Vibrational Subsystem Research Articles

Robust low-complexity vibration suppression control of rolling mill with time-varying state constraints

In this paper, a novel robust low-complexity vibration suppression control scheme is proposed for the vertical-torsional-horizontal coupling vibration of the rolling mill. To facilitate the control design, the overall coupling vibration system is decoupled into vertical-horizontal coupling vibration subsystem and torsional vibration subsystem. For the vertical-horizontal coupling vibration subsystem, a novel robust low-complexity controller is designed via constructed error transformations to provide strong robustness against uncertainties and disturbances. For the torsional vibration subsystem, a new robust state feedback controller is constructed via a backstepping technique to ensure the vibration angle of the motor rotor within given constraints via a proper asymmetric barrier function. The overall coupling vibration system is proved to be stable in the sense of uniform ultimate boundedness, and the vibration amplitude of the rolling mill can be reached arbitrarily small by selecting appropriate controller parameters. The numerical simulation is performed to verify the effectiveness and the superiority of the proposed control strategy.

Dipole-monopole criticality and chargeless half mode in an integrable gauge-coupled pseudoexciton-phonon system on a regular one-dimensional lattice.

A one-dimensional nonlinear dynamical system of gauge-coupled intrasite excitations and lattice vibrations on an infinite one-dimensional regular lattice is studied. The system as a whole is shown to be integrable in the Lax sense and it admits the exact four-component analytical solutions. Two mutually PT-conjugated symmetry broken solutions are explicitly isolated in the framework of the Darboux-Bäcklund dressing technique. Each of the obtained four-component solutions demonstrates the pronounced interplay between the interacting subsystems in the form of an essentially nonlinear superposition of two principally distinct types of traveling waves characterized by two physically distinct spatial scales and by two distinct running velocities. Depending on the relationships between the spatial scaling parameters the system can manifest itself in three qualitatively distinct dynamical regimes referred to as the monopole regime, dipole regime, and threshold regime. The threshold value of the localization parameter separating the monopole and dipole dynamical regimes is strictly established in terms of basic physical parameters. The phenomenon of dipole-monopole crossover for the spatial distribution of pseudoexcitons is shown to initiate the partial splitting between the pseudoexcitonic and vibrational subsystems in the threshold dynamical regime specified by the threshold value of the localization parameter. This partial splitting is manifested by the complete elimination of one pseudoexcitonic component accompanied by the actual conversion of another pseudoexcitonic component into a pseudoexcitonic chargeless half mode. The integrable nonlinear pseudoexciton-phonon system under study is expected to be applicable for modeling the nonlinear dynamical properties of properly designed PT-symmetric metamaterials.

Pressure effect of the charge density wave transition on Raman spectra and transport properties of 2H−NbSe2

Charge density wave (CDW) order is widely existing and fundamentally important in solid-state physics. However, several critical issues regarding the vibrational and electronic subsystems and their coupling still need to be better understood. Here, we tune the electrical transport and collective vibrational excitation, i.e., phonon and amplitude mode, by pressure in a prototype charge density wave material, $2H\text{\ensuremath{-}}{\mathrm{NbSe}}_{2}$. A complete pressure-temperature phase diagram is revisited. The anomaly in Hall and magnetoresistivity at CDW critical temperature, ${T}_{\mathrm{CDW}}$, was suppressed by the pressure. In the Raman spectroscopy measurements, the appearance of CDW amplitude mode is accompanied by the freezing of the two-phonon mode. The frequency of CDW amplitude mode under pressure follows modified mean-field theory with power-law scaling $(\ensuremath{\beta}=0.18)$. The renormalization of the Raman phonon across the CDW transition and the mean-field temperature dependence of CDW amplitude mode emphasized the importance of electron-phonon coupling in the formation of CDW state in $2H\text{\ensuremath{-}}{\mathrm{NbSe}}_{2}$. Our work clarifies the complex vibrational and electronic subsystems and sheds light on the mechanism of the charge density state in $2H\text{\ensuremath{-}}{\mathrm{NbSe}}_{2}$.

