Mass Oscillations Research Articles

The Question of Drawing a Design Scheme of a Wagon with a Non-Symmetrically Located Freight

Violations of the stability of a wagon with an asymmetrically positioned freight can lead to a threat to the safety of train traffic, the safety of freight on the route and transport facilities. The design diagram of a wagon with an asymmetrically located freight drawn up in the article and the equations obtained in an analytical way, oscillations of the sprung mass of a wagon with an asymmetric arrangement of the freight, characterizing the longitudinal and transverse displacement of the center of mass of the freight, can be used for mathematical modeling of forced vibrations and impact on the track of a wagon with asymmetrically located freight in various operating conditions.

Suppression of Nonsynchronous Vibration Through Intentional Aerodynamic and Structural Mistuning

Abstract Nonsynchronous vibrations (NSVs) arising near the stall boundary of compressors are a recurring and potentially safety-critical problem in modern axial compressors and fans. Recent research has improved predictive capabilities and physical understanding of NSV, but prevention measures are still lacking. This article addresses this by systematically studying the influence of aerodynamic and structural mistuning on NSV. This is achieved by incorporating mistuning effects in a validated linear model, in which individual blade modes are modeled as single-degree-of-freedom mass oscillators coupled by a convected aerodynamic disturbance term. The results demonstrate that both structural and aerodynamic mistuning are effective. While structural mistuning improves stability by preventing aero-structure lock-in, aerodynamic mistuning, which locally reduces the tip blockage and attenuates the aerodynamic disturbance causing NSV. In the latter case, the circumferentially averaged conditions are shown to be most influential, while the pattern plays a minor role. A combination of moderate aerodynamic and structural mistuning (1%) was also found to be effective. These findings are relevant for design decisions, demonstrating that small blade-to-blade variations can suppress NSV.

Stability Criterion for Mass Oscillation in the Surge Tank of a Hydropower Station Considering Velocity Head and Throttle Loss

Surge tanks (STs) are important facilities for ensuring the safety of hydropower stations. Reducing the ST size under the premise of ensuring stable mass oscillations within the ST is the main issue. First, according to the basic equations of the mass oscillation for a hydropower station with an ST, a novel expression of the critical stability section of an ST is deduced considering the velocity head and throttle loss. Then, the sensitivity of each influencing factor of the proposed stability criterion is analyzed. Ultimately, through the simulation of small oscillation transients in two case studies, the water level oscillations (WLOs) in an ST based on three stability criteria are compared. The results show that a 20% smaller ST in a hydropower station may result in 10.4% larger oscillations and a 60% smaller ST in a pumped storage power station may result in 14.3% larger oscillations. Compared with the Thoma criterion and the Chinese specification criterion, the stability criterion proposed in this paper can safely reduce the size of the ST since it considers the influence of the velocity head and throttle loss. The proposed stability criterion can provide an important reference for the optimal design of the STs.

Dynamics of a degenerate Cs-Yb mixture with attractive interspecies interactions

We probe the collective dynamics of a quantum degenerate Bose-Bose mixture of Cs and $^{174}$Yb with attractive interspecies interactions. Specifically, we excite vertical center of mass oscillations of the Cs condensate, and observe significant damping for the Cs dipole mode, due to the rapid transfer of energy to the larger Yb component, and the ensuing acoustic dissipation. Numerical simulations based on coupled Gross-Pitaevskii equations provide excellent agreement, and additionally reveal the possibility of late-time revivals (beating) which are found to be highly sensitive to the Cs and Yb atom number combinations. By further tuning the interaction strength of Cs using a broad Feshbach resonance, we explore the stability of the degenerate mixture, and observe collapse of the Cs condensate mediated by the attractive Cs-Yb interaction when $a_{\mathrm{Cs}}<50 \, a_0$, well above the single-species collapse threshold, in good agreement with simulations.

