Natural Oscillations Research Articles

STUDY OF THE DYNAMICS OF A VIBRATION MACHINE CONSIDERING THE INFLUENCE OF THE PROCESSING MEDIUM

This paper presents the results of studying the dynamics of a vibration machine, takinginto account its interaction with the processing medium based on representing the medium as a continuoussystem. The application of the complex number method significantly simplifies the formation of equations ofmotion for the discrete-continuous system, which is a computational model of the vibration system "machinemedium."The study substantiates and develops a method for considering the mutual influence of the machineand the processing medium, based on representing the medium as a continuous system. The dynamicsof the vibration system "machine-medium" is studied, and oscillation parameters are determined withoutconsidering resistance forces. It is found that the overall motion of the vibration system is described by fourcomponents. The first three describe the natural oscillations of the system, of which the first two are determinedonly by initial conditions, and the third reflects the accompanying oscillations caused by the externalforce applied to the system. The last component defines the forced oscillations following the external force'schange law. This result shows that the oscillations of the vibration system are not strictly harmonic, which isconfirmed by the provided graphs. The dynamics of the "machine-medium" vibration system, consideringresistance forces, are studied, and analytical dependencies for determining oscillation amplitudes and natural and resonant frequencies are obtained. The results of the amplitude calculations of the vibration platform forvarious heights of compacted concrete mixtures reveal the influence of the resistance coefficient and theratio of oscillation frequency to the wave propagation speed in the mixture. Analysis of the obtained graphsshows that the resistance coefficient has a different effect on the amplitude of oscillations for different heightsof the compacting mixture. Certain mixture height zones of the vibration system "machine-medium" operatein a near-resonant mode. A significant influence on the amplitude is exerted by the wave propagation speed,which is included in the analytical formulas for determining the numerical values of the coefficients accountingfor reactive and active components of resistance.

Miscellaneous types of localization of natural oscillations of a gasket between parallel flanges

Both bases of a thin cylindrical gasket are fixed but the lateral side stays traction-free. For middle cross-sections with a smooth boundary as well as for a square one, we describe the asymptotics of frequencies of natural oscillations. Based on an investigation of the spectrum of the mixed boundary-value problem in the theory of elasticity in a quarter of the unit layer, we discover a new effect of localization of modes of natural oscillations near vertices of the square section and of the exponential decay at a distance from them. In the case of the smooth boundary of the cross-section eigenmodes concentrate either near the whole edge (a circular plate), or at the vicinity of points of maximum of the contour curvature.

Study on the frequencies of natural oscillations of car transporter wagon

Study on the frequencies of natural oscillations of car transporter wagon

Reduced dimension models for a plate fixed along one base and a part of the lateral side

A thin homogeneous isotropic plate has fixed the lower base and a part of the lateral side. The asymptotics of frequencies of natural oscillations of the plate is constructed. In the case of long fixation zone the model implies the two-dimensional problem of the elasticity theory on the cross-section but the reducing of this zone leads to the localization of the modes of natural oscillations near the lateral side of the plate. The asymptotic analysis is based on inspection of the spectrum of the auxiliary planar problem in the semi-infinite strip which describes the boundary layer phenomenon.

Numerical study on dilution of an oscillating jet in current environments

The mixing behavior of an oscillating jet under the influence of currents remains incomprehensive. This study uses a three-dimensional large eddy simulation model to investigate the phase-averaged and time-averaged concentration distribution of three-dimensional scalar structures in the oscillating jet under a current environment. The effects of dimensionless parameters on dilution characteristics are also analyzed. The results indicate that increasing the jet-current velocity ratio (Rjc) and the amplitude-jet velocity ratio (Raj), while decreasing the Strouhal number (St), can enhance the dilution capacity of the receiving water. To quantify the oscillatory effect of jets on the initial dilution of wastewater discharge, semiempirical equations for the cross-sectional minimum dilution (Sc) and the visual area (A25%) of the oscillating jet in a current environment are developed using the least squares method. The oscillatory nature of the jets is found to behave similarly to wave effects. Furthermore, the empirical equations for the initial dilution of oscillating jets in current environments are structurally consistent with those for non-oscillating jets in wave-current coexisting environments. This study highlights the positive impact of oscillating jets on mixing and dilution.

