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Abstract: Abstract Stacked magnetostrictive actuator (SMA) has the advantages of high energy density and high bandwidth, but the output stroke is relatively small and accompanied by strong hysteresis nonlinearity. Introducing the radial-nested stacked configuration, the stroke of a SMA can be increased without deteriorating its bandwidth. However, this configuration consists of three magnetostrictive rods of different shapes which brings more serious asymmetric hysteresis nonlinearity and poses a great challenge on the theoretical modeling of the actuator. In this paper, a magnetic equivalent circuit (MEC) model is established to describe the magnetic characteristic of radial-nested stack. Then, a nonlinear dynamic magnetization model is proposed with the combination of the MEC model and the Jiles-Atherton model. Finally, by considering the multi-degree-of-freedom (MDOF) mechanical dynamic system, a multiphysics comprehensive dynamic (MCD) model is established. What’s more, a prototype of radial-nested stacked Terfenol-D actuator (RSTA) is fabricated, a series of simulations and experiments are conducted to evaluate the proposed models. The parameters that cannot be calculated or measured in the model are identified by employing the multi-island genetic algorithm. Results show that: (a) the MEC model can accurately calculate the magnetic distribution of the RSTA with an error less than 0.2% compared with a finite element model; (b) the MCD model can accurately describe the RSTA output hysteresis nonlinearity under different operating frequencies and amplitudes with a root-mean-square (RMS) error less than 1.1 \(\upmu \hbox {m}\) (1.76%). PubDate: 2022-05-13
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Abstract: Abstract The existence of clearance joints seriously affect the kinematic accuracy and service life of precision mechanisms. So as to ensure the kinematic accuracy reliability of mechanism, it is imperative to accurately predict the dynamic behavior of precision mechanism considering clearances. At present, the studies often focus on theoretical analysis and simulation verification of mechanism with clearances, while the studies verified by experiment are relatively few and often focus on simple mechanism. Moreover, most of studies centered on simple mechanism with dry friction clearance, while the studies on complex mechanism with multiple lubricated clearances are less. In this paper, the impact of multiple clearances on dynamic behavior of 2-DOF 9-bar precision press mechanism is analyzed. Firstly, the mathematical models of dry friction clearance and lubricated clearance are established and embedded into the Lagrange dynamic equation, respectively. Then, the impact of clearance values, the material of clearance-shaft and crank driving speeds on dynamic behavior of mechanism are researched. Finally, the simplified experimental platform of 2-DOF 9-bar press mechanism considering 2D revolute joint clearances is established, and the correctness of the theoretical model is proved by experimental verification. This study not only offers theoretical guidance for the layout and life prediction of multi-link press mechanism, but also provides reference for the dynamic behavior analysis and prediction of other mechanisms. PubDate: 2022-05-13
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Abstract: Abstract The paper devotes to the slow–fast behaviors of a higher-dimensional non-smooth system with the coupling of two scales. Some novel bursting attractors and interesting phenomena are presented, especially the so-called mixed-torus bursting oscillations, in which the trajectory moves along different tori in turn, though the bursting attractor still behaves in quasi-periodic form. Based on a 4-D hyper-chaotic model with two scrolls, a modified non-smooth slow–fast version is established. Upon the smooth and non-smooth bifurcations analysis, the coexisted attractors with the variation of the slow-varying parameter are derived. With the increase in the exciting amplitude, bursting oscillations may change from periodic to quasi-periodic attractor, the mechanism of which is obtained by employing the overlap of the transformed phase portrait and coexisted attractors as well as the bifurcations. Sliding along the boundary on the trajectory can be observed on the bursting attractor, the mechanism of which can be accounted for by employing the non-smooth theory or by the in-turn influence of two pseudo-attractors in different regions. Super-cone defined by an unstable focus may lead to the period-adding or period-decreasing phenomena in the spiking oscillations, while fold limit cycle bifurcation may result in the dramatical change of the spiking amplitude. Different limit cycles may involve the full vector field, resulting in the so-called mixed-torus bursting oscillations, in which the quiescent states seem to be pivots of the oscillations. PubDate: 2022-05-13
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Abstract: Abstract Flexible robots with controllable mechanisms have advantages over common tandem robots in vibration magnitude, residual vibration time, working speed, and efficiency. However, abnormal vibration can sometimes occur, affecting their operation. Traditionally only simple mechanisms are considered in studying abnormal vibration, omitting reference to important chaotic phenomena caused by the flexibility of the mechanism rod. In order to better understand the causes of abnormal vibration, our work takes a controllable flexible robot with a complex series-parallel mechanism as a research object and uses a combination of Lagrangian and finite element methods to establish its nonlinear elastic dynamics. The effectiveness of the model is verified by comparing the calculated frequency with the frequency measured in a test. The time-domain diagram, phase diagram, Poincaré map, maximum Lyapunov exponent, and bifurcation diagram of the elastic motion of the robot wrist are studied, and the chaotic phenomena in the system are identified through the phase diagram, Poincaré map, the maximum Lyapunov exponent, and the bifurcation diagram. The relationship between the parameters of the robot motion and the maximum Lyapunov exponent is discussed, including trajectory angular speed and radius. The results show that chaotic behavior exists in the controllable flexible robot and that trajectory angular speed and radius all have an influence on the chaotic motion. Our work provides a theoretical basis for further research on the control and optimal design of flexible robot mechanisms. PubDate: 2022-05-13