Interaction of the axionic dark matter, dynamic aether, spinor and gravity fields as an origin of oscillations of the fermion effective mass

In the framework of the Einstein–Dirac-axion-aether theory we consider the quartet of self-interacting cosmic fields, which includes the dynamic aether, presented by the unit timelike vector field, the axionic dark mater, described by the pseudoscalar field, the spinor field associated with fermion particles, and the gravity field. The key, associated with the mechanism of self-interaction, is installed into the modified periodic potential of the pseudoscalar (axion) field constructed on the base of a guiding function, which depends on one invariant, one pseudo-invariant and two cross-invariants containing the spinor and vector fields. The total system of the field equations related to the isotropic homogeneous cosmological model is solved; we have found the exact solutions for the guiding function for three cases: nonzero, vanishing and critical values of the cosmological constant. Based on these solutions, we obtained the expressions for the effective mass of spinor particles, interacting with the axionic dark matter and dynamic aether. This effective mass is shown to bear imprints of the cosmological epoch and of the state of the cosmic dark fluid in that epoch.

The zonal North Pacific Oscillation: a high-impact atmospheric teleconnection pattern influencing the North Pacific and North America

Based on unfiltered daily Japanese 55 year reanalysis covering the 60 winters in 1958–2018, a new teleconnection pattern called the zonal North Pacific Oscillation (ZNPO) pattern has been detected. The ZNPO pattern describes a mass oscillation in the troposphere between the eastern and western North Pacific, persisting for a week or so. It is shown that the ZNPO pattern is a high-impact teleconnection pattern that brings the wintertime North Pacific and North America severe weather and hydroclimate events. It may cause rapid surface air temperature drop or rise over the northern North Pacific and North America, remarkable sea ice concentration anomalies over the northeastern Bering Sea, and strong convective anomalies in the lower troposphere over the eastern and western midlatitude North Pacific. The ZNPO pattern arises from two westward-moving geopotential height disturbances over the North Pacific and North America and is driven mainly by baroclinic energy conversion and feedback forcing by transient eddies. The baroclinic energy conversion acts to overcome the available potential energy (APE) loss caused by the heat flux of transient eddies and at the same time acts as a major kinetic energy (KE) source to maintain the ZNPO pattern. The barotropic feedback forcing by transient eddies acts as a major KE source to drive the ZNPO pattern during the growing stage of the ZNPO pattern and as a major KE sink to heavily damp the ZNPO pattern during the decaying stage.

Broadband tunable elastic metastructure based on one-dimensional phononic crystal

Considering the manufacturing difficulty and tunability, a one-dimensional phononic crystal-type metastructure is proposed in this paper. By adjusting the distance between the mass oscillators installed on the connecting bar, that is, changing the length of the phononic crystal unit, the phase shift of the flexural wave can span over a full range of 0–2π and then the phenomena such as abnormal refraction, beam focusing, and self-acceleration can be realized based on the generalized Snell’s law. In addition, the method of multiple mass oscillator array design is used to broaden the operating frequency domain by increasing or decreasing the number of mass oscillators. This proposed method provides an innovative concept for realizing broadband tunable metastructures and has potential applications in the fields of vibration control, energy harvesting, and noise isolation.

Sensitivity-Tunable Oscillator-Accelerometer Based on Optical Fiber Bragg Grating

We demonstrate a fiber Bragg grating (FBG)-based oscillator-accelerometer in which the acceleration sensitivity can be tuned by controlling the location of the mass oscillator. We theoretically and experimentally investigated the performance of the proposed accelerometer. Theoretical analysis showed that both the mass and location of the oscillator affect the sensitivity and resonant frequency of the accelerometer. To simplify the analysis, a nondimensional parameter, P, was introduced to tune the sensitivity of the FBG-based oscillator-accelerometer, which is related to the location of the mass oscillator. Numerical analysis showed that the accelerometer sensitivity is linearly proportional to the P parameter. In the experiment, six FBG-based oscillator-accelerometers with different P parameters (0.125, 0.25, 0.375, 0.5, 0.625, 0.75) were fabricated and tested. The experimental results agree very well with the numerical analysis, in which the sensitivity of the proposed accelerometer linearly increased with the increase in parameter P (7.6 pm/g, 15.8 pm/g, 19.3 pm/g, 25.4 pm/g, 30.6 pm/g, 35.7 pm/g). The resonance frequency is quadratically proportional to parameter P, and the resonance frequency reaches the minimum of 440 Hz when P is equal to 0.5. The proposed oscillator-accelerometer showed very good orthogonal vibration isolation.

