Approximate analytical solution to oscillations of a conductor in a magnetic field

An approximate analytical solution to a system exhibiting oscillations of a conductor in a magnetic field which is controlled by a discrete waveform is sought by means of multiple scales. The system involves the use of a solenoid driven by a RLC circuit, coupled with a solid state relay (SSRL), to generate large electromagnetic forces acting on a conductor, which oscillates within the solenoid. The steady state response of the metal bar, in terms of oscillations is described. This solution is expressed in terms of system and circuit parameters, valid in the weakly nonlinear region, which is identified to be small oscillatory displacement near the center of the solenoid. By analyzing different cases of resonance, period-1 and period-2 like motions are identified and validated through experimental studies. The solution provides a guideline to design an effective control strategy so as to guide the system to a desirable attractor.     

Approximate solving method of shock for nonlinear disturbed coupled Schrödinger system

A class of nonlinear disturbed coupled Schrödinger systems is studied. The specific technique is used to relate the exact and approximate solutions. The corresponding typical coupled system is considered. An exact shock travelling solution is obtained by a mapping method. The travelling asymptotic solutions of the disturbed coupled Schrödinger system are then found with an approximate method.     

Dynamic characteristics of self-acting gas bearing–flexible rotor coupling system based on the forecasting orbit method

This paper studies the nonlinear dynamic characteristics of a flexible rotor supported by self-acting gas bearings theoretically. The multiple degree freedom model of flexible rotor is established by the finite element method and analyzed coupled with the transient gas lubricated Reynolds equation by employing the forecasting orbit method. The Reynolds equation is solved by the alternating direction implicit method and the dynamic response of the rotor is calculated by the Newmark integral method. To settle the problem that the two kinds of transient solving processes (transient Reynolds equation for bearing and transient equation of motion for rotor) cannot be solved simultaneously, which arises from the fact that they need each other??s results as their initial values, the multi-field coupling algorithm based on the forecasting method is proposed and applied in this paper. By employing the numerical method, the rotor trajectory diagram, phase diagram, frequency spectrum, power spectrum, bifurcation diagram, and vibration mode diagram were obtained. It is to note that the dynamic characteristics of self-acting gas bearing?Crotor system and whirling instability of the system could be depicted successfully. This would establish the foundation for contributing to a further understanding of the gas bearing?Cflexible rotor system.     

An efficient formulation based on the Lagrangian method for contact–impact analysis of flexible multi-body system

In this paper,an efficien formulation based on the Lagrangian method is presented to investigate the contact–impact problems of f exible multi-body systems.Generally,the penalty method and the Hertz contact law are the most commonly used methods in engineering applications.However,these methods are highly dependent on various non-physical parameters,which have great effects on the simulation results.Moreover,a tremendous number of degrees of freedom in the contact–impact problems will influenc thenumericalefficien ysignificantl.Withtheconsideration of these two problems,a formulation combining the component mode synthesis method and the Lagrangian method is presented to investigate the contact–impact problems in fl xible multi-body system numerically.Meanwhile,the finit element meshing laws of the contact bodies will be studied preliminarily.A numerical example with experimental verificatio will certify the reliability of the presented formulationincontact–impactanalysis.Furthermore,aseries of numerical investigations explain how great the influenc of the finit element meshing has on the simulation results.Finally the limitations of the element size in different regions are summarized to satisfy both the accuracy and efficien y.     

Love–Bishop rod solution based on strain gradient elasticity theory

In the present work, the propagation of longitudinal stress waves is investigated with a strain gradient elasticity theory given by Lam et al. In principle, the analysis of wave motion is based on the Love rod model including the lateral deformation effects, but in the same time is also taken into account the shear strain effects with Bishop?s correction. By applying Hamilton?s principle, a general explicit strain gradient elasticity solution is developed for the longitudinal stress waves, and it is compared with the special solutions based on the modified couple stress and classical theories. This work gives useful information with regard to the meaning of the three scale parameters in the strain gradient elasticity theory used here.     

