factor for the resonance than that computed from the usual formula. We conclude by discussing possible implications of this mechanism for Mars, the Moon, and the long-term evolution of Earth.

Vibration-induced detachment of droplets on superhydrophobic surfaces

Vibration is a robust and efficient method for droplet removal from superhydrophobic surfaces. In the present work, we experimentally investigated the dynamics of droplets on vibrating superhydrophobic surfaces, and established a mass-spring-damper theoretical model, to clarify the underlying physics of vibration-induced droplet detachment. Different droplet oscillation patterns were experimentally observed, namely, the droplet motion is in the same/opposite direction with the substrate when the vibration frequency is less/higher than the resonance frequency, respectively, and the transition occurs at the resonant frequency. The motion of the droplet is found to be composed of a transient response by the droplet free oscillation and a steady-state response by vibrating substrates. The critical condition for droplet detachment was identified to be the droplet energy (sum of the surface energy and kinetic energy) exceeds the surface adhesion energy. At the resonance frequency, the vibrational energy of the substrate is progressively accumulated in the droplet with the highest energy maintenance efficiency, and a small amplitude of vibration could therefore yield droplet detachment. The separation time shortens with the vibration amplitude and minimizes at the resonance frequency at a given amplitude. Our findings are helpful for the utilization of vibrating superhydrophobic surfaces for droplet removal.

Regenerative Effect of Low-Intensity Pulsed Ultrasound and Platelet-Rich Plasma on the Joint Friction and Biomechanical Properties of Cartilage: A Non-traumatic Osteoarthritis Model in the Guinea Pig.

This study was aimed at investigating the effects of platelet-rich plasma (PRP) and low-intensity pulsed ultrasound (LIPUS) on the joint friction parameters and biomechanical properties of articular cartilage in a non-traumatic knee osteoarthritis (OA) model. Fifty adult male Dunkin Hartley guinea pigs were randomly divided into five groups: control, OA60, OA+US, OA+PRP and OA+US+PRP). Non-traumatic knee OA was induced with a single dose of 3 mg of mono-iodoacetate (MIA) by intra-articular injection. Intra-articular PRP was injected twice in the OA+PRP and OA+US+PRP groups. LIPUS was delivered in 10 sessions in the OA+US and OA+US+PRP groups. By use of the pendulum free oscillation test, joint friction (coefficient of friction) was measured. In addition, the instantaneous elastic modulus and aggregate modulus were measured using the stress-relaxation test. MIA injection decreased cartilage thickness, instantaneous elastic modulus and aggregate modulus, and increased joint friction. The friction coefficients in the OA+US and OA+US+PRP groups reached near-normal values, and there was no significant difference compared with the control group (p=0.232 and p=0.459, respectively). The instantaneous elastic modulus and aggregate modulus in the OA+US group increased significantly compared with the OA+PRP group (p < 0.05). It seems that both LIPUS and PRP injection effectively improved joint lubrication, but LIPUS was superior to PRP in improving the mechanical properties of the articular cartilage.

Global residue harmonic balance method for strongly nonlinear oscillator with cubic and harmonic restoring force

Abstract This paper focuses on the numerical investigation of a strongly nonlinear oscillator with cubic and harmonic restoring force. We transform this oscillator as a free damped cubic-quintic Duffing oscillator equation by Taylor approximation. The approximated solutions with high accuracy are provided by using the global residue harmonic balance method (GRHBM) without any discretization or restrict assumptions. The sensitive analysis of the approximation or the frequency with respect to the amplitude is considered in detail. Numerical comparisons with Runge–Kutta method and harmonic balance method are given to show the efficiency and stability of GRHBM.

