Nonlinear dynamic characteristics and bifurcation analysis of Ti–Zr–Ni quasicrystal as hydrogen storage material

In this article, the nonlinear dynamic characteristics and bifurcation of a Ti–Zr–Ni quasicrystal impacted by hydrogen atoms are studied. New nonlinear damping terms are proposed to express the delay characteristics of Ti–Zr–Ni quasicrystal, and the accurate natural frequency is obtained by the harmonic balance method. A new method based on the developed largest Lyapunov exponent is proposed to analyze the local stability of any point in the system, and the system's global stability is determined. Finally, a new way to realize the switch between hydrogen storage and release based on stochastic Hopf bifurcation is proposed. The results of theoretical analysis and numerical simulation show that the system's motion can be switched between a periodic orbit and a balanced point near the bifurcation boundary with little energy consumption, which is helpful for hydrogen storage and release.     

Stumped nature hyperjerk system with fractional order and exponential nonlinearity: Analog simulation,bifurcation analysis and cryptographic applications

This article presents the construction and consumption of hyperjerk system having chaotic nature with the commensurate ordered fractional derivative on rapidly digitalized emerging technologies. The system analyzed analytically using Lipschitz condition and numerically with the help of predictor corrector approaches. Originality of constructed system is confirmed using log error plots which gives satisfactory small values on finite time scale. The dynamical performances of the complex system are termed in multiple phase planes by the mean of their significant nature. Stability and bifurcation analysis around the fractional derivative is also studies for the various parameter of system to check the visibility of chaotic solution. The system is also designed in analog circuit simulator with the aid of operational amplifier, anti-parallel semiconductor diodes for validation of the system. With the help of random number generators (RNGs), binary array generated from the hyperjerk system and plugged in to the NIST 800–22 test suite to measure the randomness. The array having high randomness is used as strong cypher key for the cryptographic execution straightforwardly in both direction encryption and decryption.     

动态轧制过程下轧机辊系分岔与混沌特性

基于热连轧机的机械结构和工艺结构,考虑态轧制力对轧机振动的影响,建立了轧机辊系的非线性动态轧制振动模型。根据Lagrange原理,得到了轧机辊系的动力学方程,应用多尺度法求解了系统的分岔响应方程,采用奇异性理论分析得到了系统稳态响应的转迁集及其相应的分岔曲线拓扑结构,利用Melnikov函数法研究了系统发生分岔与混沌的参数临界条件。最后进行数值仿真,通过分岔混沌图、最大Lyapunov指数、相轨迹和Poincare截面验证了理论的有效性,这为抑制和控制轧机系统非线性振动提供了理论参考和借鉴。     

Prediction of dynamic voltage stability status based on Hopf and limit induced bifurcations using extreme learning machine

Evaluation of voltage stability status considering its dynamic boundaries is a key issue for saving global stability of power systems. However, this evaluation is a computationally demanding task and its implementation is very hard (if not impossible) for on-line environments such as dispatching centers of power systems. In this paper, a new viewpoint for the problem based on modeling it as a forecast process is proposed, which can be implemented with a low computation burden for practical power systems. For this purpose, a voltage stability classification model considering Hopf and limit induced bifurcations is proposed and a new forecast strategy to predict voltage stability class label based on the proposed classification is suggested. The suggested forecast strategy is composed of an information theoretic feature selection technique, extreme learning machine (ELM) as the forecast engine and a line search procedure to fine-tune the settings. The effectiveness of the proposed classification model and forecast strategy is extensively illustrated on the New England 39-bus and IEEE 145-bus test systems.     

Robust constrained stabilization of boost DC–DC converters through bifurcation analysis

This paper proposes a new methodology for designing robust affine state-feedback control laws, so that wide-range safe and efficient operation of switched-mode DC–DC boost converters is guaranteed. Several undesirable nonlinear phenomena such as unstable attractors and subharmonic oscillations are avoided through bifurcation analysis based on the bilinear averaged model of the converter. The control design procedure also relies on constrained stabilization principles and the generation of safety domains using piecewise linear Lyapunov functions, so that robustness to supply voltage and output load variations is ensured, while input saturation is avoided and additional state constraints are also respected. The technique has been numerically and experimentally validated.     

Thin-walled structures with slotted connections stability problems

In this paper the linear and non-linear stability analyses of elastic structures with unilateral supports or connections are presented. Local and global buckling phenomena are analysed for a wide range of columns’ lengths to encounter coupled instability, which appears when local buckling occurs close to global one. Influence of clearances on buckling and post-critical response is examined. This phenomena is illustrated using simplified models, where the clearances are introduced as translation or rotation gaps. Main attention is focused on modelling the double sigma members, where the cross-sections are composed of two sigma members, connected in discrete points distributed along the webs. The influence of spacing and way of numerical modelling of connectors on buckling behaviour of beams is studied. Numerical examples illustrate the importance of proper modelling of the structures with slotted connections accounting for initial imperfections. The examples are solved using FEM.     

二元稀溶液合金凝固界面稳定性分析

采用热力学计算技术,研究了凝固过程中Al-Zn稀溶液合金的固/液界面形态线性稳定性及非线性稳定性,讨论了热力学计算技术和采用线性化二元参数在固/液界面线性稳定性和非线性稳定性判断上的差别,分析了固/液界面失稳后的界面形态演化过程,给出了固/液界面亚临界分叉范围.结果表明,采用耦合热力学计算技术能更好的与试验结果吻合,所获得的失稳区域大于采用线性化二元参数所得结果,尤其在线性稳定性判据条件下更为突出.     

Auto-parametric semi-trivial and post-critical response of a spherical pendulum damper

The pendulum vibration damper modelled as a two degree of freedom strongly non-linear auto-parametric system is investigated. A kinematic external excitation in the suspension point is applied. The excitation is considered to be horizontal and harmonically variable in time. A semi-trivial solution and its stability are analyzed. Special attention is paid to the resonance domain. In certain domains of pendulum and excitation parameters the semi-trivial solution does not exist in this domain and various post-critical three-dimensional regimes occur. Some of them are non-stationary despite the harmonic excitation. Three different types of the resonance domain are investigated. Their main properties depend significantly on dynamic parameters of the pendulum and of the external excitation amplitude. An analytical and numerical study brings forth several recommendations for designers of these devices. Their aim is to avoid any post-critical response regimes endangering the pendulum functionality.     

Dynamics of liquid-liquid systems based on linear thermodynamics of irreversible processes

The use of non-equilibrium models for integrated processes involving liquid-liquid systems has increased in recent years. These processes often exhibit complex dynamic behavior. These dynamical systems still pose many open questions, e.g. with regard to the sources of multiple steady states (MSS). This article analyzes the effect of mass transfer on the MSS of these systems. A generalized non-equilibrium modeling approach based on linear thermodynamics of irreversible processes (LTIP) is presented, and the dynamics of the system is studied systematically. It is shown that the non-linearity present in even the simplest non-ideal activity model acts as a source for MSS. The parameters that affect the solubility, e.g. temperature, can play a critical role on the existence of MSS in the system. A geometrical visualization of the MSS is also illustrated.     

Predicting the onset of bifurcation and stability study of a hybrid current controller for a boost converter

The proposed method develops a continuous-time averaging model of a nonlinear current controller for a continuous conduction mode (CCM) boost converter in the lack of a closed outer voltage loop. The controller associates peak-current and sliding mode controls. The advantages of the proposed approach are the capability to show the onset of fast-scale bifurcation, and the reduction of numerical calculation effort. To confirm the validity of the proposed method, simulation and experimental results are detailed.