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Abstract: Abstract This paper proposes an optimal parameter design of control scheme for mechanical systems by adopting the Stackelberg game theory. The goal of the control is to drive the mechanical system to follow the prescribed constraints. The system uncertainty is (possibly fast) time-varying and bounded. A \(\beta \) -measure is defined to gauge the performance. A robust control is proposed to render the \(\beta \) -measure uniformly ultimately bounded. This control scheme is based on feasible design parameters (i.e., parameters within prescribed range), and the choices of these parameters may not be unique. For optimal (unique) parameter selection, a Stackelberg game is formulated. By taking the control design parameters as the players, for each player, a cost function is built with the consideration of the performance cost, the time cost and the control cost. To follow, the Stackelberg strategy is then carried out via backward induction, which results in the choice of the optimal parameters. PubDate: 2022-05-13
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Abstract: Abstract Irregular wear is one of the main reasons leading to the failure of mechanical equipment and mechanical parts. The coupling between irregular wear and system dynamic behavior has an important influence on the performance of the mechanism. A modeling and calculation method for planar multi-link mechanism considering multiple wearing clearances is proposed. Taking 2 DOFs nine bars mechanism as research object, iterative wear prediction process based on Archard model is applied to calculate wear characteristics, wear prediction process is combined with multi-body system dynamics to obtain dynamic model considering wearing clearance of revolute pair, and its dynamic response is analyzed. The nonlinear characteristics are analyzed qualitatively and quantitatively by phase diagram, Poincare map, and Largest Lyapunov exponent. At the same time, experimental platform of 2 DOFs nine bars mechanism is built to analyze influence of wearing clearance on response of mechanism. Correctness of theoretical model is verified by experimental results. PubDate: 2022-05-12
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Abstract: Abstract This paper investigates the problem of robust output feedback control for a class of time-delay nonlinear systems with unknown continuous time varying output function. Unlike the previous studies, the considered systems allow the presence of dead-zone nonlinearities, continuous disturbances and time-varying delays. A new robust control scheme is constructed by introducing coordinate transformations that draws the dead-zone characteristic as well as modifying a double-domination method cooperating with integral Lyapunov functions. A combined system is established to perform a one-step mechanism for constructing a continuous controller which guarantees that all closed-loop signals are ultimately uniform bounded. The proposed scheme is finally applied to a two-stage chemical reactor system with dead-zone input and external disturbances to illustrate the effectiveness and performances. PubDate: 2022-05-12
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Abstract: Abstract For various nonlinear physical equations, we describe the features of their rogue waves using simplified forms of their intensities and also by finding ‘volumes’. We present some analysis relating to other higher-order equations, that can be relevant to studies of optical fibres, ocean waves and other aspects of physics. These are related to several low-order KdV and mKdV equations. We investigate details of formations consisting of a central rogue wave with 1 or more solitons emerging from it. We thus classify solutions into rogue waves, semi-rogue waves and formations consisting of a ‘central rogue with soliton tails’. PubDate: 2022-05-12
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Abstract: Abstract A systematic approach for constructing exact periodic-background solutions of integrable nonlinear evolution equations associated with \(3\times 3\) spectral problems is developed by combining the algebro-geometric method with the Darboux transformation. As an application, periodic-background rogue-wave solutions and periodic-background breather solutions for the Yajima–Oikawa long-wave–short-wave equation are obtained. The relation between the periodic-background solitons and periodic-background breathers is discussed. In addition, the interaction dynamics of various periodic-background solutions is analyzed by choosing appropriate parameters. PubDate: 2022-05-12
