Dynamic Behavior Of System Research Articles

A hybrid rotordynamic modeling method for a rotor system with flexible foundation and nonlinear support force: Numerical and experimental investigation

The dynamic characteristics of a flexible foundation would greatly affect the dynamic behavior of the rotor system. In this paper, a hybrid dynamic model method in time domain combines the finite element (FE) method and the subspace-based identification method to model a rotor system with the consideration of a flexible foundation and nonlinear support forces. The state-space model of flexible foundation is identified by the subspace state-space system identification algorithm with measured frequency response functions (FRFs). To solve the calculation problem of the hybrid dynamic model in time domain, a general algorithm named the hybrid model fusion solution (HMFS) method is proposed, which combines the linear and nonlinear nodes separation method used in the FE model and the trapezoidal rule used in the state-space model, improving the calculation efficiency of solving transient response with nonlinear forces. Simulations for the hybrid dynamic model under constant speed and speed-up cases were carried out, resulting that the dynamic characteristics of the entire system can be represented when the nonlinear factors of rolling bearings and gravity were also taken into consideration. Additionally, owe to the consideration of tested dynamic behaviors of flexible base, experimental results in the laboratory test rig are well agreed with the numerical ones under two different test configurations. The investigation provides a complete modeling and highly efficient solution framework for the rotor system with a flexible foundation and nonlinear rolling bearings, with the abilities of further consideration of more nonlinear components such as squeeze film dampers and rubbing forces.

Droop-Based DC Microgrids Analysis and Control Design Using a Weighted Dynamic Aggregation Modeling Approach

In this paper, Weighted Dynamic Aggregation (WD agg) approach is used for modeling, analyzing and control loop design of islanded DC microgrids. The proposed approach models <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><inline-formula><tex-math notation="LaTeX">$ \textbf {n}$</tex-math></inline-formula></i> DC-DC converters and their controllers with a single equivalent converter and an equivalent control system, which without sacrificing the accuracy, reduces the complexity of such large-scale system studies. It is shown that the model equivalent converter and control system parameters can be determined by the weighted average of the corresponding parameters of the large-scale system. The weight of each converter is quantified based on the contribution of that converter in the overall dynamic behavior of the large-scale system. WD agg model can accurately predict the transient response and can be employed in power planning, stability and sensitivity analyses with high accuracy. It is also shown that the proposed model can be used in designing the controller parameters of the large-scale system to ensure desirable system performance. The accuracy and applications of the proposed WD agg model are evaluated through time-domain simulations, and experiments of an islanded microgrid consisting of three paralleled converters with different control parameters connected to a Constant Power Load (CPL) emulating a challenging system stability case.

Dynamic Analysis of Impulsive Differential Chaotic System and Its Application in Image Encryption

In this paper, we study the dynamic behavior of an impulse differential chaotic system which can be applied to image encryption. Combined with the chaotic characteristics of the high dimensional impulsive differential equations, the plaintext image can be encrypted by using the traditional Henon map and diffusion sequences encryption algorithm. The initial values and control parameters serve as keys for encryption algorithms, and the algorithm has a larger key space. The key is resistant to minor interference and the accuracy can reach 10−12. The simulation results show that the impulsive differential chaotic system has a good application prospect in image encryption.

Dynamic analysis of a dielectric elastomer – Based bistable system

Bistable structures, which are capable of oscillating between two stable states, have garnered significant attention and have been applied in many engineering domains due to their nonlinear behaviors. This paper presents for the first time a physical nonlinear bistable structure comprising a circular dielectric elastic membrane (DEM) coupled with four linear springs, enabling the DEM to achieve large deformations with the system oscillating between two stable equilibrium states. The nonlinear dynamics of the proposed bistable system under harmonic excitation is investigated through analytical, experimental, and numerical methods. First, the system structure is introduced and the corresponding dynamic model is established using Euler-Lagrange equations. Subsequently, the restoring forces of the DEM are experimentally measured, and the dynamic behavior of the bistable system is experimentally tested to validate the theoretical model. Furthermore, the dynamic responses of the system under different excitations are fully studied, and the influences of some key system parameters on the system response are analyzed. Research results demonstrate that the proposed structure exhibits bistable behavior under external excitation and the dynamic behavior of the system can be accurately predicted using the derived theoretical model. The proposed bistable structure contains rich dynamic behaviors including periodic motion, period-doubling bifurcations, and chaotic vibrations. The obtained parameters adjusting rules provide guidelines for the control of system's responses, which have potential applications in many fields such as vibration mitigation and energy harvesting.

