Nonlinear dynamics of a non-autonomous network with coupled discrete–continuum oscillators

A network model of a multi-modular floating platform incorporated with a runway structure, viewed as a non-autonomous network with discrete–continuum oscillators, is developed for a general purpose of dynamic analysis. Numerical analysis shows the coupling effect between the two different types of oscillators on various complex dynamics, including sudden leaps, torus motions, beating vibrations, the synergetic effect of phase lock and anti-phase synchronizations. The amplitude death phenomenon, a suppressed weak oscillation state, is studied by using the fundamental solution derived by the averaging method. The parametric domain of the onset of amplitude death is illustrated to show the great significance to the stability design of the floating platform. The effect of the flexural rigidity of the runway on the distribution of amplitude death state is also discussed.     

Dynamic elastoplastic analysis by a hybrid BEM–FEM time-domain formulation

This study presents a hybrid BEM–FEM procedure for the dynamic analysis of elastoplastic models. In this hybrid approach, boundary node and internal point displacements are evaluated considering the time-domain BEM formulation (initial stress approach), and stresses are computed taking into account FEM techniques (domain discretization is only necessary where non-linear behaviour is expected to occur). This hybrid methodology is very appropriate to model infinite or semi-infinite elastoplastic models and, at the end of the paper, three numerical applications are presented, illustrating the potentialities of the proposed formulation.     

Bifurcations and chaos in a two-dimensional discrete Hindmarsh–Rose model

In this paper, the dynamics of a two-dimensional discrete Hindmarsh–Rose model is discussed. It is shown that the system undergoes flip bifurcation, Neimark–Sacker bifurcation, and 1:1 resonance by using a center manifold theorem and bifurcation theory. Furthermore, we present the numerical simulations not only to illustrate our results with the theoretical analysis, but also to exhibit the complex dynamical behaviors, including orbits of period 3, 6, 15, cascades of period-doubling bifurcation in orbits of period 2, 4, 8, 16, quasiperiodic orbits, and chaotic sets. These results obtained in this paper show far richer dynamics of the discrete Hindmarsh–Rose model compared with the corresponding continuous model.     

Bifurcations and chaos in a discrete predator–prey model with Crowley–Martin functional response

In this paper, a discrete-time predator–prey model with Crowley–Martin functional response is investigated based on the center manifold theorem and bifurcation theory. It is shown that the system undergoes flip bifurcation and Neimark–Sacker bifurcation. An explicit approximate expression of the invariant curve, caused by Neimark–Sacker bifurcation, is given. The fractal dimension of a strange attractor and Feigenbaum’s constant of the model are calculated. Moreover, numerical simulations using AUTO and MATLAB are presented to support theoretical results, such as a cascade of period doubling with period-2, 4, 6, 8, 16, 32 orbits, period-10, 20, 19, 38 orbits, invariant curves, codimension-2 bifurcation and chaotic attractor. Chaos in the sense of Marotto is also proved by both analytical and numerical methods. Analyses are displayed to illustrate the effect of magnitude of interference among predators on dynamic behaviors of this model. Further the chaotic orbit is controlled to be a fixed point by using feedback control method.     

Limit analysis and homogenization of porous materials with Mohr–Coulomb matrix. Part I: Theoretical formulation

The present two-part study aims at investigating the specific effects of Mohr–Coulomb matrix on the strength of ductile porous materials by using a kinematic limit analysis approach. While in the Part II, static and kinematic bounds are numerically derived and used for validation purpose, the present Part I focuses on the theoretical formulation of a macroscopic strength criterion for porous Mohr–Coulomb materials. To this end, we consider a hollow sphere model with a rigid perfectly plastic Mohr–Coulomb matrix, subjected to axisymmetric uniform strain rate boundary conditions. Taking advantage of an appropriate family of three-parameter trial velocity fields accounting for the specific plastic deformation mechanisms of the Mohr–Coulomb matrix, we then provide a solution of the constrained minimization problem required for the determination of the macroscopic dissipation function. The macroscopic strength criterion is then obtained by means of the Lagrangian method combined with Karush–Kuhn–Tucker conditions. After a careful analysis and discussion of the plastic admissibility condition associated to the Mohr–Coulomb criterion, the above procedure leads to a parametric closed-form expression of the macroscopic strength criterion. The latter explicitly shows a dependence on the three stress invariants. In the special case of a friction angle equal to zero, the established criterion reduced to recently available results for porous Tresca materials. Finally, both effects of matrix friction angle and porosity are briefly illustrated and, for completeness, the macroscopic plastic flow rule and the voids evolution law are fully furnished.     

An atomistic–continuum hybrid scheme for numerical simulation of droplet spreading on a solid surface

We present an atomistic–continuum hybrid method to investigate spreading dynamics of drops on solid surfaces. The Navier–Stokes equations are solved by the finite-volume method in a continuum domain comprised of the main body of the drop, and atomistic molecular dynamics simulations are used in a particle domain in the vicinity of the contact line. The spatial coupling between the continuum and particle domains is achieved through constrained dynamics of flux continuities in an overlap domain.     

Chaotic and subharmonic oscillations in a DC–DC boost converter with PWM voltage–current hybrid controller and parallel MR load

Nonlinear Dynamics - This paper reports a pulse-width modulation voltage-mode- and current-mode-controlled DC–DC boost converter with parallel memristance and resistance loads. This circuit...     

Propellant-efficient station-keeping using a hybrid sail in the Earth–Moon system

Nonlinear Dynamics - The problem of propellant-efficient station-keeping using a hybrid sail in the Earth–Moon system is investigated in this paper. To achieve high-precision station-keeping...     

