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A new method of multibody system dynamics, named discrete time transfer matrix method of multibody system (MS-DT-TMM) is developed and widely used in engineering field in recent years. When using this method for the problems of multibody system dynamics, the global dynamics equations of the system are not needed and the orders of involved system matrices are always small. The advance in MS-DT-TMM in recent years has been studied in this paper as following: 1 Discrete time transfer matrix method of rigid-flexible multibody system is developed to study rigid-flexible multibody system dynamics. 2 Mixed method of MS-DT-TMM and finite element method is developed to study rigid-flexible multibody system dynamics. 3 Mixed method of MS-DT-TMM and multibody system dynamics method is developed to study rigid-flexible multibody system dynamics. 4 Riccati discrete time transfer matrix method of multibody system is developed to increase the computation speed and the computation stability. 5 Discrete time transfer matrix method of controlled multibody system is developed to study dynamics of controlled multibody system. Several corresponding numerical examples are done to validate these proposed methods. All this implies that the proposed methods provide a powerful tool for the study of multibody system dynamics.

Gears are commonly used design elements, typically used to convert torque. However, gears are also used in mechanisms or gear drives to transmit motion. Typical applications of gear drives are gear trains, used to drive the camshaft by the crankshaft in large-scale diesel engines. There, normally the transmitted rated torque is relatively small compared to the dynamical loads. They often introduce vibrations of the entire drive train, caused by gas forces or auxiliary devices. These dynamic loads cause the flanks of teeth to lift-off. The re-establishment of contact is mostly in the form of impacts and may occur on both sides of the teeth. Because of the noise induced by these impacts, this phenomenon is called gear hammering. In gear trains, the gears are often designed with thin gear bodies to reduce inertia effects and the total weight of the engine. As a result not only noise, but also endurance problems may arise due to the high peaks in the contact forces. Thus, the precise knowledge of the contact forces is necessary for the design process. However, contact forces between rotating gears are extremely difficult and expensive to measure. Therefore, the simulation of contact forces inheres great importance. Nowadays, the contact simulations are mainly done with commercial multibody packages, assuming rigid gears connected by elastic elements. These elastic elements somehow describe the contact stiffness as well as the elasticity of the gear bodies.

In case of planning a building demolition, the information about geometry, quality of building materials, the design of the load carrying system and documentation of the structural calculation is often incomplete and imprecise. Thus for the analysis of a collapse event, engineers are forced to consider the uncertainty of primary parameters influencing e. g. the resistance of structural elements of a building. This kind of uncertainty can be described using suitable data models such as fuzziness and fuzzy randomness []. Within such an ‘uncertain’ structural analysis the deterministic fundamental solution is applied repeatedly. A comprehensive overview over algorithms of fuzzy analysis and fuzzy stochastic analysis is given in []. First applications of uncertainty collapse analyses can be found in [, ]. However, considering several uncertain parameters in an analysis the problem dimension and the necessary effort can be quite high. To receive a good prediction for a complex building collapse, several hundred or even more deterministic solutions are needed. This requires an efficient and fast scheme to perform the analysis for highly nonlinear problems, concerning geometry, material and changing boundary conditions such as contact.

For many engineering applications the multibody system approach proves to be most efficient for the analysis of the overall motion. Collisions between moving bodies might result in impacts which interrupt the overall motion. During impact kinetic energy is lost by wave propagation in the bodies and/or by plastic deformation of the contact region, see Goldsmith [], Johnson [] and Stronge []. For multibody system simulation on the macroscale, these kinetic energy losses during impact are represented by the coefficient of restitution, see e.g. Glocker [] and Pfeiffer and Glocker []. However, the coefficient of restitution cannot be computed within the multibody system approach and must be estimated from costly experiments or experience. Alternatively the coefficient of restitution may be evaluated by additional numerical simulations on a fast time scale, resulting in a multiscale simulation approach as presented in References [, , , ].

The paper presents results of eccentric flows of amaranth and flaxseed in a flat-bottomed Plexiglas model of silo. The images of the flowing grains were registered by a camera of high resolution. The Digital Particle Image Velocimetry technique was used to analyse the seed flow. For this purpose long sequences of digital images of the flowing grains were processed to obtain full velocity vector fields as well as selected velocity profiles for the analysed discharge processes. Deformations occurred in the flowing material are also evaluated. The experiments were made in the model of three different roughness of the walls, the smooth and lined with sand paper of two different roughness. To investigate effects of eccentricity, both during filling and discharge, the model was filled centrally at the symmetry axis, close to the left edge of the silo, and near its right edge. The filling pipe was also located centrally or eccentrically above the model. The differences between different modes of flow are described and analysed in detail.

Classic rigid body mechanics does not provide frictional forces acting in a 2D contact interface between two bodies during sticking. This is due to the statical undeterminacy related to this problem. Many technical systems, e.g. disk clutches, have such surface-to-surface contacts and it is sometimes desirable to treat them as rigid body systems despite the 2D contact. Alternatively, it is possible to model the systems using elastic instead of rigid bodies, but this might lead to certain drawbacks. A new regularization model of such 2D contacts between rigid bodies is proposed. It is based on the similarity to a material model for elasto-plasticity in continuum mechanics. Only dry friction is taken into account.

The rapid increasing production of cohesive to very cohesive ultra- fine powders ( < 10 µm), e.g. very adhering pigment particles, micro-carriers in medicine, auxiliary materials in catalysis make technical problems much serious like undesired adhesion in particle processing, powder handling, and desired, in agglomeration or coating. Thus, it is very essential to understand the fundamentals of particle adhesion with respect to product quality assessment and process performance in powder technology. The state of arts in modelling of elastic, elastic-adhesion, elastic-dissipative, plastic-adhesion and plastic-dissipative contact deformation response of a single, normal loaded, isotropic contact of two smooth spheres is briefly discussed. Then the force-displacement behaviour of elastic-plastic and adhesive contacts is shown. Using the model “stiff particles with soft contacts”, the combined influence of elastic and elastic-plastic repulsions in a characteristic particle contact is demonstrated. A sphere-sphere model for van der Waals forces without any contact deformation describes the “stiff” attractive particle adhesion term. A plate-plate model is used to calculate the micro-contact flattening or overlap. Various contact deformation paths for loading, unloading, reloading and contact detachment are discussed. Thus, the varying adhesion forces between particles depend directly on this “frozen” irreversible deformation, the so-called contact pre-consolidation history. The adhesion force is found to be load dependent (). The contribution of this history dependent adhesion on the tangential force in an elastic-plastic frictional contact (, ()), the rolling resistance (, ()) and the torque of mobilized frictional contact rotation (, ()) are shown. With this increasing load, normal and tangential contact stiffness, energy absorption, Coulomb friction limit and friction work increase.These constitutive models are generally applicable for solid micro- or nanocontacts but have been shown here for an ultrafine limestone powder ( = 1.2).

Non-smooth nonlinearity is abundant in nature being usually related to either the friction phenomenon or the discontinuous characteristics as intermittent contacts of some system components. Non-smooth systems appear in many kinds of engineering systems and also in everyday life. Examples may be mentioned by the stick-slip oscillations of a violin string or grating brakes []. Some related phenomena as chatter and squeal causes serious problems in many industrial applications [].

The paper investigates the interactions between impacting rigid bodies and the induced elastic waves in planar beam structures. Therefor, the framework for non-smooth dynamics of multibody systems including elastic impacts is applicated to a finite element description for beams in free planar motion. The model is used for two numerical examples: a cantilever beam with multiple impacts to several point masses and an elastic model of the rocking rod, which is used to adapt the restitution coefficient for a rigid model.