Natural Oscillation Frequency Research Articles

Influence of Rocking Shallow Foundation Parameters and Analysis of Seismic Response Characteristics

Rocking shallow foundations interrupt the seismic transmission path from the base of the structure and possess advantages, such as effective seismic isolation, self-resetting capabilities post-earthquake, and low costs. A numerical model of the rocking shallow foundation was developed in OpenSees (version: Opensees 3.5.0) based on field test data using numerical simulation. The effect of different parameters (column height, foundation sizes, top mass, and soil softness and stiffness) on the seismic response characteristics of rocking shallow foundations is investigated, and the seismic response characteristics of rocking shallow foundations are analyzed under the action of sinusoidal waves of different frequencies and various seismic wave types. The results of the study show that, as the height of the column increases, the bending moment decreases and settlement decreases; as the size of the foundation increases, the bending moment increases and settlement increases; as the mass of the top increases, the bending moment increases and settlement increases; and as the soil becomes softer, the bending moment decreases, and settlement increases. Inputting a sine wave that matches the structure’s natural oscillation frequency may induce resonance. This phenomenon can significantly amplify the structure’s vibrations; thus, it is essential to avoid external excitation frequencies that coincide with the foundation’s natural oscillation frequency. Under seismic loading, the rocking shallow foundation can mitigate the bending moment in the superstructure. When the displacement ratio remains within −0.5 to 0.5 percent, the foundation settlement is minimal. However, when the absolute displacement ratio exceeds 0.5 percent, the soil exhibits plastic deformation characteristics, resulting in increased foundation settlement. This study is an important contribution to the improvement of seismic performance of buildings and an important reference for improving seismic design standards and practices for buildings in earthquake-prone areas. In the future, the seismic response characteristics of rocking shallow foundations under bidirectional seismic action will be investigated.

Equation of motion of split conductor of anchor section at icing in wind flow

The relevance of the examined problem is connected with the necessity to develop measures to combat conductor galloping and the design of power transmission lines (ETL). The purpose of the research – to analyse statistical observation data on conductor galloping and apply a mathematical model to determine the parameters of galloping, to develop effective measures to combat conductor galloping and to improve the design of power lines. A sophisticated mathematical model was developed using Mathcad software to analyze conductor galloping in overhead power lines. This model, based on the equations of motion, predicts various galloping parameters under different conditions such as wind speed, span length, and initial mechanical stress. Time diagrams were constructed to represent linear and torsional motions, revealing correlations between amplitudes and frequencies. A comprehensive statistical analysis was performed on wire characteristics and split phase parameters to evaluate their impact on galloping patterns. Numerical methods, including the Runge-Kutta method, were employed to solve the equations and compute time-dependent behaviors. Results were visualized through graphs and diagrams to facilitate interpretation. The results revealed that conductor galloping occurs at wind speeds between 5 to 18 m/s, with significant occurrences at temperatures from 0°C to -10°C. The study identified that conductor galloping occurs within a wind velocity range of 5 to 13 m/s, predominantly with wind orientations between 30˚ and 90˚. The analysis showed that the frequency of galloping closely matches the natural oscillation frequency at low wind speeds but diverges with increasing wind speed and span length. These findings provide insights into the conditions under which conductor galloping is likely to occur and can inform design and operational strategies for overhead power lines.

Modern risk assessment of the influences of natural and military man-made factors on the state of the historical buildings of the Kyiv-Pechersk Lavra

