Envelope frequency Response Function Analysis of Mechanical Structures with Uncertain Modal Damping Characteristics
D. Moens; M. De Munck and D. Vandepitte

doi:10.3970/cmes.2007.022.129
Source CMES: Computer Modeling in Engineering & Sciences, Vol. 22, No. 2, pp. 129-150, 2007
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Keywords envelope frequency response functions, interval finite element analysis, uncertainty
Abstract Recently, an interval finite element methodology has been developed to calculate envelope frequency response functions of uncertain structures with interval parameters. The methodology is based on a hybrid interval implementation of the modal superposition principle. This hybrid procedure consists of a preliminary optimization step, followed by an interval arithmetic procedure. The final envelope frequency response functions have been proved to give a very good approximation of the actual response range of the interval problem. Initially, this method was developed for undamped structures. Based on the theoretical principles of this approach, this paper introduces a new method for the analysis of structures with uncertain modal damping factors. In the proposed procedure, next to the classical interval parameters that affect stiffness and mass properties of the model, additional independent modal damping parameter intervals describe the uncertainty on the damping factor of each mode that is taken into account in the response function. The algorithm adopts the general modal superposition strategy of the undamped procedure. The effect of the introduction of the modal damping intervals in the interval arithmetic part of the procedure is studied analytically, and a new interval arithmetic procedure is developed according to the observations from this study. In order to validate the procedure, it is applied to a realistic industrial model with geometric as well as modal damping uncertainty.
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