СОБСТВЕННЫЕ КОЛЕБАНИЯ КРУГОВЫХ СЭНДВИЧ-ПЛАСТИН В ТЕМПЕРАТУРНОМ ПОЛЕ

The effect of a homogeneous temperature field on the frequencies of natural oscillations of a circular sandwich plate is investigated. The hypothesis of a broken line is used as a kinematic one: for identical high-strength thin load-bearing layers, the Kirchhoff hypothesis; for a light incompressible thicker filler, the Timoshenko hypothesis on the straightness and incompressibility of a deformed normal. The differential equations of the transverse vibrations of the plate are obtained by the variational method. The desired functions are plate deflection and displacement in the filler. The analytical solution of the initial boundary value problem is constructed by decomposing into a series according to a system of proper orthonormal functions with hinged support or sealing of the plate contour. Calculation formulas for displacements are given. A numerical parametric analysis is carried out for the dependence of the oscillation frequencies of the plate on the materials of the bearing layers and temperature.

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.

Peculiarities of flexural wave propagation in a notched bar

The results of numerical modeling and experimental studies of the propagation of flexural elastic waves in a metal notched bar approximates the effect of an acoustic black hole are presented. The sample is a bar with notches, the depth of which increases according to the power law with an exponent equal to (4/3). It has been confirmed experimentally and with the simulation results, that such bars slow down the propagation of an elastic wave to the end of the bar. It is shown in such structures flexural waves have dispersion and their localization at the end of the bar is higher for some natural frequencies than that of a solid rod. The natural oscillations of the whole and notched bars are compared, i.e. the shape of the amplitude of the flexural wave along the rods. The dependence of the flexural wave length in a notched bar on the frequency is investigated as a wave propagates to the end of the bar.

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.

The natural oscillations of perforated sifting surfaces with epicycloidal holes

The natural oscillations of perforated sifting surfaces with epicycloidal holes

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.

Drainage gradient versus seasonal cycles: Differential response of microbial community composition to variations in soil moisture

AbstractThe variation in the soil microbial community composition over time was assessed at monthly time steps for 1 year in three neighboring Mollisols spanning a drainage gradient. This was done to distinguish between natural oscillations in the community composition versus lasting adaptations to environmental factors such as soil water availability. To isolate soil water availability as a controlling factor, we selected three soils sharing the same soil order (fine‐silty, superactive Argixerolls/Argialbolls); slope (0%–1%); temperature regime (mesic); moisture regime (xeric); and land use history (continuous grassland for the past 10 years) but differing in drainage class (well‐drained vs. moderately well‐drained vs. poorly drained). Changes in microbial diversity were quantified by monitoring the bacterial community at monthly intervals for 1 year. Within individual soils, α‐diversity varied little with season and drainage classes. Despite the three soils experiencing the same climate regime and vegetation/land use, they exhibited distinct community composition and turnover, which we attribute to differences in moisture availability across drainage and seasons. We posit that a seasonal recurring drop in soil redox potential induced by seasonal water saturation in the poorly drained soil is the most probable cause setting the microbial community of that soil apart from those in the better drained soils. Our investigation suggests that not all indicators of microbial diversity share the same sensitivity to seasonal and drainage‐related soil moisture variations.

Tornado Occurrence in the United States as Modulated by Multidecadal Oceanic Oscillations Using Empirical Model Decomposition

Studies have analyzed U.S. tornado variability and correlated F1–F5 tornado occurrence with various natural climate oscillations and anthropogenic factors. Using a relatively new empirical mode decommission (EMD) method that extracts time-frequency modes adaptively without priori assumptions like traditional time-series analysis methods, this study decomposes U.S. tornado variability during 1954–2022 into intrinsic modes on specific temporal scales. Correlating the intrinsic mode functions (IMFs) of EMD with climate indices found that 1. the U.S. overall tornado count is negatively (positively) correlated with the Atlantic Multidecadal Oscillation (AMO) index (the Southern Oscillation Index (SOI)); 2. the negative (positive) correlation tends to be more prevalent in the western (eastern) U.S.; 3. the increase in weak (F1–F2) and decrease in strong (F3–F5) tornadoes after around 2000, when both the AMO and the Pacific Decadal Oscillation (PDO) shifted phases, are likely related to their secular trends and low-frequency IMFs; and 4. the emerging Dixie Tornado Alley coincides with an amplifying intrinsic mode of the SOI that correlates positively with the eastern U.S. and Dixie Alley tornadoes. The long-term persistence of these climate indices can offer potential guidance for future planning for tornado hazards.