Dipole–Monopole Crossover and Chargeless Half-Mode in an Integrable Exciton–Phonon Nonlinear Dynamical System on a Regular One-Dimensional Lattice

A new form of the integrable nonlinear exciton–phonon dynamical system characterized by two physically independent parameters is suggested. The system is settled along an infinite one-dimensional regular lattice, and it admits the semi-discrete Lax representation in terms of 3 × 3 auxiliary spectral and evolution matrices. The explicit analytic four-component solution to the system’s dynamical equations found by means of the Darboux–Backlund dressing technique turns out to be of broken PT-symmetry. Each component of the solution consists of two nonlinearly superposed traveling waves that inspires the dipole–monopole crossover for the equal values of two physically distinct spatial scaling parameters of the nonlinear wave packet. The phenomenon of the dipole–monopole alternative for the spatial distribution of pseudoexcitons is shown to initiate the partial splitting between the pseudoexcitonic and vibrational subsystems at the threshold point manifested by the complete elimination of one pseudoexcitonic component and the conversion of another pseudoexcitonic component into the pseudoexcitonic chargeless half-mode.

Dipole–monopole alternative as the precursor of pseudo-excitonic chargeless half-mode in an integrable nonlinear exciton–phonon system on a regular one-dimensional lattice

The new form of an integrable exciton–phonon nonlinear dynamical system distinguished by the two physical parameters is suggested. The system is settled along an infinite one-dimensional regular lattice and it admits the semi-discrete Lax representation in terms of 3 × 3 auxiliary spectral and evolution matrices. The explicit analytical four-component solution to the system’s dynamical equations found by means of Darboux–Bäcklund dressing technique turns out to be of broken PT-symmetry giving rise to the crossover between the monopole and dipole regimes of system’s dynamics. The crossover effect is proved to be inseparable from the mutual influence between the interacting subsystems in the form of specific nonlinear superposition of two qualitatively distinct types of traveling waves characterized by the two spatial scales and by the two velocities of two physically distinct origins. The threshold value of localization parameter separating the monopole and dipole dynamical regimes is strictly established in terms of the basic physical parameters. The phenomenon of dipole–monopole alternative for the spatial distribution of pseudo-excitons is shown to initiate the partial splitting between the pseudo-excitonic and vibrational subsystems in the so-called threshold dynamical regime specified by the threshold value of localization parameter. This partial splitting is manifested by the complete elimination of one pseudo-excitonic component accompanied by the actual conversion of another pseudo-excitonic component into the pseudo-excitonic chargeless half-mode. Relying upon the inherent PT-symmetry of system’s dynamical equations the four-component symmetry broken PT-conjugated counterpart solution is also analytically recovered. The integrable nonlinear exciton–phonon system under study is expected to be useful in modeling the nonlinear dynamical properties of PT-symmetric metamaterials. The critical overviews of several relevant and several irrelevant model systems are given to rebuff certain misleading but dogmatically accepted notions and statements circulating in scientific literature.

Theory of thermal properties of magnetic materials with unknown entropy

Theoretical approaches to study thermal properties of magnetic materials typically require accurate models of magnetic interactions in order to define the entropy. Here we introduce a complementary approach for examining thermal properties in magnetic systems where an accepted model for such interactions does not exist. In place of a specific model for magnetic interactions, the approach integrates measurements of temperature dependent magnetization of the studied material into a first principles computational scheme. The approach calculates system pressure from thermally disordered microstates that properly incorporate vibrational and spin subsystems at each temperature as well as the coupling between these subsystems. We apply the approach to calculate phonon modes and to investigate the anomalously low thermal expansion of the classical Invar alloy ${\mathrm{Fe}}_{0.65}{\mathrm{Ni}}_{0.35}$. The calculated phonon dispersions for Invar are in excellent agreement with measured data. The Invar thermal expansion is shown to remain small between 50 K and room temperature, consistent with the experimentally observed low thermal expansion value in this same temperature range. This anomalously small thermal expansion is directly connected to a small positive contribution from lattice thermal disorder that is nearly canceled by a large negative magnetic disorder contribution. By contrast, calculations for bcc Fe show a much larger thermal expansion, consistent with experiment, which is dominated by a large contribution from lattice thermal disorder that is reduced only slightly by a small negative contribution from that of magnetism. These findings give insight into the unusual nature of magnetism and spin-lattice coupling in Invar and Fe. In addition, they give promising preliminary support to the presented methodology as a complementary way to investigate thermal properties of magnetic materials. The success achieved on Invar and Fe motivates future testing of the approach on other magnetic materials.

