Envelope frequency response function calculation of un- certain structures

Requirements for the dynamic properties of a mechanical structure are commonly expressed in terms of eigenfrequencies. Therefore, during the design phase of a mechanical structure much attention is paid to natural frequencies and mode shapes. However, these modal properties tend to vary strongly if small variations are applied on the design model. Therefore, the presence of open design decisions or other uncertain parameters complicates strongly a meaningful dynamic design validation in an early design stage. A fuzzy finite element method for the eigenvalue analysis has been developed to cope with this problem. This method results in fuzzily defined modal properties indicating the degree of uncertainty on the eigenfrequencies and eigenmodes resulting from the uncertain model. However, rather than eigenfrequencies, the specification of responses at frequencies that are critical in the operating conditions of the structure would be a more realistic concept for dynamic design requirements. In order to facilitate the use of such design requirements, a tool is needed to analyze the influence of design decisions on responses at these specific frequencies. Therefore a method for the calculation of fuzzy frequency response functions of uncertain structures is presented. The procedure calculates guaranteed bounds on the envelope on the response function starting from interval bounded uncertainties on the input model. It necessitates the calculation of guaranteed boundaries on the contribution of each individual mode to the total frequency response function.