Effect of the dipolar interaction on the dynamic hysteresis properties of 2D-nanodisks: out of plane driving field case

We have systematically investigated the effect of dipolar interaction strength on the dynamical hysteresis behavior of the in-plane uniaxial anisotropic nanodisk system modeled by the classical Heisenberg model under the effect of the time-dependent external out-of-plane periodic magnetic field. Dynamical hysteresis loops, as well as hysteresis quantities (hysteresis loop area, coercive field, remanent magnetization), have been examined both in-plane and out-of-plane magnetization components by means of Monte Carlo simulation based on Metropolis Algorithm. Our simulation results suggest that the response of the in-plane and out-of-plane components of the magnetization have different hysteresis characteristics. For instance, while the out-of-plane component of the magnetization has ordinary dynamically disordered hysteresis curves, bowtie-shaped hysteresis loops have been obtained for the in-plane component of the magnetization. Disappeared dynamical order has been observed with the rising strength of the dipolar interaction.

A new fractional-order 5D memristive chaotic system with special extreme multistability and its application to image encryption

Introducing memristor into the chaotic system can enrich the dynamic behaviors of the chaotic system. We propose a symbolic function memristor model and introduce it into a chaotic system to construct a fractional-order 5D memristor chaotic system. Through dynamic analysis of equilibrium point, Lyapunov exponents, phase diagram and bifurcation diagram, it is found that the system has abundant dynamic behaviors, for example, the change of equilibrium point type with parameters, transient chaos, offset-boosting and a special kind of extreme multistability. And with the change of parameters, the attractor state and shape will appear rich changes. Then the correctness of the system is verified by circuit simulation. The chaotic system is introduced into the process of image encryption, and an encryption system is constructed, which is composed of Zigzag scrambling, Hilbert curve scrambling, DNA encryption and GF257 diffusion algorithm. Finally, through a variety of security verification, the results show that the encryption system has good security and can resist many kinds of attacks effectively.

A novel financial system with one stable and two unstable equilibrium points: Dynamics, coexisting attractors, complexity analysis and synchronization using integral sliding mode control

In the world of economics, financial risk is a significant issue that concerns countries and all economic agents. It refers to the potential for experiencing losses due to unpredictable fluctuations in financial or investment activities caused by endogenous factors. Chaos theory provides an explanation for the complexity observed in economic time series, as it supports an endogenous view. This article proposed an enhanced chaos-based financial risk system with one stable and two unstable equilibrium points. The existence of stable and unstable equilibrium points shows that the proposed system has both hidden and self-excited chaotic attractors. By analyzing its dynamic behavior, the study unveils the transition from stability to chaos in the improved financial risk system, while also describing how the complex dynamics of the system affect changes in financial market risk. In addition, this study explores the fundamental dynamic behavior of the financial risk system, including stability analysis, Lyapunov exponent, bifurcation analysis, coexisting attractors, 0–1 test, algorithm and spectral entropy (SE). Finally, with the help of integral sliding mode control (ISMC), we discover the outcomes for the asymptotic synchronization of two chaotic financial systems that are constructed as master and slave systems. Simulations are provided to accompany and support the findings from this research.

Research on dynamic characteristics of the turnover system of rail belt conveyor

The rail belt conveyor is a new bulk material conveying system that combines the advantages of traditional belt conveyors and railway systems. However, the turnover system, which is a key part of the carriage’s direction-changing mechanism, experiences severe vibration and impact problems that affect its performance and reliability. In this study, a dynamic model of the carriage-rail coupling in the turnover system is established, and the vibration characteristics of the rail are analyzed. The influence of carriage speed, wheelbase, and wheel diameter on the vibration acceleration of the rail is investigated. The results show that higher carriage speeds intensify the vibration response of the rail when the carriage leaves the turnover wheel. The wheel diameter has a significant effect on the vibration acceleration, especially at high speeds. Additionally, the wheelbase affects the vibration acceleration, with smaller wheelbases resulting in more prominent effects. The established dynamic model is validated using measured data, providing insights into the dynamic behavior of the turnover system in rail belt conveyors.