During its thousand-year history, the Kyiv-Pechersk Lavra has experiences many disasters. At the time when the fight against religion was part of the state ideology, the cathedral and monastery were closed, and its countless treasures were confiscated. Even in the turbulent 1930s, when the bolsheviks destroyed dozens of unique temples and churches in Kyiv, the Assumption Cathedral remained intact. Black days for the age-old shrine came during the German occupation in the fall of 1941. First, the shrine was looted, and many material and artistic valuables were taken. In November 1941, a series of explosions destroyed the main temple of the Kyiv-Pechersk Lavra, which had served as a tomb for the Kiev princes. In February 2022, the war had started again in our country, and modern scientific technology allows us to assess the impact of military events on buildings of Kyiv-Pechersk Lavra from viewpoint of the level of seismic hazard assessment, which have lasted in Ukraine for more than two years, because Kyiv-Pechersk Lavra is listed as a UNESCO World Heritage Site. The article presents the results of the analysis of the operation of devices for various purposes ― from the recording of seismic-acoustic waves, which have a high frequency of natural oscillations, to low-frequency ones, which are recorded by a laser inclinometer. The article also presents the results of modern automated data processing using various methods ― from the spectral method of signal recognition to the modern autopicker method of determining the time of arrival of waves AIC, which allows you to clearly determine the arrival time of vibration waves of various origins ― from the formation of cracks in historical buildings of the Kyiv-Pechersk Lavra to vibration waves of technical and natural origin.

Rhythmic states and first-order phase transitions in adaptive coupled three-dimensional limit-cycle oscillators.

This paper reports a phase transition in coupled three-dimensional limit-cycle oscillators with an adaptive coupling. We reveal that the multiple-cluster rhythmic states emerge when natural frequencies of oscillators follow uniform distribution (case I), but disappear for Gaussian distribution (case II). Furthermore, as the coupling strength K increases, two first-order phase transitions occur sequentially. When K→0^{+}, an inevitable and nonhysteretic discontinuous phase transition occurs. For K>0, another discontinuous phase transition with a hysteresis loop emerges, and its occurrence depends on the width of the natural frequency distribution. From the microscopic perspective of the system, there are double switches between suppression and revival of oscillations as K varies in case I, but only one switch occurs in case II. Theoretical analyses of the incoherent states and the fixed points are given, which can be accurately verified by numerical simulations. This paper provides insights into our understanding of high-dimensional oscillators and their variants.

Development of linear bearing equipment for modal testing of low-frequency weakly damped spacecraft structures

This article presents the results of a study of the bearing capacity and dissipative properties of an aerostatic linear bearing developed at JSC RESHETNEV for modal testing of complex structures. When selecting equipment for modal testing, the main condition is the requirement to minimize the distortions introduced into the determined dynamic characteristics: frequencies of natural vibration modes, the vibration modes themselves, as well as modal masses and damping coefficients. In other words, all equipment used for ground-based modal testing should ideally have zero added mass, stiffness and friction. The main systems containing elements that create dissipative forces that affect the determination of damping coefficients are systems for weight compensation and vibration excitation on natural modes. The weight compensation system usually contains either elastic elements or a system of guides with rolling or sliding bearings. If the former bring additional rigidity and mass to the test object, the latter bring mass and friction (dry or viscous), which increases the error in determining the dynamic characteristics. The excitation of vibrations on natural modes, in most cases, is carried out by electrodynamic vibrators consisting of a magnetization coil (or permanent magnet) and a movable coil moving in a magnetic gap. The movable coil is oriented in the magnetic gap using a special system containing either elastic elements or a linear guide bearing. Vibrators with elastic coil suspension elements cannot be used for modal tests of extended structures with low rigidity. The problem of creating an ideal bearing to replace classic linear (sliding or roller) ones arose during preparation for modal tests of the wing of a solar battery of a spacecraft (SC). Aerostatic bearings (supports) have virtually zero friction and sufficient load-bearing capacity, in which compressed air acts as a lubricant, eliminating physical contacts of the interacting surfaces. To confirm the possibility of using aerostatic bearings in equipment for conducting modal tests of extended structures with low frequencies of natural oscillations, comparative tests of a roller and aerostatic bearing were carried out. During the tests, optimal air flow parameters (nozzle diameter, operating pressure and gap) were selected, which ensure the required load-bearing capacity for radial forces and torques (bending and torsion). A comparative assessment of dissipative properties was carried out when measuring the attenuation parameters of single-mass harmonic oscillators, which include aerostatic and roller linear bearings. With a nozzle diameter of 0.6 mm, a working gap of 40 μm and a bearing input pressure of 1.0 bar, the logarithmic decrement of oscillations of the harmonic oscillator with an aerostatic bearing was 0.084, which is more than 28 times lower than the logarithmic decrement of oscillations of an oscillator with a roller bearing. The conducted studies confirmed the possibility of using the developed aerostatic bearing in test systems used in modal tests of large-sized transformable spacecraft structures.

