Hilde De Gersem

Frequency response function analysis of structures with fuzzy modal damping parameters

The ability to include non-deterministic properties in a numerical simulation process is of great value for a design engineer. In this context, the fuzzy concept has been introduced as a tool for modeling subjective uncertainty in a numerical environment. Recently, a fuzzy finite element methodology has been developed to calculate fuzzy frequency response functions (FRF) of uncertain structures. The methodology for the interval problem at the core of this procedure is based on a new hybrid approach, which consists of a preliminary optimization step, followed by an interval arithmetic procedure. The final envelope FRFs have been proven to give a very good approximation of the actual response range of the interval problem. Initially, the fuzzy method for FRF analysis was developed for damped structures based on the proportional damping principle. This paper introduces a more general approach for the damping uncertainty based on general modal damping. In the proposed procedure, the analyst can define independent modal damping parameter intervals for each mode that is taken into account in the response function. The modal damping intervals are introduced directly into the procedure. This means that there is no extra preliminary optimization necessary. It is shown how the introduction of the modal damping intervals influences the interval arithmetical procedure that calculates the envelope response function based on the modal superposition principle. In order to validate the procedure, it is applied to a realistic model with fuzzy modal damping parameters.

Non-probabilistic Uncertainty Assessment in Finite Element Models with Superelements

The exponential growth of the computational capacity has, amongst other things, enabled the design engineer to include non-deterministic properties in the numerical simulation and validation of new designs. In this context, the fuzzy concept has been introduced for the description of incomplete data, subjective knowledge and modelling uncertainties in a non-probabilistic manner. The use of the fuzzy concept in the finite element context has led to the development of the fuzzy finite element method for eigenfrequency and frequency response function analysis. For industrially sized models with a large number of uncertainties, the computation time of these methods can be considerable. A reduction in calculation time can be achieved by the substructuring of large models into superelements, which are then independently processed and reduced, and afterwards recombined. In the presented work, the fuzzy finite element method is combined with the Craig-Bampton component mode synthesis substructuring technique, in which the static and dynamic behaviour of each superelement are represented by a set of component modes. Special attention is paid to the consequences of uncertain parameters on the numerical representation of an uncertain superelement. A concept for the description of uncertain component modes is presented, and the influence of global as well as local uncertainties on the accuracy of the interval results of the reassembled model is studied. A numerical case study is presented to illustrate the concepts used in this paper.