Due to manufacturing and assembly inaccuracies, real rotors are always slightly imbalanced. This produces their lateral vibration and forces that are transmitted through the bearings to the stationary parts. The oscillation of the system can be reduced if damping devices are added to the constraint elements. To achieve the optimum performance of the rotor in a wide range of angular velocities and when passing through the critical speeds their damping effect must be controllable. For this purpose, the application of semiactive magnetorheological (MR) dampers has been analysed. The investigated problem focuses on studying the influence of their damping effect and of its control on the amplitude of the rotor vibration, on the magnitude of the force transmitted to the rotor casing, and on the amount of dissipative power generated in the MR films. The developed mathematical model assumes cavitation in the lubricating layer, and the MR liquid is modelled as a Bingham material. The derivation of the equation governing the pressure distribution in the oil film is completed by a new methodology making it possible to determine the yielding shear stress needed for its solution. The equations of motion of the rotor are nonlinear due to the damping forces and to solve them a Runge–Kutta integration method was applied. Computer simulations show that a suitably proposed current–rotor angular speed relationship enables one to fully eliminate the resonance peaks and to achieve the optimum compromise between the attenuation of the rotor lateral vibration, the magnitude of the forces transmitted to the rotor casing and the amount of energy dissipated in the lubricating layers.

Reduction of noise and vibrations is one of the major requirements put on operation of modern machines. It can be achieved by application of new materials. The ability to utilize them properly requires learning more about their mechanical properties. Vibration attenuation depends on material damping as an important factor. This paper presents the results of research in a carbon composite material focusing on its internal damping, on the measurement of the damping coefficients and on its implementation into mathematical models. The obtained results were used for investigation of suppressing lateral vibrations of a long homogeneous carbon composite bar oscillating in the resonance area. During the transient period and due to nonlinear effects, the harmonic time-varying loading excites the bar response consisting of a number of harmonic components. The specific damping capacity referred to several oscillation frequencies determined by measurement. The results were evaluated from the point of view of two simple damping theories — viscous and hysteretic. The experiments showed that internal damping of the investigated material could be considered as frequency independent. Therefore, in order to carry out simulations, the bar was represented in the computational model by an Euler beam constituted of Maxwell–Weichert theoretical material. A suitable setting of material constants enabled reaching a constant value of the damping parameters in the required frequency range. The investigated bar vibration is governed by the motion equation in which the internal damping forces depend not only on instantaneous magnitudes of the system’s kinematic parameters but also on their past history. Solution of the equations of motion was performed after its transformation into the state space in the time domain. Results of the computational simulations showed that material damping significantly reduced amplitude of the bar vibrations in the resonance area. The producers of composite materials usually provide material parameters allowing to solve various stationary problems (density, modulus of elasticity, yielding point, strength, etc.), but there is only little or almost no information concerning the data needed for carrying out dynamical or other time-dependent analyses such as internal damping coefficients, fatigue limit, etc. Therefore, determination of the hysteretic character of material damping of the investigated carbon composite material, measurement of its specific damping capacity and implementation of the frequency-independent damping into the computational model are the principal contributions of this article.

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