Exploring the dynamics of HIV and CD4+ T-cells with non-integer derivatives involving nonsingular and nonlocal kernel

It is important to examine and comprehend how HIV interacts with the immune system in order to manage the infection, enhance patient outcomes, advance medical research, and support global health and socioeconomic stability. In this study, we formulate the dynamics of HIV infection to investigate the intricate interactions between HIV and \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\ ext{CD}}4^{ + }$$\\end{document} T-cells. The Atangana-Baleanu and Caputo-Fabrizio derivative frameworks are applied to comprehensively examine the phenomenon of HIV viral transmission. The basic concepts and results of fractional calculus are presented for the analysis of the model. In our work, we focus on the dynamical behavior of HIV and immune system. We introduce numerical schemes to elucidate the solution pathways of the recommended system of HIV. We have shown the influence of various input factors on the solution pathways of the recommended fractional system and highlighted the oscillatory behavior and chaotic nature of the dynamics. Our findings demonstrate the complexity of the system under study by revealing the existence of the chaotic and oscillatory nature in the dynamics of HIV. In order to quantitatively characterize HIV dynamics, a number of simulations are carried out, providing a visual representation of the effects of different input variables. It has been observed that the chaos and the oscillatory behaviour is strongly related to the nonlinearity of the system. The present study provides a basis for further initiatives that try to enhance interventions and policies to lessen the worldwide burden of infection.

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.

Entrainment and multi-stability of the p53 oscillator in human cells

The tumor suppressor p53 responds to cellular stress and activates transcription programs critical for regulating cell fate. DNA damage triggers oscillations in p53 levels with a robust period. Guided by the theory of synchronization and entrainment, we developed a mathematical model and experimental system to test the ability of the p53 oscillator to entrain to external drug pulses of various periods and strengths. We found that the p53 oscillator can be locked and entrained to a wide range of entrainment modes. External periods far from p53's natural oscillations increased the heterogeneity between individual cells whereas stronger inputs reduced it. Single-cell measurements allowed deriving the phase response curves (PRCs) and multiple Arnold tongues of p53. In addition, multi-stability and non-linear behaviors were mathematically predicted and experimentally detected, including mode hopping, period doubling, and chaos. Our work revealed critical dynamical properties of the p53 oscillator and provided insights into understanding and controlling it. Arecord of this paper's transparent peer review process is included in the supplemental information.

Dynamical response of a floating ice sheet due to a forced oscillation in a running stream

This paper explores the response of a floating ice sheet to a forced, time-harmonic oscillatory pressure applied to the ice-covered surface of a uniform, finite depth fluid. The floating ice sheet is modeled as a thin elastic plate following the Euler–Bernoulli beam equation, with the additional consideration of in-plane compressive forces acting on the ice. Employing linear wave theory, the problem is presented as an initial boundary value problem and is solved using Laplace and Fourier transforms to obtain a mathematical expression for the ice sheet's deflection in terms of infinite integrals. These integrals are thereafter solved asymptotically for large time and distance using the stationary phase method. The asymptotic analysis indicates a growing response over time when the poles and stationary points of the phase functions coalesce. The deflection of the floating ice sheet is graphically presented, highlighting the effects of various non-dimensional parameters, such as flexural rigidity, compressive force, uniform current speed, and the angular frequency of the oscillatory pressure. Additionally, the group velocity and phase velocity of flexural gravity waves are derived from the dispersion relation and elucidated using diagrams. The results show that compressive force and current speed significantly influence wave amplitude, enhancing the oscillatory nature, while the flexural rigidity of the elastic plate and the angular frequency of the applied pressure have a substantial impact on the plate's deflection.

