Nonlinear Responses of a Magnetoelastic Beam in a Step-Pulsed Magnetic Field

A theoretical study is carried out on the dynamics of a magnetoelastic beam being in a step-pulsed magnetic field. For this aim, the magnetic potential and elastic energies are determined for the beam and partial differential equations are established according to Hamilton's principle. It is proven that the magnetoelastic beam can give a variety of complex behavior in the case of step-pulsed field excitations. An intermediate regime of two-well chaos is observed. Theoretical findings were found to be in a good agreement with the experimental results for the specific system parameters. On leave from Institute of Physics, University of Bayreuth, 65440 Bayreuth, Germany An erratum to this article is available at .     

Almost Automorphic and Almost Periodic Dynamics for Quasimonotone Non-Autonomous Functional Differential Equations

The occurrence of almost automorphic dynamics for monotone non-autonomous recurrent finite-delay functional differential equations is analyzed. Topological methods are used to ensure its presence in the case of existence of semicontinuous semi-equilibria. When these semi-equilibria are continuous and strong, the presence of almost automorphic extensions is persistent under small perturbations. The above method provides a minimal set isomorphic to the base in the case of a convex semiflow. Some examples show the applicability of these results.     

Stability and Oscillations in a Time-Delayed Vehicle System with Driver Control

In this paper, linear stability and chaotic motion of a time-delayednonlinear vehicle system are studied. The stability is determined bycomputing the spectrum associated with a system of linear retardedfunctional differential equations, which reveals that a loss ofstability occurs following a Hopf bifurcation. Beyond the critical valuefor linear stability, the system exhibits limit cycle motions.Subharmonic, quasi-periodic and chaotic motions are observed for asystem excited by a periodic disturbance.     

Non-linear normal modes,invariance, and modal dynamics approximations of non-linear systems

Non-linear systems are here tackled in a manner directly inherited from linear ones, that is, by using proper normal modes of motion. These are defined in terms of invariant manifolds in the system's phase space, on which the uncoupled system dynamics can be studied. Two different methodologies which were previously developed to derive the non-linear normal modes of continuous systems — one based on a purely continuous approach, and one based on a discretized approach to which the theory developed for discrete systems can be applied-are simultaneously applied to the same study case-an Euler-Bernoulli beam constrained by a non-linear spring-and compared as regards accuracy and reliability. Numerical simulations of pure non-linear modal motions are performed using these approaches, and compared to simulations of equations obtained by a classical projection onto the linear modes. The invariance properties of the non-linear normal modes are demonstrated, and it is also found that, for a pure non-linear modal motion, the invariant manifold approach achieves the same accuracy as that obtained using several linear normal modes, but with significantly reduced computational cost. This is mainly due to the possibility of obtaining high-order accuracy in the dynamics by solving only one non-linear ordinary differential equation.     

Direct modeling of flow of FENE fluids

Direct simulations of macromolecular fluids are carried out for flows between parallel plates and in expanding and contracting channels. The macromolecules are modeled as FENE dumbbells with soft disks or Lennard-Jones dumbbell-dumbbell interactions. The results are presented in terms of profiles and contour plots of velocity, pressure, temperature, density, and flow fields. In addition the data for potential energy, shear stress, and the normal components of the stress tensor are collected. In general, an excellent agreement is found between the simulated profiles and the well-known flow structures, such as flow separation and formation of viscous eddies, indicating that micro-hydrodynamics is a viable tool in linking macroscopic phenomena with the underlying physical mechanisms. The simulations are performed in the Newtonian regime, for medium-size systems comprising up to 3888 dumbbells. This number is sufficiently large to control boundary and particle number effects. The flow is induced by gravity. The traditional stochastic (thermal) and periodic boundary conditions are employed. Also, diffusive boundary conditions, which could include a stagnant fluid layer and repulsive potential walls, are developed. The scaling problems, which are related to the application of a large external force in a microscopic system (of the size of the order 100 Å), result in extreme pressure and temperature gradients. In addition, the viscosity and thermal conductivity coefficients obtained from velocity and temperature profiles of the channel flow are presented. These results are confirmed independently from modeling of Couette flow by the SLLOD equations of motion and from the Evans algorithm for thermal conductivity.     