Strong discontinuity analysis of a class of anisotropic continuum damage constitutive models – Part I: Theoretical considerations

Several modeling techniques aiming at considering cracks as kinematics discontinuities have been proposed for the past years. Within this scope, the embedded finite element method (E-FEM) was introduced a couple of years ago. Among the features of this approach, it has been shown that a kinematic enhancement of the displacement field allows constructing a discrete model (expressed in terms of traction vector–displacement jump) from any continuous model (expressed in terms of stress–strain). This result has been rigorously established if the continuous model is formulated within the framework of either isotropic continuum damage or plasticity theories. The objectives of this study are (i) to extend this result in case where the continuous model belongs to a class of anisotropic continuum damage constitutive models and (ii) to show the main features of a specific traction/separation law derived from the aforementioned class of constitutive models through several numerical case-studies. In this paper, the light is put on the theoretical considerations which allow deriving discrete models in a consistent way.     

Modeling wall effects in a micro-scale shock tube using hybrid MD–DSMC algorithm

Wall effects in a micro-scale shock tube are investigated using the Direct Simulation Monte Carlo method as well as a hybrid Molecular Dynamics–Direct Simulation Monte Carlo algorithm. In the Direct Simulation Monte Carlo simulations, the Cercignani–Lampis–Lord model of gas–surface interactions is employed to incorporate the wall effects, and it is shown that the shock attenuation is significantly affected by the choice of the values of tangential momentum accommodation coefficient. A loosely coupled Molecular Dynamics–Direct Simulation Monte Carlo approach is then employed to demonstrate incomplete accommodation in micro-scale shock tube flows. This approach uses fixed values of the accommodation coefficients in the gas–surface interaction model, with their values determined from a separate dynamically similar Molecular Dynamics simulation. Finally, a completely coupled Molecular Dynamics–Direct Simulation Monte Carlo algorithm is used, wherein the bulk of the flow is modeled using Direct Simulation Monte Carlo, while the interaction of gas molecules with the shock tube walls is modeled using Molecular Dynamics. The two regions are separate and coupled both ways using buffer zones and a bootstrap coupling algorithm that accounts for the mismatch of the number of molecules in both regions. It is shown that the hybrid method captures the effect of local properties that cannot be captured using a single value of accommodation coefficient for the entire domain.     

Order and disorder in particle–liquid flows in a pipe

The spherical expanded polystyrene particle–oil two-phase flow in a vertical pipe was used to simulate the dispersed phase distribution in laminar bubbly flows. A three-dimensional particle image tracking technique was used to track the particles in the flow to study the ordered structure of dispersed phase distribution and its transition to disorder. The ordered structures behaved as particle strings aligned in the flow direction as induced by the flow shear. The structures were quite durable in high liquid velocity flows and dispersed gradually as the liquid velocity decreased. In lower velocity flows, the particles tended to form clusters in the horizontal direction, as predicted by potential theory for spherical bubbles rising in a quiescent inviscid liquid and as observed in experiments on non-shear bubbly water flows.     

Global stability and Hopf-bifurcation in a zooplankton–phytoplankton model

We deal with a predator–prey model, representing a resource (phytoplankton) and two predators (zooplankton) system with toxin-producing delay. The response function is assumed here to be concave in nature. Firstly, the stability criterion of the model is analyzed both from a local and a global point of view. Our results imply that the toxin’s intrinsic characteristics, such as toxic liberation rate and toxin-producing delay, will not change the stability of the system irreversibly. Secondly, Hopf bifurcation of both systems with delay and without delay can occur via system parameters pertaining to the toxin. Our results indicate that the toxin produced by phytoplankton may be used as a bio-control agent for the Harmful Algal Bloom problems. Furthermore, the explicit algorithm for determining the direction of Hopf bifurcation and the stability of bifurcating periodic solutions are obtained using the normal form method and center manifold theorem. Finally, some numerical simulations are carried out to illustrate the results.     

Analysis of gas–solid flow and shaft-injected gas distribution in an oxygen blast furnace using a discrete element method and computational fluid dynamics coupled model

Ironmaking using an oxygen blast furnace is an attractive approach for reducing energy consumption in the iron and steel industry. This paper presents a numerical study of gas–solid flow in an oxygen blast furnace by coupling the discrete element method with computational fluid dynamics. The model reliability was verified by previous experimental results. The influences of particle diameter, shaft tuyere size, and specific ratio (X) of shaft-injected gas (SIG) flowrate to total gas flowrate on the SIG penetration behavior and pressure field in the furnace were investigated. The results showed that gas penetration capacity in the furnace gradually decreased as the particle diameter decreased from 100 to 40 mm. Decreasing particle diameter and increasing shaft tuyere size both slightly increased the SIG concentration near the furnace wall but decreased it at the furnace center. The value of X has a significant impact on the SIG distribution. According to the pressure fields obtained under different conditions, the key factor affecting SIG penetration depth is the pressure difference between the upper and lower levels of the shaft tuyere. If the pressure difference is small, the SIG can easily penetrate to the furnace center.     

Dynamics of 1D mass–spring system with a negative stiffness spring realized by magnets: Theoretical and experimental study

Realization of negative stiffness(NS)in damping low frequency acoustic and mechanical vibration is relevant in engineering applications.In this work,assemblage of two repelling magnets was used to produce negative magnetic spring(NMS).A mass–spring system with NMS is experimented where the free and forced vibrations of the system are examined.The anti-phase movement is observed due to the presence of proposed NMS,confirming the analytical solution.We further showed the dynamics of the system containing NS spring could also be derived from Hamilton’s principle.     

The wheeled three-link snake model: singularities in nonholonomic constraints and stick–slip hybrid dynamics induced by Coulomb friction

Nonlinear Dynamics - The wheeled three-link snake model is a well-known example of an underactuated robotic system whose motion can be kinematically controlled by periodic changes of its internal...