ВБУДОВАНА СИСТЕМА УЛЬТРАЗВУКОВИХ П’ЄЗОЕЛЕКТРИЧНИХ СЕНСОРІВ З ФУНКЦІЄЮ САМОДІАГНОСТИКИ

The informative signal of the vast majority of sensors on piezoelectric transducers is the ToF (Time-of-Flight) of ultrasonic oscillations, and its formation is realized by measuring the delay between the pulses of oscillations emitted by the actuator and the pulses of these oscillations received by the sensor. However, the processes of forming this informative signal and the electronic means of implementing these processes are characterized by a significant influence of extraneous factors, the compensation of which is largely problematic. Following this problem, this work solves the problem of embedded self-diagnosis of piezoelectric sensors signal converters. Methods of intellectualization of measurement processes are used based on the redundancy theory and its further development in the field of redundancy information theory, measuring technology, and sensors. It is proposed to supplement the input signal path of the sensor device with a specialized circuit for activating self-oscillations of the piezoelectric transducer. The proposed method is based on the monitoring of transient processes and oscillations at the frequency of natural oscillations of piezoelectric transducers during periodic switching of the latter to the input of the transimpedance amplifier TIA. In accordance with the proposed solution, the transimpedance amplifier is used to form damping self-oscillations, the frequency, amplitude and decay rate of which are monitored by the drift of the parameters of the piezoelectric transducer. The task of optimizing the operation modes of the circuit unit based on the transimpedance amplifier based on the criterion of maximum efficiency in the formation of an informative signal of the stability of the operation of piezoelectric transducers has been solved. The signal path of the built-in system of ultrasonic piezoelectric sensors with the self-diagnosis function UCQD (U-sound Front-end with in-situ CQ Diagnostic) is implemented using a programmable system on a PSoC (Programmable System on Chip) PSoC 5LP series (Cypres, Infineon Technologies).

MHD free convective heat and mass transfer flow passing through semi‐infinite plate for Cu‐water and TiO2‐water nanofluids in presence of radiation embedded in porous medium

AbstractThis research presents an analytical study of magnetohydrodynamics (MHD)‐free convective heat and mass transfer flow of a nanofluid bounded by a semi‐infinite flat plate. A magnetic field of strength is applied throughout the fluid region. The plate is moving with a constant velocity , temperature, and the concentration are assumed to be fluctuating with time harmonically from a constant mean at the plate. The frontier equations are assumed to be of an oscillatory nature and cracked analytically using the perturbation technique. The novelty of the present work is to examine the heat and mass transfer MHD flow for Cu‐water and TiO2‐water nanofluids in the presence of thermal radiation. The influence of physical parameters on the flow domain is described in the discussions by graphically and in tabular form. It was found that the fluid temperature and skin friction were reduced with the increased values of the radiation parameters for Cu‐water and TiO2‐water nanofluids. Also, it is noticed that the concentration boundary layer thickness decreases with an increase in chemical reaction parameters.

In the heat of the moment: Including realistic thermal fluctuations results in dramatically altered key population parameters.

Temperature is commonly acknowledged as one of the primary forces driving ectotherm vector populations, most notably by influencing metabolic rates and survival. Although numerous experiments have shown this for a wide variety of organisms, the vast majority has been conducted at constant temperatures and changes therein, while temperature is far from constant in nature, and includes seasonal and diurnal cycles. As fluctuating temperatures have been described to affect metabolic processes at (sub)cellular level, this calls for studies evaluating the relative importance of temperature fluctuations and the changes therein. To gain insight in the effects of temperature fluctuations on ectotherm development, survival, and sex ratio, we developed an inexpensive, easily reproducible, and open-source, Arduino-based temperature control system, which emulates natural sinusoidal fluctuations around the average temperature. We used this novel setup to compare the effects of constant (mean) temperatures, most commonly used in experiments, block schemes, and natural sinusoidal fluctuations as well as an extreme variant with twice its amplitude using the cosmopolitan mosquito species Culex pipiens s.l. as a study organism. Our system accurately replicated the preprogrammed temperature treatments under outdoor conditions, even more accurately than traditional methods. While no effects were detected on survival and sex ratio within the ranges of variation evaluated, development was sped up considerably by including temperature fluctuations, especially during pupation, where development under constant temperatures took almost a week (30%) longer than under natural fluctuations. Doubling the amplitude further decreased development time by 1.5 days. These results highlight the importance of including (natural) oscillations in experiments on ectotherm organisms - both aquatic and terrestrial - that use temperature as a variable. Ultimately, these results have major repercussions for downstream effects at larger scales that may be studied with applications such as ecological niche models, disease risk models, and assessing ecosystem services that rely on ectotherm organisms.