Oscillatory excitation of Faraday waves on the interface of immiscible fluids in a slotted channel

Recent studies of the oscillatory dynamics of the interface between fluids in Hele–Shaw cells have revealed a new type of instability termed the “oscillatory Saffman instability” in the case of fluids with high-viscosity contrast. The present study is dedicated to the experimental investigation of the dynamics of the interface between low-viscosity fluids of different densities oscillating in a vertical narrow channel. It is discovered that as the amplitude of oscillations increases, a threshold excitation of parametric oscillations of the interface in the form of a standing wave is observed in the plane of the fluid layer. This phenomenon bears a resemblance to Faraday waves, but the dependence of the standing wave wavelength on the oscillation frequency does not align with the classical dispersion relation for low-viscosity fluids. The damping effect of viscous boundary layers near the cell walls and the out-of-plane curvature of the oscillating interface leads to a decrease in the natural frequency of oscillations. The experiments demonstrate a significant role of the dimensionless layer thickness. With its decrease (increase in the dimensionless out-of-plane interface curvature), the threshold oscillation acceleration rises in accordance with a power law. To the best of the authors' knowledge, this type of instability has been discovered and studied for the first time. Another important finding is the excitation of intense time-averaged vortical flows in the channel plane within the supercritical region. The physical mechanism underlying the excitation of the time-averaged vortices is clarified, and the dimensionless parameters that govern their intensity are identified.

Change of Natural Oscillation Frequencies of Buildings and Structures Depending on External Factors

Abstract —This work is devoted to the development of the engineering seismic monitoring method created in Geophysical Survey of the Russian Academy of Sciences (GS RAS). In previous years, the “method of standing waves” was created and put into practice. It helps to separate natural oscillation modes of buildings and other engineering structures. The natural oscillations of hundreds of various objects (buildings, bridges, dams, etc.) had been studied and identified. We assumed that the physical condition of studied constructions could be controlled during exploitation by measuring the changes of natural oscillation frequencies. That would help to identify the appearance of defects in constructions, to prevent the risk of their destruction. However, it turned out that not everything is that simple: changes in frequency values are logically affected by changes in the environment around the studied objects. This article provides examples of these relations, influence of changes in environmental temperature, mass of objects and precipitation on the frequencies of natural oscillations.

RESEARCH METHODOLOGY AND CHARACTERISTICS OF NORMAL NONLINEAR RESONANT OSCILLATIONS OF THE SYSTEM ” SPRUNG AND UNSPRUNG PARTS OF WHEELED VEHICLES”

The authors have discussed the method applicable for the system of sprung-unsprung parts of the vehicle, carrying out vertical oscillations under nonlinear elastic force interactions, which allow evaluating the influence of the elastic characteristics of tires, the suspension system, and road irregularities on the determining parameters of the oscilla-tions of the sprung-unsprung parts. What’s obtained: a) the analytical dependence of natural oscillation frequencies on the system amplitudes and parameters; b) the relationship between the levels of amplitude of the sprung and unsprung parts oscillations, at which an internal resonance occurs; c) the condition for occurrence of the resonance in case of the motor vehicle movement along the road, which is described by the ordered system of inequalities; d) the ratios that set the main parameters of vibrations of the sprung and unsprung parts in case of the resonant and non-resonant vibrations. It is shown that a larger value of the oscillation amplitude of the sprung part corresponds to a larger value of the natural frequency in a suspension system with a progressive law of changes in the elasticity of shock absorbers, and the opposite is true when a regressive law; speaking of shock absorbers and elastic tires with their progressive or regressive power characteristics, a larger value of the oscillation amplitude of the unsprung part corresponds to a larger value of the oscil-lation amplitude of the sprung part, when an internal resonance is possible; for regressive power characteristics of tires and progressive power characteristics of shock absorbers – vice versa; the resonance value of the oscillation amplitude of the unsprung part is higher for the lower speeds of movement with regressive power characteristics of the tires and, on the contrary, – for the progressive power characteristics of tires; the amplitude of the transition through the resonance of the unsprung part takes a larger value for elastic tires with a smaller value of their static deformation and a slower transition to resonance. Keywords: sprung and unsprung parts of the wheeled vehicle, natural frequencies of oscillations, resonant oscillations, internal resonance of the unsprung and sprung parts of the wheeled vehicle.

