Abstract This paper aims at analyzing the sensitivity of the structural response of flexible rotors subjected to uncertain interval parameters. The interval approach encompasses both an uncertainty and sensitivity analyses. The uncertainty analysis consists in computing the interval uncertain structural responses by using the global optimization method. The sensitivity analysis computes the normalized relative sensitivity indices that quantify the degree of importance of each uncertain interval parameter on the uncertain structural responses of the flexible rotor. The uncertain structural responses and the sensitivity of the flexible rotor subjected to interval parameters are analyzed in terms of the Frequency Response Function (FRF), orbits, Campbell diagram, and run-up operating condition. Numerical simulation results illustrate the interval approach conveyed.

Abstract In the present paper, a simplified homogenized beam theory is used in the context of a numerical investigation regarding the dynamic behavior of a rotating composite hollow shaft. For this aim, a horizontal flexible composite shaft and a rigid disc form the considered simple supported rotating system. The mathematical model of the rotor is derived from the Lagrange’s equation and the Rayleigh-Ritz method, which is obtained from the strain and kinetic energies of the disc and shaft, and the mass unbalance. In this case, a convergence procedure is carried out in terms of the vibration modes to obtain a representative model for the rotor system. Therefore, the proposed analysis is performed in both frequency and time domains, in which the frequency response functions, the unbalance responses, the Campbell diagram, and the orbits are numerically determined. Additionally, the instability threshold of the rotor system is obtained. This study illustrates the convenience of the composite hollow shafts for rotor dynamics applications.

Abstract In engineering systems design, theoretical deterministic solutions can be hardly applied directly to real-world scenarios. Basically, this is due to manufacturing limitations and environmental conditions under which the real system will operate. Therefore, a small variation in the design variables vector can result in a meaningful change on the theoretical optimal design as represented by the minimization of the corresponding vector of objective functions. In this context, it is important to develop methodologies that are able to produce solutions (even suboptimal) that are less sensitive to perturbations in the design variable vector and, consequently, leading to a robust optimal design. In this contribution, first the proposed approach is tested on various mathematical functions. Then, the methodology is applied to the design of two representative engineering systems through multi-objective optimization using the Firefly Colony Algorithm in association with the Effective Mean Concept is presented.The results obtained demonstrate that the design strategy conveyed represents an interesting alternative approach to obtain robust design for a number of engineering applications.

Abstract The components of flexible rotors are subjected to uncertainties. The main sources of uncertainties include the variation of mechanical properties. This contribution aims at analyzing the dynamics of flexible rotors under uncertain parameters modeled as fuzzy and fuzzy random variables. The uncertainty analysis encompasses the modeling of uncertain parameters and the numerical simulation of the corresponding flexible rotor model by using an approach based on fuzzy dynamic analysis. The numerical simulation is accomplished by mapping the fuzzy parameters of the deterministic flexible rotor model. Thereby, the flexible rotor is modeled by using both the Fuzzy Finite Element Method and the Fuzzy Stochastic Finite Element Method. Numerical simulations illustrate the methodology conveyed in terms of orbits and frequency response functions subject to uncertain parameters.

This paper presents a numerical study devoted to the evaluation of the possibility of monitoring and controlling the dynamic behavior of a rotating machine with a cracked shaft by using an Electro-Magnetic Actuator (EMA). The EMA is located at the mid-span of the rotor to provide active control. The opening and closure (breathing) of the crack is determined by the stress field over its cross section resulting from the dynamic bending moment. The system is nonlinear due to the fact that the crack parameters must be determined for each time step and the EMA introduces forces that are inversely proportional to the square of the gap value between the stator and the rotor. The model developed takes into account the behavior of the crack and the in uence of the EMA. Simulations were carried out to access the possibility of controlling the breathing mechanism. The results obtained demonstrate the possibility of using the EMA in order to keep the crack closed along the rotation of the rotor, thus forming a self-healing scheme for the cracked rotor.

Piezoelectric elements connected to shunt circuits and bonded to a mechanical structure form a dissipation device that can be designed to add damping to the mechanical system. Due to the piezoelectric effect, part of the vibration energy is transformed into electrical energy that can be conveniently dissipated. Therefore, by using appropriate electrical circuits, it is possible to dissipate strain energy and, as a consequence, vibration is suppressed through the added passive damping. From the electrical point of view, the piezoelectric element behaves like a capacitor in series with a controlled voltage source and the shunt circuit, commonly formed by an RL network, is tuned to dissipate the electrical energy, more efficiently in a given frequency band. It is important to know that large inductances are frequently required, leading to the necessity of using synthetic inductors (obtained from operational amplifiers). From the mechanical point of view, the vibration energy can be attenuated in a single mode, or in multiple modes, according to the design of the damping device and the frequency band of interest. This work is devoted to the study of passive damping systems for single modes or multiple modes, based on piezoelectric patches and resonant shunt circuits. The present contribution discusses the modeling of piezoelectric patches coupled to shunt circuits, where the basics of resonant shunt circuits (series and parallel topologies) are presented. Following, the devices used in passive control (piezoelectric patch and synthetic inductors) are analyzed from the electrical and experimental viewpoints. The modeling of multi-degree-of-freedom mechanical systems, including the effects of the passive damping devices is revisited, and, then a design methodology for the multi-modal case is defined. Also, it is briefly reviewed the optimization method used for design purposes, namely the LifeCycle Model. Finally, experimental results are reported, illustrating the success of using the methodology presented in passive damping applications applied to mechanical and mechatronic systems.

This paper examines two passive techniques for vibration reduction in mechanical systems: the first one is based on dynamic vibration absorbers (DVAs) and the second uses resonant circuit shunted (RCS) piezoceramics. Genetic algorithms are used to determine the optimal design parameters with respect to performance indexes, which are associated with the dynamical behavior of the system over selected frequency bands. The calculation of the frequency response functions (FRFs) of the composite structure (primary system + DVAs) is performed through a substructure coupling technique. A modal technique is used to determine the frequency response function of the structure containing shunted piezoceramics which are bonded to the primary structure. The use of both techniques simultaneously on the same structure is investigated. The methodology developed is illustrated by numerical applications in which the primary structure is represented by simple Euler-Bernoulli beams. However, the design aspects of vibration control devices presented in this paper can be extended to more complex structures.