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Abstract: Abstract A (3+1)-dimensional coupled nonautonomous NLS model with partially nonlocal coupled nonlinearities under the linear and harmonic potentials becomes the center of attention. Two kinds of the reductions from the nonautonomous coupled NLS model to autonomous (2+1)-dimensional and (1+1)-dimensional NLS models are erected, respectively, and the comparison of two reductions is performed and analyzed. Based on solutions of autonomous (2+1)-dimensional and (1+1)-dimensional NLS models, via the Hirota and Darboux methods, two kinds of vector nonautonomous soliton pairs with localized and non-localized structures in three-dimensional space are constructed. Evolutional behaviors of these vector solitons are explored in the periodical system. PubDate: 2022-05-11
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Abstract: Abstract The paper describes the use of active structures technology for deformation and nonlinear free vibrations control of a simply supported curved beam with upper and lower surface-bonded piezoelectric layers, when the curvature is a result of the electric field application. Each of the active layers behaves as a single actuator, but simultaneously the whole system may be treated as a piezoelectric composite bender. Controlled application of the voltage across piezoelectric layers leads to elongation of one layer and to shortening of another one, which results in the beam deflection. Both the Euler–Bernoulli and von Karman moderately large deformation theories are the basis for derivation of the nonlinear equations of motion. Approximate analytical solutions are found by using the Lindstedt–Poincaré method which belongs to perturbation techniques. The method makes possible to decompose the governing equations into a pair of differential equations for the static deflection and a set of differential equations for the transversal vibration of the beam. The static response of the system under the electric field is investigated initially. Then, the free vibrations of such deformed sandwich beams are studied to prove that statically pre-stressed beams have higher natural frequencies in regard to the straight ones and that this effect is stronger for the lower eigenfrequencies. The numerical analysis provides also a spectrum of the amplitude-dependent nonlinear frequencies and mode shapes for different geometrical configurations. It is demonstrated that the amplitude–frequency relation, which is of the hardening type for straight beams, may change from hard to soft for deformed beams, as it happens for the symmetric vibration modes. The hardening-type nonlinear behaviour is exhibited for the antisymmetric vibration modes, independently from the system stiffness and dimensions. PubDate: 2022-05-11
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Abstract: Abstract This paper is concerned with event-triggered control problem for unknown nonlinear systems with input constraints. By introducing a nominal system and a discounted cost function, the original event-triggered control problem is equivalently transformed into an event-triggered optimal control problem. Then, a data-driven model is designed by recurrent neural networks to approximate the unknown dynamics of the considered system to make the obtained results have wide applicability. After obtaining the system dynamics, a single critic neural network is constructed to acquire an approximate solution of the Hamilton–Jacobi–Bellman equation with multiple nonlinear terms. To achieve the purpose of relaxing the persistence of excitation condition, the update law of the critic NN is designed by using the current data and historical data. By resorting to the Lyapunov stability theory, the proposed event-triggered optimal controller can ensure that the state variables and the critic NN weight errors are bounded. Finally, the effectiveness of the developed control scheme is demonstrated by two simulation examples. PubDate: 2022-05-10
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Abstract: Abstract Complex pendulum-sloshing dynamics induced with specific payloads such as the suspension liquid container increase incredibly the difficulty of the anti-swing control for overhead cranes. Especially, it would be a greater challenge for anti-swing control with simultaneously considering the transportation time and the energy consumption while guaranteeing actuated/unactuated states constraints. In this paper, an optimal trajectory planning strategy for overhead crane with pendulum-sloshing dynamics is proposed by taking transportation time, the energy consumption and full-state constraints into account. First, the dynamic model of overhead crane system with pendulum-sloshing effects is established. Then, based on the formulation as a quasi-convex optimization, three optimal trajectory planning strategies including minimum-time trajectory planning (MTTP), minimum-energy trajectory planning (METP) and time-energy optimal trajectory planning (TEOTP) are proposed to suppress the container swing and liquid sloshing simultaneously. In the three trajectory planners, quasi-convex optimization theory is used to guarantee actuated states (trolley acceleration and velocity) and unactuated states (container swing angle and liquid level sloshing displacement) constraints to be satisfied. Finally, numerical simulation and real experiments results prove that the control performance of the proposed optimal trajectory planning strategy is better than existing methods. PubDate: 2022-05-10
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Abstract: Abstract By introducing an absolute value function for polarity balance, a unique hyperchaotic map with complete control and conditional symmetry is designed. Firstly, coexisting conditional symmetric bifurcations and hyperchaotic phase trajectories are found in the map. Then, two independent parameters are proven to provide a direct knob for partial and total amplitude control. Finally, a STM32-based hardware experiment is carried out to verify the theoretical finding. PubDate: 2022-05-10
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Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.