Flow dynamics studies in the NETmix reactor for a large range of flowrate ratios between feed streams

The mixing dynamics that occur inside the NETmix reactor have been previously thoroughly studied for equal feed streams distributed through the inlets. To broaden the applicability of this static mixer, this work intends to expand the knowledge of the mixing dynamics mechanisms for cases where dissimilar inlet flowrates are imposed. Computational Fluid Dynamics (CFD) tools were used to simulate flow dynamics experiments in a reduced NETmix geometry for different inlet flowrate ratios. The simulation results show that this reactor can attain the desirable condition of similar outlet flowrates for several dissimilar inlet flow conditions. A flow dynamics analysis enabled the determination of the natural frequency of oscillation of the flow and related it to the volume of the chambers occupied by vortices. Finally, the velocity fluctuations at the centre of NETmix chambers were characterised in terms of the intensity of turbulence.

Monoreactive multimass oscillator of non-fixed frequency

Introduction. The work relates to the field of mechanical engineering, namely to oscillating mechanical systems. The relevance of the study is determined by the fact that vibrations of inertial masses occur everywhere.Target. Development of a mathematical model of a monoreactive multimass oscillator of non-fixed frequency.Research methods. It is proved that the points that are the coordinates of the end of an arbitrary vector in the coordinate system are the vertices of a regular polygon. The shape and dimensions of the polygon are not related to the coordinates of the vector, i.e. unchangeable. The center of a regular polygon in all cases coincides with the middle of the vector. In the considered (idealized) case, the polygon, at the vertices of which oscillating loads of masses m are located, lies in the Z plane. In technical applications, the loads should not interfere with each others movements, therefore, each load should have its own plane, and all planes should be parallel (like multi-piston mechanism).Results. The condition for the occurrence of free harmonic oscillations is the equality to zero of the total energy of the system, which in the case under consideration is exclusively kinetic, which determines the monoreactive nature of the oscillator. In the considered multidimensional flat monoreactive oscillator, free harmonic linear oscillations of weights can occur.Conclusion. Only kinetic energy is involved in energy exchange. There is no need for elastic elements. The oscillator does not have a fixed natural frequency of oscillation. The frequency depends on the initial speeds and positions of the weights. A regular polygon undergoes a double rotation - around point 0 and around point r. At the same time, the loads carry out linear harmonic oscillations with amplitude . The use of a crank-slider or crank-rod mechanism will allow for parallel movement of loads.

Mathematical Model of Vibration-Centrifugal Processing of Parts Using Loose Abrasive

The article presents some new theoretical and experimental solution of a scientific and applied problem of technological support for vibratory centrifugal processing of complex-profiled parts in a bulk abrasive environment. This solution aims to increase productivity while ensuring the desired quality of the processed surfaces. The authors have developed a mathematical model that describes the action of abrasive particles on the surface of the parts, taking into account the parameters of the granular abrasive medium based on Voigt’s law. This allows the description of dynamic processes in the processing environment for a wide range of material types. The natural frequencies of oscillations of the processed medium layer have been determined, which depend on the amplitude of its vibrations for different densities of soft and hard materials of the processed medium and the medium with linear-elastic properties. The methodology includes the use of test equipment to conduct experimental research on the process, which involves determining changes in specific metal removal rates and surface roughness using the frequency converter Altivar 71 with the PowerSuite v.2.5.0 software.