Space-time perturbation modes for non-linear dynamic analysis of beams

In this work an attempt is made at bridging the powerful perturbation methods of analytical dynamics to the versatile finite element techniques which can readily handle arbitrarily complex structures. The proposed analysis methodology has two distinguishing features. First, a space-time finite element formulation is used, and hence the concept of modes is here naturally extended to that of space-time modes, where the time dependency is implied in the assumed modes. As a result, the partial differential equations of motion are directly reduced to purely algebraic non-linear simultaneous equations. Second, perturbation modes, rather than the usual vibration mode shapes are used and shown to be an appropriate basis for non-linear dynamic analysis. These modes bring information about the non-linearities of the system through the higher order derivatives of the strain and kinetic energies. The procedure is illustrated on non-linear beam problems and the results are compared with those of a full finite element model, i.e., when all the degrees of freedom are considered, as well as with analytical results, when available.     

Numerical Analysis of the Influence of Thermal Stresses on the Nonlinear Thermomolecular Pressure Difference Effect

On the basis of a numerical analysis of the non-Navier-Stokes gas-dynamic equations for slow non-isothermal gas flows, the nonlinear thermomolecular pressure difference effect due to a large temperature gradient along the lateral surface of a capillary is investigated. It is shown that the magnitude of the effect is substantially different from the values calculated using the Navier-Stokes equations. For two models of molecular interaction (Maxwell molecules and hard spheres), the possibility of a quasi-one-dimensional interpretation of the effect for experimental estimation purposes is demonstrated. The solutions of the relaxation kinetic equation for flow in a plane capillary at small Knudsen numbers and the gas-dynamic equations for slow non-isothermal flows are compared and the range of their applicability is estimated.     

改进的 Morse 势和冲击压缩

用分子动力学方法模拟凝聚介质中一维分子链上的激波传播，以得到与冲击压缩实验相一致的结果。通过比较分子链上的孤立波解与激波的实验结果，提出对分子间Ｍｏｒｓｅ作用势进行与考虑量子效应相一致的修正，从而使分子动力学模拟得到的激波Ｕｓ－Ｕｐ关系与实验结果在波后粒子速度达到声速的范围内一致。     

Quasi-steady deformation of a two-dimensional bubble placed within a potential viscous flow

The shape evolution of a two-dimensional bubble, bounded by a simple closed curve, which is initially placed within a potential viscous flow, is analysed. It is assumed that the influence of gravity and inertia forces is negligible, so the quasi-steady approximation can be applied. Reformulating the problem for Stokes equations with relevant boundary conditions at the free surface in terms of the bianalytic stress-stream function, and using the time-dependent conformal mappingz(,t) of a unit disk onto an unbounded flow domain sought, an infinite system of ordinary differential equations for the Laurent coefficients ofz(,t) is derived. A class of exact solutions is found for the case when the principal part of the complex velocity of the dominant flow at infinity is a polynomial, and the problem of formation of a pointed bubble is discussed.

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Sommario E analizzata l'evoluzione di una bolla bi-dimensionale, limitata da una curva chiusa semplice, inizialmente posta in un flusso potenziale viscoso. Si assume che l'influenza della gravità e delle forze inerziali sia trascurabile, cosicchè si può applicare l'approssimazione quasi-stazionaria. Riformulando il problema per le equazioni di Stokes con le opportune condizionial contorno sulla superficie libera in termini della funzione stress-stream bianalitica, e usando la tecnica delle trasformazioni conformi dipendenti dal tempoz(,t) di un disco unitario su un dominio di flusso non limitato incognito, viene derivato un sistema infinito di equazioni differenziali ordinarie per i coefficienti di Laurent diz(,t). Viene trovata una classe di soluzioni esatte per il caso in cui la parte principale della velocità complessa del flusso dominante all'infinito è una polinomiale, ed è discusso il problema della formazione di una bolla lenticolare.

     

Near-wall model for boundary layer turbulence

The evolution of an intermittently created isolated three-dimensional turbulent eddy near a wall is followed in space and time on the assumption that its structure evolves on three separate time scales, a shear interaction one, a viscous one, and a nonlinear one. The large-time limit of the solution for the shear interaction stage shows many of the observed features of the near-wall turbulence structure such as the formation of shear layers, of streaks, and of streamwise vortices. It also provides initial conditions for the viscous and nonlinear stages showing viscous decay of convected structures and the possibility of a singularity in the nonlinear development. The eddy model is also used to construct a new model for the turbulent shear stress showing strong similarity to Prandtl's mixing-length model.