A fuzzy finite element procedure for the calculation of uncertain frequency-response functions of damped structures: Part 1—Procedure

This work introduces a numerical algorithm to calculate frequency-response functions (FRFs) of damped finite element (FE) models with fuzzy uncertain parameters. Part one of this paper describes the numerical algorithm for the solution of the underlying interval finite element (IFE) problem. First, the IFE procedure for the calculation of undamped envelope FRFs is discussed. Starting from the undamped procedure, a strategy is developed to analyse damped structures based on the principle of Rayleigh damping. This is achieved by analysing the effect of the proportional damping coefficients on the subsequent steps of the undamped procedure. This finally results in a procedure for the calculation of fuzzy damped FRFs based on an analytical extension of the undamped algorithm. Part one of this paper introduces the numerical procedure. Part two of this paper illustrates the application of the methodology on four numerical case studies.