Revues

Arbitrary order expansions for the automatic reduction and solutions of nonlinear vibratory systems have been developed successfully within the realm of the direct parametrisation of invariant manifolds. Whereas the method has been used with high-order expansions and large dimensional systems, this article proposes to look at the same problem from the opposite view angle. By using low-dimensional systems, symbolic computations, analytical developments and numerical verifications, this contribution analyzes the reduced dynamics appearing in cases where a single master mode is involved, reviewing typical scenarios in nonlinear vibrations: primary resonance, sub- and superharmonic resonances and parametric excitation. To achieve this task, the normal form style is preferentially used. A symbolic open-source package is also provided to generalize the presented results to other styles, higher orders, and different scenarios. It is shown how the low-order terms allow recovering the classical solutions given by perturbation methods, and how the automated expansions allow one to generalize the analysis to arbitrary orders. When analytical solutions are not tractable anymore, numerical solutions are employed to underline how converged solutions are at hand when the validity limit of the expansions is not reached. All the results presented in this paper can thus be used to better understand the nonlinear dynamical solutions occurring in nonlinear vibrations, as well as from a system identification perspective, since the normal form is the simplest dynamical system displaying a given resonance scenario.

de Figueiredo Stabile, André

Sintering is a high temperature process for the consolidation of ceramic, metal and polymer powders. The Discrete Element Method (DEM) has been effectively used to model the sintering process at the particle scale considering spherical particles. However, standard manufacturing processes rarely deal with spherical particles. As sintering is a curvature-controlled process, it is important to take into account the deviation from sphericity. This study presents a DEM sintering model for non-spherical particles. The description and dynamic evolution of arbitrary shape particles is achieved by using the Level Set discrete element method (LS-DEM). The original LS-DEM approach uses boundary nodes on the particles to detect contacts. We employ an optimization-based contact detection approach. This improves the capture of small contacts, which is important for a correct description of sintering evolution with reasonable CPU-time consumption. A Newton-Raphson scheme is employed for the optimization algorithm. The normal force and neck size evolution expressions of spherical particles are adapted for arbitrary shape particles by using the local curvature at the contact. The developed model is validated for elastic contacts on superquadric ellipsoids. It is compared with standard DEM on spheres for sintering. The model is applied to investigate the consolidation kinetics of a packing of ellipsoidal particles. It is shown, that a deviation from sphericity is beneficial for both prolate and oblate ellipsoids. An optimum aspect ratio is evaluated, demonstrating that particles that are too elongated slow down densification kinetics.

Paredes-Goyes, Brayan