Relationship between natural muscle oscillation frequency and lower limb muscle performance during instrumented sit-to-stand and stand-to-sit movements on a novel device in sedentary subjects

BackgroundDespite the significance of muscle oscillation frequency, previous research has not established a correlation with muscle performance due to the challenges of applying resistance without altering natural motion during functional tests. Research questionWhat is the correlation between muscle oscillation frequency and lower limb muscle strength, power, and work during an instrumented sit-to-stand and stand-to- sit (iSTS-TS) task among sedentary subjects? MethodsIn a cross-sectional study, the oscillation frequency of the gastrocnemius medialis (GM), biceps femoralis (BF), and vastus medialis (VM) muscles in both the dominant (D) and non-dominant (ND) legs was assessed with a handheld myotonometer in 34 sedentary individuals before performing the iSTS-TS task. ResultsIn the isokinetic mode, no significant correlations were found. In the isotonic mode, the BF muscle oscillation frequency in the D and ND legs exhibited significant positive correlations with peak force, peak power, and work during sitting down, as well as peak power and work during standing up. Positive correlations were observed in both legs between the GM oscillation frequency and sitting down peak force and work. Additionally, significant positive correlation was found with standing up work in the D leg. Muscle oscillation frequency of the VM exhibited a positive correlation with sitting down peak force in the ND leg. SignificanceDue to a greater number of correlations found, it is advisable to use the isotonic mode when assessing muscle oscillation frequency in relation to muscle performance during functional iSTS-TS tasks in sedentary subjects.

Experimental studies of the impact of fluid sloshing in the tank on the dynamic characteristics of the “wing model – fuel tank” system

Flexible response of the airframe structural elements under operational loads are one of the main sources of fatigue damage accumulation. It is known that fuel sloshing in tanks can change the dynamic (frequencies and shapes of natural oscillations) and dissipative properties (oscillation damping decrements) of an elastic system, including partially or completely fuelfilled tanks. It is specified that fuel sloshing in tanks due to the additional oscillation energy dissipation of the elastic system can have a significant impact on both the fatigue and aeroelastic characteristics of aircraft structural elements. Theoretical and experimental studies, applicably to the majority of currently operating transport aircraft, have shown that when modeling dynamic phenomena and solving aeroelasticity problems, fuel can be considered conditionally solidified, which actually does not affect the resultant effect. The advent of modern heavy transport aircraft with a high aspect ratio wing and four engines on pylons under the wing has led to a considerable change in the dynamic picture of the aircraft interaction with the environment. The main feature is that, under this arrangement, the first horizontal bending mode of the wing is embedded in the main flexible modes that determine the dynamic response to external effects. In this case, the model of solidified fuel can have a significant impact on the accuracy of predicting dynamic loads and, as a consequence, on the quantitative characteristics of durability and aeroelasticity. The article presents the results of experimental studies of the impact of fluid sloshing in the tank on the dynamic characteristics (frequencies of natural oscillations and amplitudes of forced oscillations) of the “wing model – fuel tank” system. The design of the experimental installation and the methodology of conducting experiments are described. During the experiment, the tank was partially filled with liquid or full, and horizontal bending modes of the wing model, for which considering liquid sloshing in the tank is the most relevant, were studied. The tank refueling levels are determined at which the maximum effect of the system oscillation damping is achieved due to energy dissipation under liquid sloshing. The effect of various factors (presence of a top cover, internal structural frame, perforation in the structural frame) on the amplitudes and frequencies of forced oscillations is analyzed.

Experimental studies of the influence of elastic-dissipative parameters of engine mounting units on the dynamic characteristics of the “wing model – elastic pylon – engine” system

A feature of modern heavy transport aircraft is their layout with engines on elastic pylons under the wing, with the fuel tanks located in the wing consoles. In this case, the main elastic tones of the aircraft’s own oscillations, which determine its dynamic response to external disturbing influences, include the so-called motor tones (vertical and horizontal (lateral) oscillations of engines on elastic pylons). A new type of flutter has appeared – pylon, which for some aircraft determines the critical flutter speed of the aircraft as a whole. The main reason for this phenomenon is the low oscillation damping of the engine on the pylon under the wing. Therefore, research aimed at modernizing the engine mounting points on the pylon in order to reduce the level of elastic oscillations during aircraft operation seems relevant. One of the possible ways to solve this problem is to use the concept of a freed engine, when the engine attachment points to the pylon are modernized, providing more effective damping of engine oscillations. In order to confirm the possibility of practical implementation of these solutions, corresponding experimental studies were carried out on an experimental setup developed by the authors. A design of engine mounting units has been developed that allows specified displacements of the engine relative to the pylon during forced elastic oscillations of the system, which includes a hinged suspension, installation of additional elastic elements and hydraulic dampers.The article presents the results of studies of the influence of elastic-dissipative parameters (partial frequency of natural oscillations and partial decrement of oscillations) of an engine mount on an elastic pylon on the dynamic characteristics of the dynamic system “wing model – elastic pylon – engine”. It is shown that by introducing specially designed engine suspension units on pylons, it is possible to significantly change the dynamic characteristics (frequencies and amplitudes of natural oscillations) of the elastic system as a whole. Thus, the amplitudes of oscillations of the engine’s center of mass in the region of motor tones decrease by 3...7 times during forced harmonic oscillations.