СТІЙКІСТЬ КОЛИВАНЬ ТРАКТОРА ЯК ДВОМАСОВОЇ СИСТЕМИ З ДВОМА НЕЛІНІЙНОСТЯМИ ТИПУ СУХОГО ТЕРТЯ В РЕЖИМАХ РЕЗОНАНСІВ

Purpose of the study is to assess the possibility of calculating the stability of tractor oscillations as a system with nonlinearities such as dry friction due to the inverse problem. Research methods. The methodological basis of the work is the generalization and analysis of known scientific results regarding the dynamics of two-mass systems in resonance modes and the use of a systematic approach. The analytical method and comparative analysis were used to form a scientific problem, determine the goal and formulate the research objectives. When creating empirical models, the main provisions of the theory of stability of systems, methodology of system analysis and research of operations were used. The results of the study. Oscillations of the system with harmonic excitation by its base are considered (for example, the movement of a tractor on an uneven supporting surface). Oscillations of this system are described by nonlinear differential equations. To solve this equation, instead of friction dampers with friction forces, linear dampers with corresponding drag coefficients are included in the system. By solving the obtained system of linear inhomogeneous differential equations for the steady-state mode of oscillation, the amplitudes of oscillations of masses and deformation of springs with certain stiffness are determined. To clarify the effect of friction forces on mass oscillations in resonance modes, the obtained expressions were analyzed. A diagram of stability of mass oscillations in resonance modes is obtained. Conclusions. It has been established that if the coefficients of relative friction have such values that the point that is determined by them lies within the region bounded by segments 1-2 and 2-3 and coordinate axes, then during oscillations in the low-frequency resonance mode, the friction forces do not limit the increase in amplitudes fluctuations of masses, but only reduce the rate of their growth. If the point, which is determined by the coefficients of relative friction, lies in the region 1-1'-2'-3 '3-2-1, then the springs have intermittent deformation, that is, during the period of oscillation, one mass of the system has stops relative to another mass, or the last has stops relative to the support surface, or both masses move part of the period as a whole with the support surface. At resonance with a high frequency, the friction forces limit the amplitudes of mass oscillations if the coefficients of relative friction have such values that the point that is determined by them does not lie in the region bounded by segments 4-5 and 5-6 and the coordinate axes. Sections 4-5 and 5-6 define the boundaries of vibration stability at resonance (lines of critical ratios of the coefficients of relative friction).

SEED-G: Simulated EEG Data Generator for Testing Connectivity Algorithms.

EEG signals are widely used to estimate brain circuits associated with specific tasks and cognitive processes. The testing of connectivity estimators is still an open issue because of the lack of a ground-truth in real data. Existing solutions such as the generation of simulated data based on a manually imposed connectivity pattern or mass oscillators can model only a few real cases with limited number of signals and spectral properties that do not reflect those of real brain activity. Furthermore, the generation of time series reproducing non-ideal and non-stationary ground-truth models is still missing. In this work, we present the SEED-G toolbox for the generation of pseudo-EEG data with imposed connectivity patterns, overcoming the existing limitations and enabling control of several parameters for data simulation according to the user’s needs. We first described the toolbox including guidelines for its correct use and then we tested its performances showing how, in a wide range of conditions, datasets composed by up to 60 time series were successfully generated in less than 5 s and with spectral features similar to real data. Then, SEED-G is employed for studying the effect of inter-trial variability Partial Directed Coherence (PDC) estimates, confirming its robustness.