Strength analysis of prestressed vertical cylindrical steel oil tanks under operational and dynamic loads

This paper reports a study into the effect of the winding type on the stressed-strained state of the wall of a steel cylindrical tank filled with oil to the predefined level. The shapes of free oscillations of oil in the tank and the effect of the winding type on the natural frequencies of the structure were analyzed. Stress in the tank wall was estimated on the basis of finite-element simulation of the deformation of a three-dimensional structural model under the influence of distributed oil pressure on the inner surface of the wall and stresses on the outer surface of the wall. The stresses were induced by the winding of various types, taking into consideration the level of oil loading, the winding step of the winding, and the mechanical characteristics of the thread. The stressed-strained state of a cylindrical tank with winding was investigated at its full filling with oil, half-filling with oil, and without oil. Three winding options were simulated: single, double, and triple intervals. Two types of winding were considered: made from high-strength steel wire and made from composite thread. It was established that when winding the tank wall with steel wire at a triple interval, the stress in the structure does not exceed 34.2 % of the yield strength. At the same time, the height of oil loading does not significantly affect its strength. Applying a composite thread leads to an increase in the stress of up to 47.2 % of the yield strength but makes it possible to reduce the mass of the tank with winding. When winding with a composite thread at a triple interval, the mass of the structure increases by only 3.6 %. The results reported here make it possible to effectively use pre-stress in order to improve the strength and dynamic characteristics of the studied structures, taking into consideration their windings made of different materials

DETERMINATION OF NATURAL FREQUENCIES AND FORMS OF FREE VIBRATIONS OF THE GRATE OF THE RAW COTTON CLEANER

The article discusses the operation of the grate proposed by the authors with grates made of composite material, with a polyamide matrix and a filler of basalt fibre. Experimental grates are mounted on elastic rubber supports with non-linear rigidity. On the basis of finite element modelling, the analysis of the forms and natural frequencies of free oscillations of the grate of cotton cleaner from large litter was carried out. It is shown that the first 12 natural frequencies are located in a narrow range from 2.579 to 2.692 Hz. This is due to the design features of the grate. It is shown that during operation the grate performs forced oscillations with frequencies 45…75 Hz.

New insights on rocking of rigid blocks: Analytical solutions and exact energy‐based overturning criteria

AbstractIn this paper, the underlying energy flow in rocking dynamics of rigid blocks is utilized to elucidate their response details and overturning conditions. Based merely on the law of the conservation of energy, the exact criteria for a rigid block to overturn in the free vibration regime are established for the first time in the context of both nonlinear and linear theory. That is, if the initial conditions of the free oscillation fall within the prescribed stable libration region, then it is a priori determined that the block will not overturn and vice versa. The analytical solution to the nonlinear free rocking problem is also derived, utilizing integration techniques originating from the solution of the nonlinear pendulum. Regarding the forced rocking problem, an approximate analytical solution is presented based on a Taylor series expansion of the equation of motion. Moreover, employing the newly derived overturning criterion richer pulse‐type overturning spectra are constructed, revealing stability and instability regions that had never been shown before in the literature. The new characteristics of the overturning spectra are elucidated using color maps. Finally, some new results concerning the design of solid blocks against rectangular and half‐sine acceleration pulses are presented.

A building energy models calibration methodology based on inverse modelling approach

Nowadays, building energy models (BEMs) are widely used, particularly in the assessment of energy consumption in buildings to address the potential savings that can be generated. The realisation of a dynamic energy model based on high-fidelity physics (white-box models) requires a tuning process to fit the model to reality, due to many uncertainties involved. Currently some research trends try to reduce this performance gap by modulating different types of experimental parameters such as: capacitances or infiltration. The EnergyPlus simulation software, in its latest versions, has implemented an object: HybridModel:Zone that calculates the infiltration and internal mass of buildings using an inverse modelling approach that employs only the measured indoor temperature data to invert the heat balance equation for the zone under study. The main objective of this paper is to reduce the execution time and uncertainties in the development of quality energy models by generating a new calibration methodology that implements this approach. This uses, as a starting point, a research created by the authors of this study, which was empirically and comparatively validated against the energy models developed by the participants in Annex 58. It is also worth highlighting the empirical validation of the HybridModel:Zone object, since it was activated in all scenarios where its execution is possible: periods of seven days or more of free oscillation and periods in which the building is under load. The findings are promising. The data generated with the new methodology, if compared with those produced by the baseline model, improve their resemblance to the real ones by 22.9%. While those of its predecessor did it by 15.6%. For this study, the two dwellings foreseen in Annex 58 of the IEA ECB project have been modelled and their real monitoring data have been used.