Собственные колебания упругой прямоугольной CFCF-пластинки при одноосном растяжении-сжатии ее плоскости

The influence of a uniaxial distributed load in the plane of a thin rectangular plate on the value of the first natural frequency of its oscillations has been studied. We considered a plate, two opposite faces of which are clamped, and the other two are free (CFCF-plate, C-clamped edge, F-free edge). The load is applied to the clamped edges. The main differential equation for the coordinate component of the deflection function and all the boundary conditions of the problem are fulfilled exactly using two hyperbolic-trigonometric series in two coordinates and an additional function depending on one variable x. The problem was reduced to an infinite system of linear algebraic equations with respect to one sequence of uncertain coefficients, containing as parameters the magnitude of the load and the frequency of oscillations. For a number of load values, the natural frequencies of oscillations were found by enumerating frequency values in combination with the method of successive approximations when solving a reduced system of linear algebraic equations. To ensure acceptable accuracy of calculations, the number of terms in the series (the size of the reduced system), the number of iterations and the number of significant digits in the mantissa when calculating non-trivial coefficients of the system were changed. A square plate was considered as an example. Based on the calculation results, a graph was constructed of the dependence of the first natural frequency of oscillations on the magnitude of tension-compression forces, which is a curve close to a parabola. Under Eulerian compressive load, the oscillations stop. The shapes of natural vibrations changed slightly and were similar to the shape of the curved surface of a plate under the action of a uniform transverse load. The purpose of this study is to create an effective algorithm for calculating the natural frequencies of oscillations of a CFCF-plate when the uniaxial tensile-compression load of its clamped faces changes.

Study of the Dynamics and Strength of the Detachable Module for Long Cargoes under Asymmetric Loading Diagrams

This article highlights the structural features of the detachable module for the transportation of long cargoes. The choice of profiles for the detachable module was based on the resistance moments of its components. The detachable module was considered a rod structure on four supports. To determine the longitudinal loads acting on the detachable module, mathematical modeling of its longitudinal dynamics was carried out, provided they were placed on a flat car during a shunting impact. The accelerations obtained were used for the calculations of the detachable module. This article presents the results of the strength calculation of the detachable module under asymmetric loading diagrams, i.e., the action of longitudinal and lateral forces on the detachable module structure. The results of the calculations show that the maximum stresses in the structure of the detachable module when it receives longitudinal loads are 7.7% lower than the permissible ones, and when it receives lateral loads, they are 5.8% lower. Thus, the strength of the detachable module is maintained under the loading diagrams considered. This study also included a modal analysis of the detachable module structure. The first natural frequency of oscillations is found to be 20 Hz. Thus, the safety of the detachable module movement in terms of frequency analysis is ensured. This research will help to create recommendations for the design of modern modular vehicles and improve the efficiency of the transport industry.

Mechanical responses of nanoplates resting on viscoelastic foundations in multi-physical environments

This paper presents an analysis of the static bending, thermal buckling, free vibrations, and forced vibrations of nanoplates using analytical approaches. This study introduces analytical formulations for all three aforementioned difficulties concerning nanoplates, taking into account the simultaneous impact of elements such as magnetic effects, temperature, and viscoelastic basis. The research at hand is characterized by its intricate nature and captivating subject matter, as it explores the phenomenon of the flexomagnetic impact on a plate. Furthermore, the plate is exposed to both mechanical and magnetic stresses concurrently inside a temperature-controlled environment. The plate is supported by a viscoelastic foundation, with the drag coefficient of the foundation being explicitly specified. The mathematical methods used in this study are derived from classical plate theory. An explicit expression is derived for the natural oscillation frequency, critical load resulting from thermal buckling, as well as the static and dynamic displacements of the plate, taking into account the drag coefficient offered by the foundation. The study further conducts a quantitative analysis to investigate the impact of several parameters, including temperature, viscoelastic foundation, and natural frequency of external stimulation force, on the mechanical behaviors of nanoplates. The findings of this study provide a scientific foundation for addressing practical challenges in the design, production, and use of nanoplates.

