Computational Mechanics New advances in the forced response computation of periodicstructures using the wave finite element ( WFE ) method
The wave finite element (WFE) method is investigated to describe the harmonic forced response of onedimensional periodic structures like those composed of com plex substructures and encountered in engineering applica tions. The dynamic behavior of these periodic structures is analyzed over wide frequency bands where complex spatial dynamics, inside the substructures, are likely to occu r. Within the WFE framework, the dynamic behavior of periodic structures is described in terms of numerical wave modes. Their computation follows from the consideration of the finite element model of a substructure that involves a large number of internal degrees of freedom. Some rules of thumb of the WFE method are highlighted and discussed to circumvent numerical issues like ill-conditioning and i stabilities. It is shown for instance that an exact analytic relation needs to be considered to enforce the coherence between positive-going and negative-going wave modes. Besides, a strategy is proposed to interpolate the frequency r esponse functions of periodic structures at a reduced number of discrete frequencies. This strategy is proposed to tackl e the problem of large CPU times involved when the wave modes are to be computed many times. An error indicator is formulated which provides a good estimation of the level of accuracy of the interpolated solutions at intermediate poi nts. Adaptive refinement is carried out to ensure that this error indicator remains below a certain tolerance threshold. Numerical experiments highlight the relevance of the propose d approaches.
A wave finite element‐based formulation for computing the forced response of structures involving rectangular flat shells
The harmonic forced response of structures involving several noncoplanar rectangular flat shells is investigated by using the Wave Finite Element method. Such flat shells are connected along parallel edges where external excitation sources as well as mechanical impedances are likely to occur. Also, they can be connected to one or several coupling elements whose shapes and dynamics can be complex. The dynamic behavior of the connected shells is described by means of numerical wave modes traveling towards and away from the coupling interfaces. Also, the coupling elements are modeled by using the conventional finite element (FE) method. A FE mesh tying procedure between shells having incompatible meshes is considered, which uses Lagrange multipliers for expressing the coupling conditions in wave‐based form. A global wave‐based matrix formulation is proposed for computing the amplitudes of the wave modes traveling along the shells. The resulting displacement solutions are obtained by using a wave mode expansion procedure. The accuracy of the wave‐based matrix formulation is highlighted in comparison with the conventional FE method through three test cases of variable complexities. The relevance of the method for saving large CPU times is emphasized. Its efficiency is also highlighted in comparison with the component mode synthesis technique. Copyright © 2013 John Wiley & Sons, Ltd.
Ozonation of polycyclic aromatic hydrocarbons in oil/water-emulsions: mass transfer and reaction kinetics.
The ozonation of highly condensed polycyclic aromatic hydrocarbons (PAH) was studied in oil/water-emulsions, which are comparable to poorly water-soluble PAH in industrial wastewaters and at contaminated sites. As there was a lack of knowledge about the ozonation in oil/water-emulsions, first the ozone mass transfer was studied and optimized from the gas to the water phase and from the water to the oil phase. The ratio of mass transfer and oxidation reaction was determined by the Hatta-number and revealed a slow, quasi homogeneous reaction of ozone with PAH inside the oil droplets. Because the ozone gas concentration had no influence under the optimized conditions, the selective PAH-ozonation could be described microkinetically by a direct ozone reaction of pseudo-first order regarding PAH-concentrations. The determined PAH mean reaction rate constants of 1.02 min(-1) in oil/water-emulsions are in the upper range as found for PAH dissolved in water. These results give a new insight into the ozonation in the three-phase systems and into the treatment of highly condensed, hardly biodegradable PAH.