Hydroelastic vibrations of shells of revolution under combined vertical and horizontal loadings

The operation of modern structures occurs under conditions of high technological loads. Shells of rotation are among the most applicable structural elements. The operating conditions of such elements provide for the influence of the environment such as the interaction of elastic shell elements with liquid or gas. The oscillations of the elastic shell of rotation, which are partially filled with liquid, under external loads in the vertical and horizontal directions simultaneously, are considered in the paper. The liquid is supposed to be ideal and incompressible, and its motion under the applied loads is irrotational. This allows us to introduce the velocity potential to calculate the pressure of the fluid on the surface of the shell and determine the function which describes the level of the free surface lift. At the first stage, the frequencies and forms of free oscillations of the shell with liquid are determined. These frequencies are usually divided into two separate spectra: the free surface vibration frequency and the elastic wall vibration frequency. The boundary element method is used for numerical implementation. It is found that for sufficiently thin elastic tank walls, the fundamental frequency of the coupled vibrations can be much lower than the frequency of the fluid in a shell with rigid walls. As the tank wall thickness increases, this effect becomes insignificant, and the lower vibration frequency of the shell with liquid approaches the vibration frequency of the liquid in a rigid tank. The second stage of the study is related to the analysis of combined horizontal and vertical loads. The cases when the load frequencies are close to the fundamental frequency of sloshing and to the lower frequency of vibration of elastic walls are considered. The effect of parametric resonance has been investigated. The influence of the presence of partitions on the motion of the shell with the liquid at free and forced oscillations has been found out.

Numerical simulation on free oscillation interfacial dynamics of single-core compound droplet driven by shell deformation

Compound droplets are often used as microcontainers in biomedical, material encapsulation, and so on, and a good understanding of their free oscillatory behavior is essential for controllable product preparation. Herein, the free oscillatory deformation behavior of single-core compound droplet induced by shell deformation is studied computationally using the volume-of-fluid (VOF) method. The effects of the inner droplet diameter, the outer droplet initial deformation and physical properties are considered. The results show that outer droplet oscillation has obvious periodicity and damping attenuation mechanism, and the inner droplet has two oscillation forms: large-deformation forced oscillation and small-deformation free oscillation. The oscillation period is positively correlated with the inertial force, while the damped attenuation mechanism is dominated by the viscous force, and the presence of the inner droplet and the increase of its diameter will enhance the inertial and viscous forces of the outer droplet. The deformation degree of the inner and outer droplet is related to the energy transfer between the two and the initial interfacial energy, which is generally greater for the outer droplet than for the inner droplet, but the larger diameter ratio makes the opposite situation, and the critical value lies between the diameter ratio of 0.625–0.75. The obtained results will provide the possibility to control the morphological structure of the compound droplets after preparation.

Dynamics of saline oscillator under sinusoidal and bounded noise excitation

In this paper, we investigate the effects of harmonic and bounded noise excitations on the saline oscillator dynamics. To this end, we first of all modify an existing coupled saline oscillators model to account for an external excitation. We next analytically derive the system response to harmonic driving by the mean of the harmonic balance method. Then we study the effects of the excitation amplitude and frequency on the dynamic of a sole oscillator and two coupled oscillators. We find that over a wide range of the excitation parameters, the oscillator exhibits period- T oscillations whose amplitude increases with the excitation amplitude. This result is supported by simulations. Moreover, simulations show that periodically excited saline oscillator mainly exhibits, in addition, subharmonic and quasi-periodic oscillations. The above oscillatory modes are determined by the values of the excitation amplitude and frequency. By the mean of stochastic averaging method and Monte-Carlo simulations, the probabilistic response of the oscillator under bounded noise excitation is determined. We find that the saline oscillator does not display the stochastic P-bifurcation when its physical parameters remain in appropriate ranges. However, we find that the bounded noise excitation affects the oscillation period, midpoint and amplitude. Both harmonic and random excitations can be used to induce oscillations in the parameter region where free oscillations are dead.