Surging glaciers in Scotland

ABSTRACT Glacier surges are cyclic oscillations of velocity and mass resulting from internal dynamic instabilities. For surge-type glaciers, cycles of advance and retreat are decoupled from climate forcing, so it is important to consider the possibility that former glaciers may have been surge-type when making climatic inferences from their dimensions and chronologies. In this paper, climatic and glacier geometric data are used to show that Scotland was likely the location of a surge cluster during the Loch Lomond Stade (∼12.9–11.7 ka), with high probabilities of surging for outlets of the West Highland Icefield and the larger glaciers in the Inner Hebrides and Northern Highlands. Terrestrial and marine landforms consistent with surging occur in all of these areas, and it is proposed that surge-type glaciers existed on the Islands of Skye and Mull, in the Northern Highlands, and in a ‘surging arc’ along the western, southern and south-eastern margins of the West Highland Icefield. The possibility that surge-type glaciers were widespread in Scotland during the Loch Lomond Stade offers a fresh perspective on some long-standing issues, including the relationship between style of deglaciation and climate change, the climatic significance of glacial chronologies, palaeoclimatic reconstructions, and the interpretation of numerical model results.

Study of the antivibration suspended seat oscillations with quasi-zero stiffness effect under sinusoidal excitation

The relevant task of reducing the vibrations transmitted to a human operator of a construction or road vehicle during operating process is accomplished, among other things, by conducting the research on mathematical models. Oscillations simulation of the human operator’s seat antivibration suspension by means of the numerical solution of the ordinary differential equations system remains one of the main methods of the study, used in particular for the discrete mathematical models verification. Therefore, the problem of determining the rational value of the maximum integration step by using the numerical method in solving the systems of the ordinary differential equations describing the operator’s anti-vibration suspended seat oscillations is relevant. A discrete mathematical model of a human operator’s seat performing the forced vertical oscillations during kinematic excitation of base movements was developed through the use of the differential equation of the translational oscillations of mass on a movable base. The prescribed displacements of the seat base are described by the harmonic oscillation equation. The numerical solution of the ordinary differential equations system is carried out via the built-in ode45 function of the MATLAB mathematical modeling system. Moreover, the parameters of the developed mathematical model are described, the calculation scheme and an example of a static force characteristic including the quasi-zero stiffness region in the middle section of the characteristic are given. The determination accuracy of the maximum acceleration of the seat in the steady-state oscillation mode is shown to decrease when the value of the maximum allowable integration step increases. It is recommended to limit the value of the maximum allowable integration step to one hundredth of a second. Besides, the effect of the values duality of the maximum acceleration and maximum internal movement of the seat relative to its own base with small changes in the base displacement amplitude, which must be taken into account in modeling, is also revealed.

Modular elastic metasurfaces with mass oscillators for transmitted flexural wave manipulation

In the present study, a modular mass oscillator elastic metasurface (MMEM) is proposed to manipulate the wavefield of flexural waves by assembling and replacing mass-oscillator-like functional units. Based on the bandgap analysis of phononic crystals, the MMEMs were found to achieve a full range of phase shift with relatively high transmission using functional unit arrangements of varying sizes (masses). According to the generalized Snell’s law, the modulation of abnormal refraction, lens focusing, and beam self-acceleration can be realized. To broaden the operating frequency domain, we present the idea of a multiple mass oscillator array design, which can control flexural waves at broadband frequencies of 13–41 kHz by adding/removing mass oscillators within a functional unit. This study presents a method to realize tunable metasurfaces and provides an innovative concept for broadening the operating frequency of elastic metasurfaces.