A Ritz’s method based solution for the contact problem of a deformable rectangular plate on an elastic quarter-space

In this article, Ritz’s method is used to calculate with unprecedented accuracy the displacements related to a deformable rectangular plate resting on the surface of an elastic quarter-space. To achieve this required three basic steps. The first step involved the study of Green’s function describing the vertical displacements of the surface of an elastic quarter-space due to vertical force applied on its surface. For this case, an explicit formula was obtained by analytically resolving a complicated integral that did not previously have an analytical solution. The second step involved the study of the coupled system of a plate and an elastic quarter-space. This portion focused on determining reactive forces in the contact zone based on Hetenyi’s solution. After determination of the reactive forces, certain features were attributed to the plate’s edges. The final step involved the application of Ritz’s method to determine the deflections of the plate resting on the surface of the quarter-space. Finally, an example calculation and validation of results are given. This is the first semi-analytical solution proposed for this type of contact problem.     

Reliability analysis for the uncertainties in vehicle and high-speed railway bridge system based on an improved response surface method for nonlinear limit states

The paper deals with the reliability analysis for the high-speed railway bridge systems. Although the bridge–vehicle interactive system has much more uncertainties in the resistance and loads of trains moving at very high speed compared with static structural analysis, little concern has been engaged to identify which random variable has to be considered in the probabilistic analysis, or what criteria should be selected to determine the probabilistic safety or serviceability. The considered design parameters thus involve uncertainties in stiffness, moment of inertia, damping ratio of primary suspension in terms of load, geometry of girders and slabs, and the mechanical properties of girders in terms of resistance. The considered limit states embrace the safety of trains and comfort of passengers, and the acceptability criteria are based on UIC code. For evaluating the reliability of the time-dependent nonlinear behavior of complex structures, an improved Response Surface Method (RSM) is developed. An adaptive technique and a weight matrix are utilized as an optimizing technique that accelerates the convergence in the reliability analysis. The results of improved RSM, compared with the basic and adaptive RSM, are verified with the improved convergence to the exact solution. The bridge response is analyzed using a new three-dimensional finite element model of high-speed train–bridge interactions. The track structures are idealized using beam elements with the offset of beam nodes and beams on a two-parameter elastic foundation. The vehicle model developed for a 300 km/h train is employed. The calculated reliabilities for performance of the considered bridges and the passenger comfort on board of high-speed trains are compared to the conventional safety indices. The results of this study allow identifying the quantification of uncertainties that can control quality of the high-speed train service.     

Determining Lyapunov spectrum and Lyapunov dimension based on the Poincaré map in a vibro-impact system

We develop a method to compute the Lyapunov spectrum and Lyapunov dimension, which is effective for both symmetric and unsymmetric vibro-impact systems. The Poincaré section is chosen at the moment after impacting, and the six-dimensional Poincaré map is established. The time between two consecutive impacts is determined by the initial conditions and the impact condition, hence the Poincaré map is an implicit map. The Poincaré map is used to calculate all the Lyapunov exponents and the Lyapunov dimension. By numerical simulations, the attractors are represented in the projected Poincaré section, and the Lyapunov spectrum is obtained. The multi-degree-of-freedom vibro-impact system may exhibit complex quasi-periodic attractors, which can be characterized by the Lyapunov dimension.     

