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Flexible rotors are characterized by inherent uncertainties affecting the parameters that influence the dynamic responses of the system. In this context, the handling of variability in rotor dynamics is a natural and necessary extension of the modeling capability of the existing techniques of deterministic analysis. Among the various methods used to model uncertainties, the stochastic finite element method has received major attention, as it is well adapted for applications involving complex engineering systems of industrial interest. In the present contribution, the stochastic finite element method applied to a flexible rotor system, with random parameters modeled as random fields is presented. The uncertainties are modeled as homogeneous Gaussian stochastic fields and are discretized according to the spectral method by using Karhunen-Loève expansions. The modeling procedure is confined to the frequency and time domain analyses, in which the envelopes of frequency response functions, the Campbell's diagram and the orbits of the stochastic flexible rotor system are generated. Also, Monte Carlo simulation method combined with the Latin Hypercube sampling is used as stochastic solver. After the presentation of the underlying theoretical formulations, numerical applications of moderate complexity are presented and discussed aiming at demonstrating the main features of the stochastic modeling procedure of flexible rotor systems.

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This paper is dedicated to the analyses of the effect of uncertain parameters on the dynamic behavior of a flexible rotor containing two rigid discs and supported by two fluid film bearings. A stochastic method has been extensively used to model uncertain parameters, i.e., the so-called Monte Carlo simulation. However, in the present contribution, the inherent uncertainties of the bearings' parameters (i.e. the oil viscosity as a function of the oil temperature, and the radial clearance) are modeled by using a fuzzy dynamic analysis. This alternative methodology seems to be more appropriated when the stochastic process that models the uncertainties is unknown. The analysis procedure is confined to the time domain, being generated by the envelopes of the rotor orbits and the unbalance responses obtained from a run-down operating condition. The hydrodynamic supporting forces are determined by considering a nonlinear model, which is based on the solution of the dimensionless Reynolds' equation for cylindrical and short journal bearings. This numerical study illustrates the versatility and convenience of the mentioned fuzzy approach for uncertainty analysis. The results from the stochastic analysis are also presented for comparison purposes.

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Modern engineering problems, such as aircraft or automobile design, are often composed by a large number of variables that must be chosen simultaneously for better design performance. Normally, most of these parameters are conflicting, i.e., an improvement in one of them does not lead, necessarily, to better results for the other ones. Thus, many methods to solve multi-objective optimization problems (MOP) have been proposed. The MOP solution, unlike the single objective problems, is a set of non-dominated solutions that form the Pareto Curve, also known as Pareto Optimal. Among the MOP algorithms, we can cite the Firefly Algorithm (FA). FA is a bio-inspired method that mimics the patterns of short and rhythmic flashes emitted by fireflies in order to attract other individuals to their vicinities. For illustration purposes, in the present contribution the FA, associated with the Pareto dominance criterion, is applied to three different design cases. The first one is related to the geometric design of a clamped-free beam. The second one deals with the project of a welded beam and the last one focuses on estimating the characteristic parameters of a rotary dryer pilot plant. The proposed methodology is compared with other evolutionary strategies. The results indicate that the proposed approach characterizes an interesting alternative for multi-objective optimization problems.

Despite the good accuracy of finite element (FE) models to represent the dynamic behaviour of mechanical systems, practical applications show significant discrepancies between analytical predictions and experimental results, which are mostly due to uncertainties on the geometry configuration, imprecise material parameters and vague boundary conditions. Thereby, different approaches have been proposed to solve the inverse problems associated with the updating of FE models. Among them, the techniques based on minimization processes have shown to be some of the most promising ones. In this paper, a self-adaptive heuristic optimization method, namely the self-adaptive differential evolution (SADE), is evaluated. Differently from the canonical differential evolution (DE) algorithm, the SADE strategy is able to update dynamically the required parameters such as population size, crossover parameter and perturbation rate. This is done by considering a defined convergence rate on the evolution process of the algorithm in order to reduce the number of evaluations of the objective function. For illustration purposes, the SADE strategy is applied to the solution of typical mathematical functions. Additionally, the strategy is equally used to update the FE model of a rotating machine composed by a horizontal flexible shaft, two rigid discs and two unsymmetrical bearings. For comparison purposes, the canonical DE is also used. The results indicate that the SADE algorithm is a recommended technique for dealing with this kind of inverse problem.

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