Abstract: Abstract The article was published with errors in equations (35), (36) and (37). PubDate: 2022-05-09
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Abstract: Abstract One of the most important problems of nonlinear dynamics is related to the development of methods concerning the identification of the dynamical modes of the corresponding systems. The classical method is related to the calculation of the Lyapunov characteristic exponents (LCEs). Usually, to implement the classical algorithms for the LCEs calculation, the smoothness of the right-hand sides of the corresponding equations is required. In this work, we propose a new algorithm for the LCEs computation in systems with strong nonlinearities (these nonlinearities cannot be linearized) including the hysteresis. This algorithm uses the values of the Jacobi matrix in the vicinity of singularities of the right-hand sides of the corresponding equations. The proposed modification of the algorithm is also can be used for systems containing such design hysteresis nonlinearity as the Preisach operator. (Thus, this modification can be used for all members of the hysteresis family.) Moreover, the proposed algorithm can be successfully applied to the well-known chaotic systems with smooth nonlinearities. Examples of dynamical systems with hysteresis nonlinearities, such as the Lorentz system with hysteresis friction and the van der Pol oscillator with hysteresis block, are considered. These examples illustrate the efficiency of the proposed algorithm. PubDate: 2022-05-09
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Abstract: Abstract In this paper, the numerical solution of time-fractional convection diffusion equations (TF-CDEs) is considered as a generalization of classical ones, nonexponential relaxation patterns and anomalous diffusion. A nonlocal model further is developed toward such problems via peridynamic differential operator, which may be utilized to derive all partial derivatives of higher orders concurrently in a simple and effective manner, with no need for shape functions. To generate the final discrete system of equations, only functionals based on nonlocal operators are required, greatly simplifying the implementation. The main contribution of this work is three-fold: (1) a finite difference/nonlocal operator method is contracted for the discretization of the TF-CDEs; (2) a detailed analysis of the proposed scheme is given by providing some stability and error estimates, and the method convergence is established; and eventually, (3) numerical experiments are presented to substantiate the theoretical analysis and demonstrate the computational efficiency of the schemes. PubDate: 2022-05-09
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Abstract: Abstract The nonaxisymmetric magnetoelastic nonlinear coupling free vibration study is performed for a conductive thin annular plate in the nonuniform toroidal magnetic field generated by a long straight current carrying wire in this article. From the electromagnetic theory, expressions for the magnetic field, electromagnetic force and torque acting on the plate are deduced. According to Hamilton principle, nonaxisymmetric magnetoelastic nonlinear vibration equation is derived. The displacement functions for plate under three different boundary conditions are solved, which is combined with Galerkin integral method for derivation of nondimensional coupling nonlinear differential equations. The method of multiple scales is introduced to solve the coupling equations and achieve the second-approximation analytical solution, and then, expressions for the first three mode nondimensional natural frequencies of plate are obtained. In numerical examples, diagrams of electromagnetic characteristics and the first three frequencies under magnetic field and modal coupling effect are presented, which shows the influence of different parameters, e.g., current intensity, plate size and time on natural frequencies and electromagnetic forces. The variation of system singularity stability is discussed, and the obtained analytical results are also validated. The results indicate that current, plate size and time parameters have obvious influence on natural frequencies, which also shows quite different variations under different boundaries. Additionally, initial conditions have significant effects on natural frequencies, which becomes more complicated under modal coupling effect. In nonaxisymmetric vibration case, electromagnetic forces show complicated changing rules along radial and circumferential directions. Furthermore, system equilibrium point will be changed by the induced nonuniform magnetic field. PubDate: 2022-05-08
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Abstract: Abstract Most existing quasi-zero stiffness (QZS) isolators with excellent vibration isolation performance in the low-frequency range are designed to attenuate vibration transmission only in one direction, but vibration suppression in multi-direction is more useful and expected in engineering practice. Hence, a novel 3-degree-of-freedom (3-DOF) passive vibration isolation unit with enhanced QZS effect in a large stroke is designed based on the X-shaped mechanism. The 3-DOF vibration isolation unit exhibits beneficial nonlinear stiffness and damping properties, and it can provide excellent ultra-low-frequency vibration isolation performance in three directions simultaneously. Combining two such isolation units can of course lead to more DOF vibration isolation. The effects of several design parameters such as spring stiffness, lengths of the rods, static equilibrium positions, spring connection parameters, damping coefficients and excitation amplitudes on vibration isolation performance are analyzed in detail. Some comparisons of the static characteristics and vibration isolation performance with a spring–mass–damper (SMD) isolator and an existing typical QZS isolator are carried out. The results reveal that (a) the proposed 3-DOF vibration isolation unit can have much enhanced QZS range with larger loading capacity in the vertical and horizontal directions and HSLD stiffness in the rotational direction; (b) when the excitation amplitudes are large, the novel vibration isolation unit exhibits beneficial nonlinear properties in all three directions without jumping and bifurcation phenomena; (c) compared with the typical QZS isolator, the X-shaped mechanism enables the proposed isolation unit to possess excellent vibration isolation performance in three directions simultaneously with guaranteed stable equilibrium; (d) the new 3-DOF isolator includes only 4 bars in the entire mechanism due to the special and totally new arrangement of the X-shaped mechanism without any guiding sliders, leading to more compact designs of multi-DOF vibration isolation systems of high performance, definitely demanded by engineering practices. PubDate: 2022-05-08
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