The problem of mathematical modelling and indication of properties of a DIP has been investigated in this paper. The aim of this work is to aggregate the knowledge on a DIP modelling using the Euler-Lagrange formalism in the presence of external forces and friction. To indicate the main properties important for simulation, model parameters identification and control system synthesis, analytical and numerical tools have been used. The investigated properties include stability of equilibrium points, a chaos of dynamics and non-minimum phase behaviour around an upper position. The presented results refer to the model of a physical (constructed) DIP system.

The motion of submicron particles involves the deterministic terms resulting from the aerodynamic convection and/or electrostatic attraction, and the stochastic term from the thermal displacement of particles. The Langevin equation describes such behavior. The Brownian dynamics algorithm was used for integration of the Langevin equation for the calculation of the single fiber deposition efficiency. Additionally the deterministic and stochastic of the particle motion were derived, using the Lagrangian and Eulerian approaches of particle movement and balance, for the calculation of the single fiber deposition efficiency due to both mechanisms separately. Combination of the obtained results allows us for calculation of the coupling effect of inertia and interception with the Brownian diffusion in a form of correlation. The results of calculation show that the omitting of the coupling effect of particular mechanism and using the simple additive rule for determination of the single fiber deposition efficiency introduces significant error, especially for particles with diameter below 300 nm.

In the presented paper, a problem of nonholonomic constrained mechanical systems is treated. New methods in nonholonomic mechanics are applied to a problem of a Forklift-truck robot motion. This method of the geometrical theory of general nonholonomic constrained systems on fibered manifolds and their jet prolongations, based on so-called Chetaev-type constraint forces. The relevance of this theory for general types of nonholonomic constraints, not only linear or affine ones, was then verified on appropriate models. On the other hand, the equations of motion of a Forklift-truck robot are highly nonlinear and rolling without slipping condition can only be expressed by nonholonomic constraint equations. In this paper, the geometrical theory is applied to the above mentioned mechanical problem. The results of numerical solutions of constrained equations of motion, derived within the theory, are presented.

A formulation developed at the Laboratory of Mechanical Engineering allows robust and efficient simulation of large and complex multibody systems. Simulators of cars, excavators and other systems have been developed showing that real-time simulations are possible even when facing demanding manoeuvres. Hydraulic actuators are presented in many industrial applications of multibody systems, like in the case of the heavy machinery field. When simulating the dynamics of this kind of problems that combine multibody dynamics and hydraulics, two different approaches are common: to resort to kinematically guide the variable length of the actuator, thus avoiding the need to consider the dynamics of the hydraulic system; or to perform a multi-rate integration of both subsystems if a more detailed description of the problem is required, for example, when the objective of the study is to optimize the pump control. This work addresses the inclusion of hydraulic actuators dynamics in the above-mentioned self-developed multibody formulation, thus leading to a unified approach. An academic example serves to compare the efficiency, accuracy and ease of implementation of the simplified (kinematic guidance), multi-rate and unified approaches. Such a comparison is the main contribution of the paper, as it may serve to provide guidelines on which approach to select depending on the problem characteristics.

The most important task in tests of resistance of aircraft structures to the terorist threats is to determine the vulnerability of thin-walled structures to the blast wave load. For obvious reasons, full-scale experimental investigations are carried out exceptionally. In such cases, numerical simulations are very important. They make it possible to tune model parameters, yielding proper correlation with experimental data. Basing on preliminary numerical analyses - experiment can be planned properly. The paper presents some results of dynamic simulations of finite element (FE) models of a medium-size aircraft fuselage. Modeling of C4 detonation is also discussed. Characteristics of the materials used in FE calculations were obtained experimentally. The paper describes also the investigation of sensitivity of results of an explicit dynamic study to FE model parameters in a typical fluid-structure interaction (FSI) problem (detonation of a C4 explosive charge). Three cases of extent of the Eulerian mesh (the domain which contains air and a charge) were examined. Studies have shown very strong sensitivity of the results to chosen numerical models of materials, formulations of elements, assumed parameters etc. Studies confirm very strong necessity of the correlation of analysis results with experimental data. Without such a correlation, it is difficult to talk about the validation of results obtained from "explicit" codes.

We apply a fluid-structure interaction method to simulate prototypical dynamics of the aortic heart-valve. Our method of choice is based on a monolithic coupling scheme for fluid-structure interactions in which the fluid equations are rewritten in the 'arbitrary Lagrangian Eulerian' (ALE) framework. To prevent the backflow of structure waves because of their hyperbolic nature, a damped structure equation is solved on an artificial layer that is used to prolongate the computational domain. The increased computational cost in the presence of the artificial layer is resolved by using local mesh adaption. In particular, heuristic mesh refinement techniques are compared to rigorous goal-oriented mesh adaption with the dual weighted residual (DWR) method. A version of this method is developed for stationary settings. For the nonstationary test cases the indicators are obtained by a heuristic error estimator, which has a good performance for the measurement of wall stresses. The results for prototypical problems demonstrate that heart-valve dynamics can be treated with our proposed concepts and that the DWR method performs best with respect to a certain target functional.