Charge transfer mechanisms in DNA at finite temperatures: From quasiballistic to anomalous subdiffusive charge transfer.

We address various regimes of charge transfer in DNA within the framework of the Peyrard-Bishop-Holstein model and analyze them from the standpoint of the characteristic size and timescales of the electronic and vibrational subsystems. It is demonstrated that a polaron is an unstable configuration within a broad range of temperatures and therefore polaronic contribution to the charge transport is irrelevant. We put forward an alternative fluctuation-governed charge transfer mechanism and show that the charge transfer can be quasiballistic at low temperatures, diffusive or mixed at intermediate temperatures, and subdiffusive close to the DNA denaturation transition point. Dynamic fluctuations in the vibrational subsystem is the key ingredient of our proposed mechanism which allows for explanation of all charge transfer regimes at finite temperatures. In particular, we demonstrate that in the most relevant regime of high temperatures (above the aqueous environment freezing point), the electron dynamics is completely governed by relatively slow fluctuations of the mechanical subsystem. We argue also that our proposed analysis methods and mechanisms can be relevant for the charge transfer in other organic systems, such as conjugated polymers, molecular aggregates, α-helices, etc.

Оценка влияния скорости реакции термодинамической подсистемы на динамику процесса резания при металлообработке

Introduction. Modern metalworking machines with CNC, allow to achieve a qualitatively new level of metal processing by cutting in metal turning. At the same time, it is possible to achieve the required shape, dimensional accuracy, as well as the relative position of the surfaces of the part, but such an indicator of the processing quality as the roughness of the treated surface, associated with the vibration activity of the tool, does not always meet the specified requirements. The factor determining the vibration mode of cutting in a metal-cutting lathe is the self-excitation factor of the cutting system, which is caused by additional feedbacks formed during the cutting process, one of which is the thermodynamic subsystem of the cutting system, which is the subject of research. Purpose of the work: due to the formation of a consistent model of the relationship between the subsystems that describe the force, heat and vibration reactions of the tool, an adequate description of the mechanism for reducing the vibration load on the cutting process is obtained. The paper studies the process of metal turning on metal-cutting machines with a detailed description of the interaction between the thermodynamic, power and vibration subsystems of the cutting system. Research methods: full-scale and numerical experiments in which the Matlab package of mathematical programs is used for data processing and analysis. Results and discussion. The results of full-scale and numerical experiments are presented, in particular, graphs of coordinate changes describing tool deformation, and data sets are obtained that reflect the dependence of the vibrational energy of tool movements on the reaction time of the thermodynamic subsystem of the cutting system. A qualitative assessment of the results of a full-scale experiment allows us to confirm the adequacy of both the model itself and the results of its modeling. The scope of application of the results obtained in the study is related to the possibility of preliminary preparation of the cutting wedge, which will provide a set value of the time constant of the thermodynamic subsystem, which in turn ensures the minimization of vibration energy. Conclusion: the mathematical model proposed in this paper adequately describes the mechanism of temperature influence on the vibration load of the turning process.

Design of an intelligent vibration screening system for armyworm pupae based on image recognition

Biological control is a green and effective pest management method to mitigate or inhibit pests and pest effects by introducing natural enemies. The stinkbug is one of the insects used for biological control and fed on armyworm. It is necessary to separate the farm-raised armyworm from the sticky substrate after pupation. At present, the work is done manually, with high labor intensity, low efficiency and high cost. In this paper, an intelligent vibration screening system of armyworm pupae based on image recognition is developed. The system can effectively separate the pupae from the sticky substrate without damaging the pupae. The system is comprised of vibration subsystem, separation subsystem, image recognition subsystem and control subsystem. The pupa material is sticky and cannot be shaken off by vibration alone. Therefore, the separation subsystem uses the reciprocating motion of the brush to separate the armyworm from the substrate. Then, the image recognition technology is used to adjust the feed quantity in real time to ensure the optimal screening effect. Finally, the optimal working parameters, including separation speed, vibration frequency and feed quantity, are determined by using the design method of linear regression and linear programming. The experimental results show that the screening rate of the screening system can reach 90%, and the damage rate can be controlled within 5%.