Minimal Theory of Bigravity: construction and cosmology

Following the path of minimalism in alternative theories of gravity, we construct the “Minimal Theory of Bigravity” (MTBG), a theory of two interacting spin-2 fields that propagates only four local degrees of freedom instead of the usual seven ones and that allows for the same homogeneous and isotropic cosmological solutions as in Hassan-Rosen bigravity (HRBG). Starting from a precursor theory that propagates six local degrees of freedom, we carefully choose additional constraints to eliminate two of them to construct the theory. Investigating the cosmology of MTBG, we find that it accommodates two different branches of homogeneous and isotropic background solutions, equivalent on-shell to the two branches that are present in HRBG. Those branches in MTBG differ however from the HRBG ones at the perturbative level, are both perfectly healthy and do not exhibit strong coupling issues nor ghost instabilities. In the so-called self-accelerating branch, characterized by the presence of an effective cosmological constant, the scalar and vector sectors are the same as in General Relativity (GR). In the so-called normal branch, the scalar sector exhibits non-trivial phenomenology, while its vector sector remains the same as in GR. In both branches, the tensor sector exhibits the usual HRBG features: an effective mass term and oscillations of the gravitons. Therefore MTBG provides a stable nonlinear completion of the cosmology in HRBG.

Evaluation on the Effect of Pressure Transients on Rock Joints in Unlined Hydropower Tunnels Using Numerical Simulation

Frequent pressure transients are identified as the cause of block failures in many unlined hydropower tunnels. The primary design objective of such tunnels is to prevent hydraulic jacking at design static pressure and mass oscillation but neglects the effect of short transients, i.e., water hammer. The issue has not been studied from the perspective of hydro-mechanical interactions due to frequent pore pressure changes in the rock mass. This article mainly focuses on the effect of pressure transients at different static heads, or different effective normal stresses across the joints and the effect of time period of pressure transient. Further, the change in such behaviour due to different mechanical properties of rock joints, such as stiffness, friction angle and dilation, is investigated. Numerical simulations of observed pore pressure response in the rock mass during a pressure transient are carried out using distinct element code 3DEC. The results show that relative joint deformation due to short pressure transients are the highest when joint normal stresses are 1.5–2.5 times higher than static water pressure in the tunnel and thus the vulnerability to weakening of such joints by hydraulic fatigue is higher. Further, results show that water hammers can travel up to 4 m into the rock mass even in stiff joint conditions and sufficiently high normal stresses. Results further indicate that the hydraulic impact due to water hammer is smaller as compared to mass oscillation. It is concluded that water hammers, wherever applicable along the waterway, can still contribute to hydraulic fatigue of rock joints in addition to the effect of mass oscillation and cannot be neglected when pressure transients occur frequently. Tunnel filling/dewatering and mass oscillations cause macroscopic joint displacements or block movements over long-term operation which is the major cause of block falls in unlined pressure tunnels.

Multi-frequency dynamic performance of hydropower plant under coupling effect of power grid and turbine regulating system with surge tank

This paper investigates the multi-frequency dynamic performance of hydropower plant (HPP) under coupling effect of power grid and turbine regulating system with surge tank. Firstly, a model of grid-connected HPP with surge tank is established and verified. Dynamic performance of grid-connected HPP with surge tank is evaluated by analyzing stability and dynamic response. Then, the number of frequencies of dynamic response is identified. The generation mechanism of multi-frequency dynamic response is revealed. Finally, the influence of system parameters on multi-frequency dynamic performance is studied. Guidance for actual applications of the obtained law and mechanism is proposed. The results indicate that the dynamic response of grid-connected HPP with surge tank has a feature of multi-frequency. There are three frequencies for the dynamic response corresponding to three subwaves i.e. mass oscillation, water hammer oscillation and grid disturbance oscillation. Low-frequency mass oscillation is induced by water flow and level oscillation in subsystem of headrace tunnel and surge tank. Medium-frequency water hammer oscillation is induced by natural hydraulic oscillation in subsystem of penstock, turbine, governor and generator. High-frequency grid disturbance oscillation is induced by power grid. The coupling effect among penstock, turbine unit and power grid on water hammer oscillation is strong.