Dynamics of a Reaction-Diffusion System with Quiescence

In this paper, the dynamical behavior of a reaction-diffusion system with quiescence in a closed environment is investigated. The global existence of the solution is obtained by the upper and lower solution method, and the dissipative structure of the system is derived by constructing Lyapunov functions.

An analytical approach for the analysis of stress wave transmission and reflection in waveguide systems based on Timoshenko beam theory

The paper presents an analytical continuous solution for the analysis of wave refraction and transmission/reflection caused by arbitrarily complex waveguide subsystems. It allows analyzing the way stress wave components are altered as they go through a substructure. The method is new in that it investigates the wave phenomena which govern the dynamic behavior of a structural system explicitly and studies the effectiveness of different serrated and fractal subsystem designs functioning as wave content filters. Timoshenko beam theory is used to model stress wave propagation in waveguides because of its accuracy and consistency over a wide range of vibration frequencies. The versatility of the method is demonstrated using a number of numerical examples characterizing stress wave refraction in single input/single output and single input/multiple output subsystems to study periodic, fractal, and serrated forms. The low computation cost and stable accuracy of the method over a very wide range of frequencies, make it an effective tool for metaheuristic optimization approaches which require massive calculations over many generations. The method is demonstrated to perform seamlessly in coupling with a genetic algorithm optimization framework to determine the optimal serrated configuration of a wave filter.

Transient state analysis of a rub-impact rotor system during maneuvering flight

Maneuvering flight substantially affects the dynamic behavior of rotors; particularly, such flight may cause rubbing between a rotor and stator, which is one of the most serious damages in aircraft engines. In this paper, a nonlinear dynamic model for describing the dynamic characteristics of a rub-impact rotor system during maneuvering flight is established based on the Lagrange equations. Subsequently, numerical simulations employing the Newmark method are performed, delving into the detailed discussion of the influence of parameters such as rotational speed and maneuvering flight on the transient and steady-state responses of the rotor system. The effect mechanism of maneuver load and its coupling with rub impact is revealed. The results show that the impact response induced by maneuvering flight is more obvious in the subcritical state than in the supercritical state. The additional stiffness and damping are also induced; in particular, the additional damping has a coupling effect. Moreover, the rub impact imposes an additional constraint on the rotor system, thereby weakening the influence of the maneuver load and becoming the major factor that determines the dynamic behavior of the rotor system at high speeds.

The thermally assisted magnetization and dielectric relaxation in spin frustrated Ca3Co2O6

The incompatibility between the antiferromagnetic exchange interaction and the triangular lattice makes Ca3Co2O6 become a frustrated system. It leads to the existence of disordered magnetic structure in the frustrated spin chains. At low temperature, the disordered spins are frozen. In this study, the Ca3Co2O6 was prepared and its low temperature dynamic behaviors were characterized. The spin freezing peak and the decay of magnetization with time well confirm the thermally assisted magnetization. Since that the flip of the spins can result in the conservation of the total angular momentum and the conserved angular momentum can make the adjacent lattice feel a transfer torque. In response to variation of magnetization, the dielectric permittivity of Ca3Co2O6 also presents relaxation feature. For the isothermal dielectric permittivity, it not only depends greatly on the sweep rates of magnetic field but also decays with time. This detectable variation of the dielectric property in Ca3Co2O6 suggests that the thermally assisted dielectric relaxation is an alternative method for characterizing the dynamic behaviors of the frustrated system.