Vibrational CARS measurements in a near-atmospheric pressure plasma jet in nitrogen: II. Analysis

The understanding of the ro-vibrational dynamics in molecular (near)-atmospheric pressure plasmas is essential to investigate the influence of vibrational excited molecules on the discharge properties. In a companion paper Kuhfeld et al (2021 J. Phys. D: Appl. Phys. 54 305204), results of ro-vibrational coherent anti-Stokes Raman scattering (CARS) measurements for a nanosecond pulsed plasma jet consisting of two conducting molybdenum electrodes with a gap of 1 mm in nitrogen at 200 mbar are presented. Here, those results are discussed and compared to theoretical predictions based on rate coefficients for the relevant processes found in the literature. It is found, that during the discharge the measured vibrational excitation agrees well with predictions obtained from the rates for resonant electron collisions calculated by Laporta et al (2014 Plasma Sources Sci. Technol. 23 065002). The predictions are based on the electric field during the discharge, measured by electric field induced second harmonic generation Kuhfeld et al (2021 J. Phys. D: Appl. Phys. 54 305204), Lepikhin et al (2020 J. Phys. D: Appl. Phys. 54 055201) and the electron density, which is deduced from the field and mobility data calculated with Bolsig+ Hagelaar and Pitchford (2005 Plasma Sources Sci. Technol. 14 722–33). In the afterglow a simple kinetic simulation for the vibrational subsystem of nitrogen is performed and it is found, that the populations of vibrational excited states develop according to vibrational-vibrational transfer on timescales of a few microseconds, while the development on timescales of some hundred microseconds is determined by the losses at the walls. No significant influence of electronically excited states on the populations of the vibrational states visible in the CARS measurements () was observed.

Normal mode analysis of membrane protein dynamics using the vibrational subsystem analysis.

The vibrational subsystem analysis is a useful approach that allows for evaluating the spectrum of modes of a given system by integrating out the degrees of freedom accessible to the environment. The approach could be utilized for exploring the collective dynamics of a membrane protein (system) coupled to the lipid bilayer (environment). However, the application to membrane proteins is limited due to high computational costs of modeling a sufficiently large membrane environment unbiased by end effects, which drastically increases the size of the investigated system. We derived a recursive formula for calculating the reduced Hessian of a membrane protein embedded in a lipid bilayer by decomposing the membrane into concentric cylindrical domains with the protein located at the center. The approach allows for the design of a time- and memory-efficient algorithm and a mathematical understanding of the convergence of the reduced Hessian with respect to increasing membrane sizes. The application to the archaeal aspartate transporter GltPh illustrates its utility and efficiency in capturing the transporter's elevator-like movement during its transition between outward-facing and inward-facing states.

Optimized state-dependent switching law design for a class of switched nonlinear systems with two unstable subsystems

This paper proposes a new method for designing a state-dependent switching law to stabilize a class of switched nonlinear system with two unstable subsystems. The main idea is to convert each subsystem to a second-order mechanical system by introducing a reversible transformation, thus the summation of its kinetic and potential energies is calculated as an energy function. Then, by defining a performance index with energy function and using the variational principle, two optimal switching curves are derived from the Euler equation. By adopting a switching law designed by such switching curves, the state of the switched system can approach to the origin at the fastest speed in a sense. In addition, for the case of switched systems with linear vibration subsystems, a critical stability condition related to the stiffness and negative damping coefficients of the subsystems is obtained to make the switched system periodic. Finally, simulation results show that the proposed method can effectively solve the stability problem of switched systems, in which each subsystem does not have any stability factors.