Isochronous n-dimensional nonlinear PDM-oscillators: linearizability, invariance and exact solvability

Within the standard Lagrangian settings (i.e., the difference between kinetic and potential energies), we discuss and report isochronicity, linearizability and exact solubility of some $n$-dimensional nonlinear position-dependent mass (PDM) oscillators. In the process, negative the gradient of the PDM-potential force field is shown to be no longer related to the time derivative of the canonical momentum, $\mathbf{p}% =m\left( r\right) \mathbf{\dot{r}}$, but it is rather related to the time derivative of the pseudo-momentum, $\mathbf{\pi }\left( r\right) =\sqrt{% m\left( r\right) }\mathbf{\dot{r}}$ (i.e., Noether momentum). Moreover, using some point transformation recipe, we show that the linearizability of the $n$-dimensional nonlinear PDM-oscillators is only possible for $n=1$ but not for $n\geq 2$. The Euler-Lagrange invariance falls short/incomplete for $n\geq 2$ under PDM settings. Alternative invariances are sought, therefore. Such invariances, like \emph{Newtonian invariance} of Mustafa \cite{42}, effectively authorize the use of the exact solutions of one system to find the solutions of the other. A sample of isochronous $n$-dimensional nonlinear PDM-oscillators examples are reported.

The effect of high-frequency stochastic actions on the low-frequency behaviour of dynamic systems.

The dynamic system described by a finite number of first-order differential equations is considered. The right side of each equation is a sum of a slow, deterministic and, in the general case, nonlinear function of dynamic variables and a stochastic excitation. The stochastic action is a superposition of a finite number of independent random processes with coefficients depending on dynamic variables and slow time. The problem statement is oriented to applications in the field of driven systems. The analysis is based on the concept of vibration mechanics proposed by I. I. Blekhman. The modified method of direct separation of slow and fast motions uses the explicit introduction of a small parameter and some ideas of the two-scale technique. The general formulas for vibrational forces (or fluxes) are obtained. These additional terms appear in the resulting system for averaged motion instead of the stochastic terms to make the averaged system equivalent to the initial stochastic system with respect to slow motions and, in particular, to low-frequency resonances. As an example, the model of a vibration machine for bulk material processing is considered. The stochastic effect is caused by random oscillations of the bulk material mass. It is transformed into a modification of the machine's frequency characteristics leading to a specific stochastic resonance. This article is part of the theme issue 'Vibrational and stochastic resonance in driven nonlinear systems (part 1)'.

Nonlinear viscoelastic oscillations of single-mass system at power excitation

Nonlinear oscillations of single-mass system at force excitation of vibration connected with fixed base by weightless viscoelastic spring are considered. To take into account the rheological properties of the spring material, the Boltzmann-Volterr principle was used. Mathematical models of the problem in question are obtained, which are described by nonlinear integro-differential equations. A solution method based on the use of quadrature formulas has been developed and a computer program has been compiled on its basis, the results of which are reflected in the form of graphs. Influence of nonlinear and rheological properties of spring on amplitude and phase of mass oscillations is investigated.

A Mathematical Modelling with Zakharov System for Langmuir Wave in Unmagnetized Plasma

In this article we present a discussion and overview of mathematical result of the self-focusing of a Langmuir wave which governs Zakharov system and has studied the self- focusing of a Langmuir wave following by Gaussian distribution. Langmuir wave propagates through uncharged plasma which governed by Zakharov systems. The phenomenon plays a vital role in the Dynamics. We present the article mathematical model with effect of Landou damping. Relativistic mass oscillation and ponderomotive force on electrons of the ionized plasma encouraged the Langmuir wave which resists the self-focusing effect when damping is ignored. The Beam radius gets narrow. when it further propagates considering the paraxial ray’s approximation, the self-focusing length Rn. It shows that characteristics of varying bandwidth distance of propagation in relativistic plasma.