A one-dimensional theory of wave-propagation in elastic rods based on the „method of internal constraints“

Conclusions The results obtained in this paper in the particular case of lateral vibrations of bars show an encouraging agreement between the values ofc/c ₀ andc _g/c₀ given by the approximate theory based on the assumption of internal constraints and the exact theory derived from the use of the equations of the Mathematical Theory of Elasticity.This approximate theory which will be referred to as the Theory of Internal Constraints is in the dynamic case completely contained in the constraint equation (1) and in the application ofHamiltons Principle. Accordingly the concept of Shear Coefficient is not used. In the general case of wave propagation in elastic straight rods this theory unifies a number of separate engineering treatments of the problem. Moreover, the same theory can be applied to the study of vibrations of curved bars taking into account the effects of shear and of rotatory inertia as has been shown in a previous paper.The mathematical simplicity of the theory and its degree of accuracy justify its use in dealing with engineering problems in vibrations of curved or straight bars for which more exact theories cannot be used because of their mathematical complexities.The author wants to express his best thanks to Mr.E. C. Zachmanoglou, student in the Department of Aeronautical Engineering, and to Mr.R. V. Milligan, graduate student in the Department of Mechanics, at Rensselaer Polytechnic Institute for the valuable help and assistance given to him in the preparation of the numerical tables and graphs which are presented in this paper.The material presented in this paper is based on an investigation which is being conducted under the sponsorship of the Office of Naval Research, Department of the U. S. Navy, Washington, D. C.; and is presented with the permission of the Office of Naval Research.     

Fully resonant soliton interactions in the Whitham–Broer–Kaup system based on the double Wronskian solutions

With the aim of exploring whether the (1+1)-dimensional coupled nonlinear evolution equations admit abundant soliton interactions, like the cases in the Kadomtsev–Petviashvili II equation, we in this paper study the double Wronskian solutions to the Whitham–Broer–Kaup (WBK) system. We give the parametric condition for two double Wronskians to generate the non-singular, non-trivial and irreducible soliton solutions. Via the asymptotic analysis of two double Wronskians, we show that the soliton solutions of the WBK system is in general linearly combined of fully resonant (M,N)- and (M?1,N+1)-soliton configurations. It turns out that the WBK system can exhibit various complex soliton structures which are different pairwise combinations of elastic, confluent and divergent interactions. From a combinatorial viewpoint, we also explain that the asymptotic solitons of a [(M,N),(M?1,N+1)]-soliton solution are identified by a pair of Grassmannian permutations.     

Optimization of multibody systems based on the generalized-α projection method for DAEs

Efficient optimization strategy of multibody systems is developed in this paper. Augmented Lagrange method is used to transform constrained optimal problem into unconstrained form firstly. Then methods based on second order sensitivity are used to solve the unconstrained problem, where the sensitivity is solved by hybrid method. Generalized-α method and generalized-α projection method for the differential-algebraic equation, which shows more efficient properties with the lager time step, are presented to get state variables and adjoint variables during the optimization procedure. Numerical results validate the accuracy and efficiency of the methods is presented.     

Compensation method for complex hysteresis characteristics on piezoelectric actuator based on separated level-loop Prandtl–Ishlinskii model

Nonlinear Dynamics - Piezoelectric ceramic actuators show nonlinear hysteresis characteristics due to material properties. In order to modify the inverse piezoelectric effect as an ideal linear...     

Development and elaboration of numerical method for simulating gas–liquid–solid three-phase flows based on particle method

A numerical method for simulating gas–liquid–solid three-phase flows based on the moving particle semi-implicit (MPS) approach was developed in this study. Computational instability often occurs in multiphase flow simulations if the deformations of the free surfaces between different phases are large, among other reasons. To avoid this instability, this paper proposes an improved coupling procedure between different phases in which the physical quantities of particles in different phases are calculated independently. We performed numerical tests on two illustrative problems: a dam-break problem and a solid-sphere impingement problem. The former problem is a gas–liquid two-phase problem, and the latter is a gas–liquid–solid three-phase problem. The computational results agree reasonably well with the experimental results. Thus, we confirmed that the proposed MPS method reproduces the interaction between different phases without inducing numerical instability.     