Tunneling current-induced entanglement between electronic and vibrational modes in coupled molecules

The formation of entanglement between the electronic and vibrational subsystems of two interacting molecules localized between tunneling contact leads was theoretically analyzed using the Keldysh diagram technique. The time evolution of concurrence after ‘switching on’ the coupling between the molecules was investigated. It was revealed that non-zero concurrence can be present in the system in the resonant case, even if the molecules are connected by the leads. It was also shown that the stationary value of concurrence can be directly expressed by the stationary tunneling current. It reveals non-monotonic behavior with increasing coupling between the molecule’s electronic states. In the regime of small tunneling rates between the molecules and the leads, ‘switching on and off’ the coupling between molecules multiple times, while detecting one of the molecules’ charge states after each ‘on’ and ‘off’ cycle, results in the appearance of non-classical phonon statistics and opens the possibility of creating a vibrational mode in a Fock state.

Автоколебательные процессы в системе двух электромагнитов, соединенных по дифференциальной схеме

A number of modern technological processes can be significantly intensified by applying vibratory excitation in a wide range of oscillation frequencies and amplitudes. In many cases, an electromagnetic vibration exciter (EMVE) may serve as the most effective source of vibration, especially at power levels up to several kilowatts and more; push-pull EMVEs developing a non-pulsating and sign-variable exciting force are considered to be the most appropriate ones. The excitation of self-oscillations in a system of two electromagnets connected according to a differential scheme, which allows the range of operating frequencies to be widened and the system power capacity to be increased, is analyzed. An equation describing the interaction between the EMVE mechanical vibration subsystem and the power supply system is given. A method for analyzing a dual-circuit self-contained electromechanical system (EMS) taking into account electromechanical links is developed. It is pointed out that during operation in the autonomous mode one stable state ensuring frequency stability is realized.

Thermoviscoplasticity in Body-Centered Cubic Metals: A Two-Temperature Model With Grain Boundary Evolution

Abstract In this work, we develop a thermo-viscoplasticity model for body-centered cubic (BCC) metals based on a two-temperature theory of nonequilibrium thermodynamics. Modeling the plastic deformation here involves two subsystems, viz., a configurational subsystem related to grain growth, dislocation motion, and a kinetic vibrational subsystem describing the vibration of atoms. Due to a separation of the time scales, the two subsystems are described by two different temperatures. In this study, we introduce a grain boundary density, in addition to the mobile and forest dislocation densities, as an internal variable. The focus in this paper is on how large plastic deformation is affected by the evolving grain boundaries. In order to check the predictive quality of the model, numerical simulations are conducted and validated against available experimental evidence wherever possible.

Dynamics of a three-parameter electromagnetic vibration energy harvester considering electromechanical coupling

The paper concerns the dynamic responses and vibration energy harvesting characteristics in an electromagnetic vibration energy harvester comprising three-parameter mechanical vibration subsystem. For completeness and comparison, a two-parameter vibration energy harvester is also presented. The analytical expressions of the amplitude-frequency and phase-frequency responses of the inertial mass and the current in the electrical circuit are respectively derived by applying dimensionless method to the studied two- and three-parameter dynamic systems. Considering the effects of different types of ambient excitation, a single-frequency harmonic load and a periodic load are introduced into the analytical expressions on the dynamic performance of the vibration energy harvester. First of all, the influences of the designing parameters from the mechanical vibration subsystem and the electrical circuit subsystem on the vibration energy harvester are investigated. For evaluating the effects due to introducing the three-parameter mechanical vibration component, comparisons are made between two- and three-parameter vibration energy harvesters to convert the ambient excitations into electrical energy. And then, the expressions of the dimensionless average power which delivered into an electrical load under a single-frequency harmonic excitation or a periodic excitation are derived. The calculating results show that the energy conversion efficiency is enhanced significantly by changing the mechanical damping efficiency and the stiffness ratio for the three-parameter mechanical component of the energy harvester. At the same time, the average power of the three-parameter vibration energy harvester, which delivered into the electrical load, is also improved. However, the influences of the electrical circuit component on the ambient energy harvesting can be omitted when keeping the designing parameters of the mechanical part constant.

