a review of particle damping modeling and testing

Abstract This survey provides an overview of the different approaches seen in the literature concerning particle damping. The emphasis is on particle dampers used on beams vibrating at frequencies between 10 Hz and 1 kHz. Design examples, analytical formulations, numerical models, and experimental setups for such dampers are gathered. Modeling approaches are presented both for particle interaction and for systems equipped with particle dampers. The consequences of the nonlinear behavior of particle dampers are brought to attention. As such, the apparent contradictions of the conclusions and approaches presented in the literature are highlighted. A list of particle simulation software and their use in the literature is provided. Most importantly, a suggested approach to create a sound numerical simulation of a particle damper and the accompanying experimental tests is given. It consists of setting up a discrete element method simulation, calibrating it with literature data and a representative damper experiment, and testing it outside of the range of operation used for the tuning

On the elastic moduli of three-dimensional assemblies of spheres: characterization and modeling of fluctuations in the particle displacement and rotation

The elastic moduli of four numerical random isotropic packings of Hertzian spheres are studied. The four samples are assembled with different preparation procedures, two of which aim to reproduce experimental compaction by vibration and lubrication. The mechanical properties of the samples are found to change with the preparation history, and to depend much more on coordination number than on density. Secondly, the fluctuations in the particle displacements from the average strain are analysed, and the way they affect the macroscopic behavior analyzed. It is found that only the average over equally oriented contacts of the relative displacement these fluctuations induce is relevant at the macroscopic scale. This average depends on coordination number, average geometry of the contact network and average contact stiffness. As far as the separate contributions from particle displacements and rotations are concerned, the former is found to counteract the average strain along the contact normal, while the latter do in the tangential plane. Conversely, the tangential components of the center displacements mainly arise to enforce local equilibrium, and have a small, and generally stiffening effect at the macro-scale. Finally, the fluctuations and the shear modulus that result from two approaches available in the literature are estimated numerically. These approaches are both based on the equilibrium of a small-sized representative assembly. The improvement of these estimate with respect to the average strain assumption indicates that the fluctuations relevant to the macroscopic behavior occur with short correlation length.Comment: Submitted to IJS

Analytical study of the accuracy of discrete element simulations

The numerical errors in idealised discrete element method (DEM) simulations are investigated analytically by comparing energy balances applied at the beginning and end of one time-step. This study focuses on the second-order velocity-Verlet integration scheme due to its widespread implementation in DEM codes. The commercial DEM software PFC2D was used to verify the correctness of key results. The truncation errors, which are larger than the round-off errors by orders of magnitude, have a superlinear relationship with both the simulation time-step and the interparticle collision speed. This remains the case regardless of simulation details including the chosen contact model, particle size distribution, particle density or stiffness. Hence, the total errors can usually be reduced by choosing a smaller time-step. Increasing the polydispersity in a simulation by including smaller particles necessitates choosing a smaller time-step to maintain simulation stability and reduces the truncation errors in most cases. The truncation errors are increased by the dissipation of energy by frictional sliding or by the inclusion of damping in the system. The number of contacts affects the accuracy and one can deduce that because 2D simulations contain fewer interparticle contacts than the equivalent 3D simulations, they therefore have lower accrued simulation errors

Modeling of ground excavation with the particle finite element method

The present work introduces a new application of the Particle Finite Element Method (PFEM) for the modeling of excavation problems. PFEM is presented as a very suitable tool for the treatment of excavation problem. The method gives solution for the analysis of all processes that derive from it. The method has a high versatility and a reasonable computational cost. The obtained results are really promising.Postprint (published version

A micro finite-element model for soil behaviour

This paper describes a numerical model that virtualises the fabric of a natural sand obtained from micro computed tomography (μCT) to simulate the mechanical response of the material, termed here a micro finite-element (μFE) model. The grain-to-grain interactions under loading are modelled in a framework of combined discrete–finite-element method. The basis of this approach is that using a true representation of soil fabric and deformable grains will enable a more realistic representation of the physics of granular behaviour. Each individual grain is represented in a numerical mesh and modelled as a continuum body allowed to deform according to a prescribed constitutive model with appropriate friction contact conditions. An important feature of this model is the ability to compute the map of stress distribution inside the grains. A case study of an intact sand subjected to oedometer compression is presented to demonstrate the insights that can be gained into the stress transmission mechanisms and yield initiation within the grains. The displacement field, inertia tensor and active contact number are used to quantify grain kinematics as the virtual fabric deforms. By coupling contact dynamics with contact topology, this approach provides a robust numerical tool to infer important grain scale parameters that link the micro phenomena to the macro response of soil

Dynamics of 1d granular column

This dissertation is focused on a discrete element study of the dynamics of a one- dimensional column of inelastic spheres that it subjected to taps by prescribing a half sine wave pulse to supporting floor. Contact interactions obey the Walton-Braun soft-sphere model in which the loading (unloading) path is governing by linear springs of stiffness K1, thereby producing col lisional energy loss through a constant restitution coefficient e. Over a ‘short time scale’, computations are done to examine the floor pulse wave as it propagates through the column contact network. Comparisons of the simulated findings are made with experimental measurements in the literature where possible. Principal emphasis is placed on computing various measures of the evolution of the system that occurs over a long time scale, i.e., the time interval over which the system undergoes a dilation and contraction to a quiescent state after the application of the tap. Here the goal is to chart the column behavior as a function of the amplitude and frequency of the tap, as well as the number of particles in the system and energy dissipation as characterized by. While at the outset, it may appear that this is a simple system, the dynamics in fact are enormously complex as computed Poincaré maps of the mass center trajectories reveal periodic, period doubling and chaotic regimes