Dynamic analysis of a new 4D fractional-order financial system and its finite-time fractional integral sliding mode control based on RBF neural network

In this paper, considering the combined effect of interest rate and investment demand on the price index, a new 4D fractional-order financial system is established. Based on the local stability theory, the stability of equilibrium points and static bifurcation phenomena are discussed. Subsequently, to further analyze the dynamic behaviors of the new financial system, numerical tools such as bifurcation diagrams, Lyapunov exponents, phase diagrams, 0–1 test diagrams, and complexity diagrams are employed. It is found that, for a suitable selection of the differential order or system parameter, the proposed system can generate periodic oscillations with different period and chaotic attractors with different shapes. Furthermore, a new controller combining radial basis function (RBF) neural network with fractional-order integral sliding mode control is proposed to realize the finite-time synchronization for a class of fractional-order systems. Finally, the effectiveness of the presented control scheme is verified by numerical simulations and the influence of RBF neural network parameters on the control performance is analyzed.

Entanglement dynamics via periodic modulations in an optomechanical system with embedded double quantum dots

In our theoretical study, we explore the dynamic behavior and entanglement properties of a hybrid optomechanical system containing double quantum dots (QDs). The system is driven by a laser with amplitude modulation and we consider the modulation of the resonance frequency of the two QDs. Through the application of modulation techniques, we can achieve the targeted mean field value and effectively control the entanglement between various degrees of freedom. This innovative approach shows great potential for the development of efficient quantum memories suitable for continuous variable quantum information processing.

Generating rectilinear, elliptical, and circular oscillations of a single-mass vibratory system equipped with an enhanced twin crank-type exciter

One of the most intensively developing fields of vibratory technologies is focused on improving the design and operational parameters of the excitation mechanisms and drives. The present research is devoted to a novel twin crank-type exciter driven by a permanent-magnet direct-current motor. The research methodology consists of mathematical modeling and computer simulation of the dynamic behavior of a single-mass oscillatory system equipped with the proposed exciter. The obtained results substantiate the possibilities of generating rectilinear, elliptical, and circular oscillations of the working member by applying the corresponding design changes of the transformable vibration exciter. The major scientific novelty of the carried-out investigations consists in determining the influence of specific design parameters of the exciter on the trajectory (path) of the working member motion. The obtained results can have a significant practical value while designing new and improving existent drives of various vibratory equipment (screens, conveyors, sieves, compactors, technological (lapping, polishing) machines, etc.).

Dynamic behaviors and optimal control of a new delayed epidemic model

We are concerned in this paper with dynamic behaviors and an optimal control problem of a new delayed epidemic model. There are three major ingredients. The first one is the dynamic behaviors of the state system. The locally asymptotic stability of the disease-free equilibrium and the endemic equilibrium are investigated and the effect of time delay on stability is also discussed. It is also found that the Hopf bifurcation appears at a specific time delay. The second, which is the main new ingredient of this paper, is an optimal control problem. Applying vaccine strategy in the system, an optimal control problem is proposed to minimize the total number of infected individuals as much as possible, maximize the total number of the uninfected individuals, and reduce the total control cost. In view of Pontryagin’s maximum principle, the specific characteristics of the optimal control policy are given. The third ingredient is the numerical simulations of the theoretical results.

Dynamic coupling of multi-degrees of freedom constrained-layer vibration neutralizers: A new methodology

Dynamic neutralizers, also known as dynamic absorbers, are efficient means of mitigating vibrations in structures. They have been particularly effective in addressing broad-band passive vibration control in structures with high modal density through the use of multi-degrees of freedom (MDoF) and viscoelastic materials (VEMs). Therefore, sandwich-type or constrained-layer beams can offer great potential when used as MDoF control devices. However, there is limited literature exploring these structures as auxiliary systems, with coupling typically assumed to be single-point and limited to only translational degrees of freedom (DoFs). In this context, this article presents a methodology to determine the dynamic behavior of a compound system, coupling the displacement and rotation DoFs between a metal structure–referred to as the primary system–and a MDoF auxiliary system. The coupling is achieved by utilizing an equivalent dynamic stiffness obtained at the base of the auxiliary system through ANSYS finite-element software, providing a robust and comprehensive approach. A Matlab code transfers the auxiliary system's geometry and properties to ANSYS, where the dynamic stiffness at the base is determined and subsequently coupled to the primary system. A MDoF auxiliary system of the constrained-layer type with VEM was studied, and both single-point and distributed coupling were analyzed. The auxiliary system was attached to a cantilever metal beam for numerical and experimental validation. The proposed generalized equivalent dynamic stiffness model accurately estimates the response of the compound system, offering a 25% reduction in response computation time compared to the finite-element model of the complete compound system. This methodology enables the accurate representation of compound system dynamics while minimizing computational time, making it valuable for the optimal design of a set of MDoF viscoelastic dynamic neutralizers.