A real-time hybrid aeroelastic simulation platform for flexible wings

The concept of real-time hybrid aeroelastic simulation for flexible wings is introduced in this paper. In a hybrid aeroelastic simulation, a coupled aeroelastic system is “broken down” into an aerodynamic simulation subsystem and a structural vibration subsystem. The coupling between structural dynamics and aerodynamics is maintained by the real-time communication between the two subsystems. As the vibration of the testing article (a wing member or a full aircraft) is actuated by actuators, hybrid aeroelastic simulation and experiment can eliminate the sizing constraint of the conventional aeroelastic testing performed within a wind-tunnel. It also significantly saves the cost of wind-tunnel testing. However, several critical technical problems (such as process noise, measurement noise, and actuator delay) need to be addressed to enable a hybrid simulation in real-time. This paper proves the concept of real-time hybrid simulation and discusses some of the critical problems underlying the technique.

Early fault diagnosis of rolling bearing based on noise-assisted signal feature enhancement and stochastic resonance for intelligent manufacturing

It is of great significance for intelligent manufacturing to study condition monitoring and diagnosis methods to realize early diagnosis of mechanical equipment faults. An early fault diagnosis method for rolling bearing based on noise-assisted signal feature enhancement and stochastic resonance was proposed. The advantage of this algorithm is that it avoids the shortage of useful information filtering in traditional noise reduction methods. The generalized multi-scale permutation entropy screening criterion was used to screen the vibration signal, and the parameters of the Duffing vibration subsystem were optimized by the particle swarm optimization algorithm to achieve the optimal matching among the Duffing vibration subsystem, the input signal, and noise, thereby improving the stochastic resonance effect. Part of the background noise energy is transferred to the early weak fault signal feature of the rolling bearing, which enhances the feature of the early weak fault signal. The proposed method was applied to the early fault diagnosis of rolling bearing life state and compared with the adaptive morphology method based on variational mode decomposition (VMD). The results show the effectiveness and feasibility of the proposed method.

Effect of PIG’s physical parameters on dynamic behavior of above ground pipeline in pigging operation

In this paper, the effects of PIG (Pipeline Inspection Gauge) parameters on dynamic response of a simply supported Above-Ground pipeline are investigated during pigging operation. The approach is based on finite element modeling verified by the experimental modal analysis (EMA). In the author’s previous study, the governing equations of motion for system (Pipe, PIG as a moving vibrational sub-system, and conveyed fluid) were obtained using Hamilton’s principle. In the present study, extracted equation are developed based on PIGs with different geometric parameters. The modal parameters of the pipeline system are calculated in the intermittent passage of PIGs along the pipe under different flow rates and their variations are extracted. Theoretical and experimental studies are performed to determine the effect various PIG parameters have on dynamic behavior of pipeline system. Changes in the system natural frequencies due to the speed and position of PIG in the pipe are also investigated. Moreover, displacement analysis for the mid-span of the considered pipe during the pigging operation is conducted using suggested theoretical model. Both numerical and experimental results show the substantial effects of PIG physical parameters, especially disc number and material, on dynamic behavior of the pipe system.

Four-component integrable systems inspired by the Toda and the Davydov–Kyslukha models

Two types of general nonlinear integrable systems on infinite quasi-one-dimensional regular lattices are proposed. In accordance with the Mikhailov reduction group theory both general systems turn out to be underdetermined, thereby permitting numerous reduced systems written in terms of true field variables. Each reduced system thus obtained can be regarded as an integrable version of two particular coupled subsystems, and under the appropriate choice of coupling parameters any reduced systems can manifest the symmetry under the space and time reversal (PT-symmetry). Thus, we have managed to unify the Toda-like vibration subsystem and the self-trapping-like exciton subsystem into a single integrable system, thereby substantially extending the range of realistic physical problems that can be rigorously modeled. Several lowest conserved densities associated with either of the relevant infinite hierarchies of local conservation laws are found explicitly in terms of prototype field functions.