Observation of fixed lines induced by a nonlinear resonance in the CERN Super Proton Synchrotron

The motion of systems with linear restoring forces and recurring nonlinear perturbations is of central importance in physics. When a system’s natural oscillation frequencies and the frequency of the nonlinear restoring forces satisfy certain algebraic relations, the dynamics become resonant. In accelerator physics, an understanding of resonances and nonlinear dynamics is crucial for avoiding the loss of beam particles. Here we confirm the theoretical prediction of the dynamics for a single two-dimensional coupled resonance by observing so-called fixed lines. Specifically, we use the CERN Super Proton Synchrotron to measure the position of a particle beam at discrete locations around the accelerator. These measurements allow us to construct the Poincaré surface of section, which captures the main features of the dynamics in a periodic system. In our setting, any resonant particle passing through the Poincaré surface of section lies on a curve embedded in a four-dimensional phase space, the fixed line. These findings are relevant for mitigating beam degradation and thus for achieving high-intensity and high-brightness beams, as required for both current and future accelerator projects.

Metal wire embrittlement monitoring by the measurement of wire oscillation frequency

In the process of irradiation of materials by fluxes of heavy particles (protons, neutrons, alpha particles), damage to material structure is often observed. As a result of the accumulation of such damages, there is a subsequent change in the properties of materials, in particular, its embrittlement and hardening. Monitoring of the embrittlement process is important for nuclear reactor vessels exposed to high neutron fluxes. In this work, to observe the effect of heavy irradiation particles on the mechanical properties of metals, we propose to use vibrating wire resonators, in which the natural frequency of oscillations of the wire strongly depends on its tension. The change in the elastic characteristics of the wire alters the value of the natural frequency of wire oscillations. The natural oscillations are generated by a special circuit. Preliminary experiments to study the embrittlement effect of a stretched wire are performed by heating the wire with an electric current. In the case of short pulses, a significant increase in frequency is achieved, which is explained by the process of hardening of the material as a result of the thermal impact on the wire (rapid heating and cooling).

Vertical convection regimes in a two-dimensional rectangular cavity: Prandtl and aspect ratio dependence

Vertical convection is the fluid motion that is induced by the heating and cooling of two opposed vertical boundaries of a rectangular cavity (see e.g. Wang et al., J. Fluid Mech., vol. 917, 2021, A6). We consider the linear stability of the steady two-dimensional flow reached at Rayleigh numbers of O( $10^8$ ). As a function of the Prandtl number, $Pr$ , and the height-to-width aspect ratio of the domain, $A$ , the base flow of each case is computed numerically and linear simulations are used to obtain the properties of the leading linear instability mode. Flow regimes depend on the presence of a circulation in the entire cavity, detachment of the thermal layer from the boundary or the corner regions and on the oscillation frequency relative to the natural frequency of oscillation in the stably temperature-stratified interior, allowing for the presence of internal waves or not. Accordingly, the regime is called slow or fast, respectively. Either the global circulation or internal waves in the interior may couple the top and bottom buoyancy currents, while their absence implies asymmetry in their perturbation amplitude. Six flow regimes are found in the range of $0.1 \leq Pr \leq 4$ and $0.5 \leq A \leq 2$ . For $Pr \lessapprox 0.4$ and $A>1$ , the base flow is driven by a large circulation in the entire cavity. For $Pr \gtrapprox 0.7$ , the thermal boundary layers are thin and the instability is driven by the motion along the wall and the detached boundary layer. A transition between these regimes is marked by a dramatic change in oscillation frequency at $Pr = 0.55 \pm 0.15$ and $A <2$ .