Investigation of nonlinear squeeze-film damping involving rarefied gas effect in micro-electro-mechanical systems

In this paper, the nonlinear squeeze-film damping (SFD) involving rarefied gas effect in the micro-electro-mechanical systems (MEMS) is investigated. Considering the motion of structures (beam, cantilever, and membrane) in MEMS, the dynamic response of the structure is affected greatly by the SFD. In the traditional model, a viscous damping assumption that the damping force is linear with the moving velocity is used. As the nonlinear damping phenomenon is observed for a micro-structure oscillating at a high velocity, this assumption does not hold and will cause error results for predicting the response of the micro-structure. Meanwhile, due to the small size of the device and the low pressure of the encapsulation, the gas in MEMS is usually rarefied gas. Therefore, to correctly predict the damping force, the rarefied gas effect must be considered. To study the nonlinear SFD problem involving the rarefied gas effect, a kinetic method, i.e., discrete unified gas kinetic scheme (DUGKS), is introduced in this paper. Also, based on the DUGKS, two solving methods, i.e., a traditional decoupled method (Eulerian scheme) and a coupled framework (arbitrary Lagrangian-Eulerian scheme), are adopted. With these two methods, two basic motion forms, i.e., linear (perpendicular) and tilting motions of a rigid micro-beam, are studied under forced and free oscillations. For a forced oscillation, the nonlinear SFD phenomenon is investigated. For a free oscillation, in the resonance regime, some numerical results at different maximum oscillating velocities are presented and discussed. Besides, the influence of oscillation frequency on the damping force or torque is also studied, and the cause of the nonlinear damping phenomenon is investigated.

Improved Resolution across the Global Seismographic Network: A New Era in Low-Frequency Seismology

Abstract The Global Seismographic Network (GSN)—a global network of ≈150 very broadband stations—is used by researchers to study the free oscillations of the Earth (≈0.3–10 mHz) following large earthquakes. Normal-mode observations can provide information about the radial density and anisotropic velocity structure of the Earth (including near the core–mantle boundary), but only when signal-to-noise ratios at very low frequencies are sufficiently high. Most normal-mode observations in the past three decades have been made using Streckeisen STS-1 vault seismometers. However, these sensors are no longer being manufactured or serviced. Candidate replacement sensors, the Streckeisen STS-6 and the Nanometrics T-360GSN, have been recently installed in boreholes, postholes, and vaults at several GSN stations and GSN testbeds. In this study, we examine normal-mode spectra following three Mw 8 earthquakes in 2021 and from one Mw 8.2 earthquake in 2014 to evaluate the change in GSN low-frequency performance on the vertical component. From this analysis, we conclude that the number of GSN stations capable of resolving normal modes following Mw 8 earthquakes has nearly doubled since 2014. The improved observational capabilities will help better understand the radial velocity and density estimates of the Earth.

IMPROVING THE QUALITY AND REDUCING THE ENERGY INTENSITY OF SHARPENING FLAT WOOD-CUTTING KNIVES

The quality of sharpening of flat wood-cutting knives in a certain way affects the quality of the parts obtained. The sharpening process is carried out by a grinding carriage performing a rectilinear reciprocating motion relative to a fixed knife. When the massive carriage is reversed, free oscillations (transients) occur, whichleads to a violation of the straightness of the cutting edge of the knife, limited by the requirements of GOST. Reducing the vibration activity of the process and achieving the required quality of knife sharpening provides a constructive solution for reversing the movement, in which the reverse is performed by a lightweight node-a base table with a knife fixed to it, and a massive sharpening carriage is stationary.