Analysis of neural network connections based on memristors and their multiple offset phenomena

The article suggests a construction method of a magnetron memristor connecting a three-dimensional Hopfield neural network and a Rulkov neuron in order to build a more complex and achieve more bio-like neural network properties, which has rarely been proposed before. It is discovered that the dynamical behavior of this high-dimensional neural network system is rich, and that the system exhibits many dynamical behaviors depending on the parameter changes. It is possible to change the attractor’s amplitude and its offset boosting behavior by varying various parameters. Changing the system parameters and modifying the system’s initial value may result in initial offset boosting behavior. Combining nonlinear dynamics research methodologies, such as phase diagram, bifurcation diagram, Lyapunov exponential spectrum, and time series diagram, demonstrates the system’s complex dynamical behavior. By analyzing the system complexity and random sequence test, we found that the system has the characteristics of large complexity and strong pseudo-randomness. Eventually, the hardware realizability is proved by the construction of the DSP platform.

Method for screening paired metal hydrides with appropriate phase change material for a thermochemical energy storage system

Thermochemical energy storage (TES) systems using coupled metal hydrides (MHs) have long been recognized as an option for sustainable energy systems such as solar power plants. The MHs-TES system consists of two linked MH beds (energy storage bed and hydrogen storage bed) that exchange hydrogen during the heat storage/release cycles. The heat reaction of the hydrogen storage bed is stored in a PCM as latent heat, which is recovered during the heat release step. One of the main issues of the MHs-TES system is selecting the best-suited combination of MHs and compatible PCM to satisfy application requirements. Herein, an approach is proposed for screening the right pairs of hydrides and the suitable PCM. To assess this procedure's effectiveness, a 2D-mathematical model is developed, and a computer code is established. In addition, using this code, the dynamic behavior of the MHs-TES system and the effect of the hydrogen storage bed temperature on the system's performance are examined. The Mg2Fe alloy as HTMH bed, and two LTMH beds as LTMH (LaNi4.25Al0.75 at medium temperature and LaNi5 at low temperature) are used. With an efficiency of 86.5%, the results show that Mg2Fe/LaNi5 is a viable MHs combination for a thermal storage system.

A comprehensive study on natural characteristics and dynamic responses of a dual-rotor system with inter-shaft bearing under non-random uncertainty

Aeroengines are usually designed with a dual-rotor configuration for the rotating part. A dual-rotor system has coupling characteristics introduced by an inter-shaft bearing, and the rotating direction of the rotors has critical influences on the performance. It becomes more complicated when the inevitable uncertainties of the dual-frequency excited dynamical system are considered. This paper delivers a comprehensive study of the natural characteristics and dynamic responses of a dual-rotor system with an inter-shaft bearing considering the non-random parametric uncertainties under co- and counter-rotating conditions. To this end, the finite element modeling and the deterministic solutions of a dual-rotor system are established. Then, the polynomial surrogate function is constructed for the desired natural characteristics and dynamic responses under non-random uncertainty. The polar interpolation technique is implemented to compute uncertain shaft orbits, overcoming difficulties in the traditional frequency-sense measure. Intensive case studies for different interval uncertain parameters are carried out and the results are comparatively discussed. It is found that the mass unbalance uncertainties only affect the respective modes excited by the rotor where the unbalance is located. The shaft stiffness has global uncertainty effects on the Campbell diagram, mode shapes, time history, shaft orbit and responses. Uncertainties in the inter-shaft bearing stiffness and speed ratio generally influence higher-order modes. The results of the present work gain insights into the modal characteristics and dynamical behaviors of the dual-rotor system under complex parametric uncertainties.