Modal description of vibratory behaviour of structures using fuzzy membership functions

Abstract

A method is developed to model vibratory systems in terms of their modal shapes estimated by fuzzy membership functions and updated by use of frequency response functions. In this method, fuzzy output membership functions are introduced based on ‘guessed’ mode shapes of the system. The approximate mode shapes can be estimated as they partially depend on the boundary conditions. The fuzzy membership functions are then updated using experimental modal analysis method which is used in refining ‘fuzzy mode shapes’. The fuzzy mode shapes are then interpolated with respect to geometry and frequency, giving full behaviour description of the system in frequency domain using fuzzy neural network. Although the method proposed is general in this paper, the case study is based on a simple beam. Two inputs of the fuzzy model are sampling positions on the beam and frequency. The natural frequencies of the system were found by experimental tests. Mode shape or deflection of the beam is introduced by zero, medium, large and positive and negative terms. These mode shapes are modified by using the data from experimental modal analysis. The corresponding magnitude in the fuzzy model is updated by magnitudes from mode shapes from modal testing. A fuzzy neural network is used to determine the mode shape curves from the updated mode shapes. This approach compliments modal analysis and enhances it by incorporating it with fuzzy reasoning. In that respect the proposed method offers two distinct benefits, firstly, the use of fuzzy membership functions provides a means of dealing with uncertainty in measured data and, secondly, it give access to a large repertoire of tools available in fuzzy reasoning field. The procedure proposed in this paper is a novel and has not been done before.