Nonlinear dynamic analysis of an optimal particle damper

We study the dynamical behavior of a single degree of freedom mechanical system with a particle damper. The particle (granular) damping was optimized for the primary system operating condition by using an appropriate gap size for a prismatic enclosure. The particles absorb the kinetic energy of the vibrating structure and convert it into heat through the inelastic collisions and friction. This results in a highly nonlinear mechanical system. Considering linear signal analysis, state space reconstruction, Poincar\'e sections and the determination of maximal Lyapunov exponents, the motion of the granular system inside the enclosure is characterized for a wide frequency range. With the excitation frequency as control parameter, either regular and chaotic motion of the granular bed are found and their influence on the damping is analyzed.Comment: 18 pages, 8 figures. arXiv admin note: text overlap with arXiv:1105.030

A Langevin Approach to One-Dimensional Granular Media Fluidized by Vibrations

We present a Langevin approach to describe the steady-state dynamics of one-dimensional granular media fluidized by a vibrating bottom plate. We adopt a linear Langevin equation to describe the motion of the center of mass. Within this framework, we derive analytical expressions for several macroscopic quantities. We also predict the power spectrum for the height of the center of mass. We find good agreement between our theoretical predictions and extensive event-driven molecular dynamics simulations.Comment: 11 pages, 3 figures, to be published in J. Phys. Soc. Jp

Molecular dynamics algorithm enforcing energy conservation for microcanonical simulations

10.1103/PhysRevE.89.053314A reversible algorithm [enforced energy conservation (EEC)] that enforces total energy conservation for microcanonical simulations is presented. The key point is the introduction of the discrete-gradient method to define the forces from the conservative potentials, instead of the direct use of the force field at the actual position of the particle. We have studied the performance and accuracy of the EEC in two cases, namely Lennard-Jones fluid and a simple electrolyte model. Truncated potentials that usually induce inaccuracies in energy conservation are used. In particular, the reaction field approach is used in the latter. The EEC is able to preserve energy conservation for a long time, and, in addition, it performs better than the Verlet algorithm for these kinds of simulations

Convection in horizontally shaken granular material

In horizontally shaken granular material different types of pattern formation have been reported. We want to deal with the convection instability which has been observed in experiments and which recently has been investigated numerically. Using two dimensional molecular dynamics we show that the convection pattern depends crucially on the inelastic properties of the material. The concept of restitution coefficient provides arguments for the change of the behaviour with varying inelasticity

Mechanisms of Cluster Formation in Force-Free Granular Gases

The evolution of a force-free granular gas with a constant restitution coefficient is studied by means of granular hydrodynamics. We numerically solve the hydrodynamic equations and analyze the mechanisms of cluster formation. According to our findings, the presently accepted mode-enslaving mechanism may not be responsible for the latter phenomenon. On the contrary, we observe that the cluster formation is mainly driven by shock-waves, which spontaneously originate and develop in the system. This agrees with a previously suggested mechanism of formation of density singularities in one-dimensional granular gases

Vertically shaken column of spheres. Onset of fluidization

The onset of surface fluidization of granular material in a vertically vibrated container, $z=A\cos\left(\omega t\right)$, is studied experimentally. Recently, for a column of spheres it has been theoretically found (see T. Pöschel, T. Schwager, C. Salueña, Phys. Rev. E 62, 1361 (2000)) that the particles lose contact if a certain condition for the acceleration amplitude $\ddot{z} \equiv A\omega^2/g = f(\omega)$ holds. This result is in disagreement with other findings where the criterion $\ddot{z}=\ddot{z}_{\rm crit}={const}$ was found to be the criterion of fluidization. We show that for a column of spheres a critical acceleration is not a proper criterion for fluidization and compare the results with theory

The rheology of a dilute suspension of Brownian dipolar spheroids in a simple shear flow under the action of an external force

The effect of rotational Brownian motion on the rheology of a dilute suspension of dipolar spheroids in a simple shear flow under the action of an external force field, is investigated through a generalized Langevin equation approach. The force field is assumed to be either constant or periodic. In the case of constant external fields earlier results in the literature are reproduced, while for the case of periodic forcing certain parametric regimes corresponding to weak Brownian diffusion are identified where the rheological parameters evolve chaotically and settle onto a low dimensional attractor. The response of the system to variations in the strengths of the force field and diffusion is also analyzed through numerical experiments. These results correspond to the region of weak Brownian motion where usual methods render the problem intractable