Analysis of a computer model of the behavior of a thin plate immersed in a liquid

Modeling the oscillation of a steel plate in water under the action of loads to assess the safety of the structure is an urgent task of modern times in the design of structures. The aim of this work was to study the behavior of a plate immersed in a fluid that makes forced oscillations under the action of an applied load; the mechanism of behavior of this interaction and the determination of the connected masses of the fluid. Knowledge of the connected masses helps to assess the effect of the liquid. In this work, the oscillations of a steel plate in water under the action of two types of loads were studied. For the harmonic analysis of the oscillations of the plate, our own frequency response was constructed, which was compared with the frequency response acquired by the method of solving a series of FSI problems. From the comparison of the obtained frequency response it is concluded that it is possible to use harmonic analysis to study the stress-strain state of the plate during its oscillations. Since FSI problems are quite resource-intensive due to their nature, solving a number of such problems about plate oscillations in a fluid under various loads to study the stress-strain state of an oscillatory system is not a very convenient method. The question arises as to whether it is possible to avoid solving FSI problems and to find a simpler way to solve the problems of vibration of structures in a fluid. Since the estimation of the attached water masses of the plate is known, it can be assumed that this attached water mass is distributed around the plate evenly and in view of this fact we can perform a harmonic analysis. Due to the viscosity, water dampens the amplitude of free oscillations of the plate. Thus, in order to be able to compare the results of a series of FSI and harmonic analysis problems, the latter must be modeled taking into account the damping in the model. The method of harmonic analysis with the addition of the attached mass of water can be used at low oscillation frequencies. At all other oscillation frequencies it is not recommended to use the method of harmonic analysis taking into account the connected mass of water.

Explanation of the Opposing Shifts in the Absorption Edge and the Optical Resonance in CuFeS2 Nanoparticles

Size-dependent change of the electronic band structure is one of the key features of nanoparticles in the quantum confinement region. CuFeS2 nanoparticles have a strong absorption feature in the visible region that has, controversially, been described as neither an excitonic transition nor a free carrier plasmon oscillation. Instead, the absorption feature in CuFeS2 nanoparticles has been attributed to quasi-static optical resonances from inter-band transitions between the valence band (VB), intermediate band (IB), and conduction band (CB). As such, we hypothesized that the feature should be subject to quantum confinement effects through modification of the electronic bands. In this paper, we show experimentally that the optical resonance absorption peak red-shifts and the optical band gap blue-shifts as the particle size decreases. Through density functional theory (DFT) and the tight binding (TB) modeling, we elucidate the size dependence of the band structure, especially focusing on the change in the IB. Using a Lorentzian oscillator optical model to simulate the absorption spectrum with inputs from the DFT-calculated band structure and band shifts from the TB model, we find that the size-dependent shifts of the optical resonance peak position in CuFeS2 are due to a tri-band quantum confinement effect that results in both the VB to IB and IB to CB gap expansion that accompanies a decrease in particle size. We also find that the transitions between the IB and CB play only a minor role in the optical spectrum. Moreover, the linear optical Lorentzian model predicts that the optical resonance peak is tunable across the visible range by partially filling the IB, lowering the CB, or expanding the IB.

Analysis of high Reynolds free surface flows

ABSTRACT In this paper, we will combine an upwind radial basis function-finite element with direct velocity–pressure formulation to study the two-dimensional Navier-Stokes equations with free surface flows. We will examine this formulation in an improved mixed-order finite element and localized radial basis function method. A particle tracking method and the arbitrary Lagrangian-Eulerian scheme will then be applied to simulate the two-dimensional high Reynolds free surface flows. An upwind improved finite element formulation based on a localized radial basis function differential quadrature (LRBFDQ) method is used to deal with high Reynolds number convection dominated flows. This study successfully obtained very high Reynolds number free surface flows, up to Re = 500 000. Finally, we will demonstrate and discuss the capability and feasibility of the proposed model by simulating two complex free surface flow problems: (1) a highly nonlinear free oscillation flow and (2) a large amplitude sloshing problem. Using even very coarse grids in all computing scenarios, we have achieved good results in accuracy and efficiency.

Fano resonance in the essentially nonlinear classic system

The classic analogue of the Fano resonance is considered for the essentially nonlinear systems. The closed expressions for the oscillation amplitudes turn out to be universal in terms of the frequency of free oscillations for the various kinds of the nonlinearity. The conditions of the transition between different branches of the amplitude–frequency relation are formulated in the framework of the concept of the limiting phase trajectory. The problem of the instability of the oscillations that leads to the beating between excited and driven oscillators is considered. The analysis of the non-stationary dynamical equations allows us to define the regions of the instability on the amplitude–frequency plane.