Modeling of multiple noncatalytic gas–solid reactions in a moving bed of porous pellets based on finite volume method

A mathematical model is presented to simulate the multiple heterogeneous reactions with complex set of physicochemical and thermal phenomena in a moving bed of porous pellets. This model is based on both heat and mass transfer phenomena of gaseous species in a porous medium including chemical reactions at interfaces whose areas vary during the conversion. This model accounts for both the exothermic and endothermic reactions which can be equimolar or nonequimolar. Furthermore it considers simultaneously the reactions in the nonisothermal transient condition. A powerful technique based upon finite volume fully implicit approach has been implemented to solve the complicated governing equations numerically. The model has been validated by comparing with various experimental and analytical results in two cases: the single pellet scale as well as the counter current moving bed reactor.

A novel method for designing S-box based on chaotic map and Teaching–Learning-Based Optimization

A new method for obtaining strong S-boxes based on chaotic map and Teaching–Learning-Based Optimization (TLBO) is presented in this paper. Our method presents eight rounds; each round contains two transformations: row left shifting and columnwise rotation. The vectors for the transformations are different from one round to another, and they are controlled by two keys to the logistic map. These two keys are optimized by using TLBO which aims to construct a strong S-box that satisfies to the criteria set in advance. Test for the following criteria such as bijectivity, nonlinearity, strict avalanche criteria, equiprobable inputs/outputs XOR distribution is analyzed. Additionally, we will provide many comparisons with other S-boxes and test of the sensitivity to keys. The results of performance test show that the proposed design S-boxes presents good cryptography proprieties and can resist to several attacks.     

Adaptive synchronization of Lü hyperchaotic system with uncertain parameters based on single-input controller

The adaptive synchronized problem of the four-dimensional (4D) Lü hyperchaotic system performed by Elabbasy et al. (Chaos Solitons Fractals 30:1133–1142, 2006) with uncertain parameters by applying the single control input is addressed in this article. Based on the Lyapunov theorem of stability, the single-input adaptive synchronization controllers associated with the adaptive update laws of system parameters are developed to make the states of two nearly identical 4D Lü hyperchaotic systems asymptotically synchronized. Numerical studies are presented to illustrate the effectiveness of the proposed chaotic synchronization schemes.     

Secure communication based on chaotic synchronization via?interval?time-varying delay feedback control

In this paper, a synchronization method of Lur??e systems for chaotic secure communication systems with interval time-varying delay feedback control is proposed. To increase communication security, the transmitted message is encrypted with the techniques of N-shift cipher and public key. Based on Lyapunov method and linear matrix inequality (LMI) formulation, new delay-dependent synchronization criteria are established to not only guarantee stable synchronization of both transmitter and receiver systems but also recover the transmitted original signal at the receiver. Throughout a numerical example, the validity and superiority of the proposed method are shown.     

Combining ?eld-modulating electroosmotic vortex and insulatingpost to manipulate particles based on dielectrophoresis?

正School of Civil Engineering and Mechanics, Huazhong University of Science and Technology, Wuhan 430074, China(Received Aug. 17, 2020/Revised Dec. 7, 2020)     

A novel numerical algorithm based on Galerkin–Petrov time-discretization method for solving chaotic nonlinear dynamical systems

Nonlinear chaotic systems yield many interesting features related to different physical phenomena and practical applications. These systems are very sensitive to initial conditions at each time-iteration level in a numerical algorithm. In this article, we study the behavior of some nonlinear chaotic systems by a new numerical approach based on the concept of Galerkin–Petrov time-discretization formulation. Computational algorithms are derived to calculate dynamical behavior of nonlinear chaotic systems. Dynamical systems representing weather prediction model and finance model are chosen as test cases for simulation using the derived algorithms. The obtained results are compared with classical RK-4 and RK-5 methods, and an excellent agreement is achieved. The accuracy and convergence of the method are shown by comparing numerically computed results with the exact solution for two test problems derived from another nonlinear dynamical system in two-dimensional space. It is shown that the derived numerical algorithms have a great potential in dealing with the solution of nonlinear chaotic systems and thus can be utilized to delineate different features and characteristics of their solutions.