Rao S.

Many engineering systems are ill-defined and imprecisely known, especially in the preliminary design stages. The vibration analysis of such systems requires a proper modeling of the imprecision and the associated uncertain parameters. This work presents analysis approaches using probabilistic, fuzzy and interval representation of the uncertain parameters. The probabilistic method assumes that the parameters are described by suitable probability distributions and the resulting vibration problems are solved using the principles of probability theory and random vibration. The procedure is illustrated with the eigenvalue analysis of discrete and continuous systems. The mean square approximation theory, linearized equations, partial derivative rule and Monte Carlo simulation are used during numerical implementation. The fuzzy method is based on developing suitable membership functions for the uncertain parameters and the resulting problems are solved using fuzzy set theory. The effect of fuzzy uncertainty on the natural frequencies and mode shapes is investigated. The finite element idealization is used in the numerical implementation. The extension of the method to the dynamic analysis is also outlined. The interval method assumes that the uncertain parameters are represented as interval numbers and the techniques of interval analysis are used to solve the resulting vibration problems. The procedure is illustrated through the eigenvalue analysis of discrete systems. The methodologies presented in this work are expected to be useful for a realistic vibration analysis of engineering systems involving a variety of uncertainties and imprecision.