Experimental identification of fuzzy structure parameters.

Abstract

Researchers have recently been developing a theory to model structures in which a primary or ‘‘master’’ structure with precisely known parameters is coupled to ‘‘fuzzy’’ substructures with parameters known only in a statistical sense. The goal of the fuzzy theory is to model complex structures with as few parameters as possible. The research presented here is an experimental investigation of the effectiveness of fuzzy parameter choices in modeling the drive-point impedance of a beam with a number of simple oscillators attached along its length. The fuzzy model makes use of ‘‘most likely’’ distributions of mass per unit resonance frequency, given limited knowledge about the attached oscillators. The oscillators are interchanged in order to achieve various realizations of mass per unit natural frequency. The magnitude and phase of the measured drive point impedance are compared to that predicted by fuzzy theory models. The use of the moments of the mass per unit natural frequency distribution as the primary descriptors of the effect of the fuzzy substructures is examined. Bounds on the differences between predicted and measured drive point impedances are established. The use of these bounds in applications such as high-performance, robust vibration control is discussed.