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The nonlinear normal modes of a horizontally supported Jeffcott rotor are investigated. In contrast with a vertically supported rotor, there are localized and nonlocalized nonlinear normal modes because the linear natural frequencies in the horizontal and vertical directions are slightly different due to both gravity and the nonlinearity of restoring force. Reflecting such nonlinear normal modes, the frequency response curves are characterized in the primary resonance. In the case where the eccentricity is small, i.e., the response amplitude is small, the whirling motion is localized in the horizontal or vertical direction in the resonance. On the other hand, when the eccentricity is large, two kinds of whirling motion, which are localized in the vertical direction and nonlocalized in any direction, coexist simultaneously in a region of rotational speed. Experiments are conducted, and the theoretically predicted nonlinear responses based on localized and nonlocalized nonlinear normal modes are observed.H. Yabuno ( )

An electromagnetic actuator has the property to convert mechanical energy to electrical energy and vice versa. In this study, an electromagnetic resonant shunt damper, consisting of a voice coil motor with an electric resonant shunt circuit, is proposed. The optimal design of the shunt circuit is obtained theoretically for this electromagnetic resonant shunt damper. Furthermore, the effects of parameter errors of the elements of the electromagnetic resonant shunt damper are also investigated. The applicability of the theoretical findings for the proposed damper is justified by the experimental analysis.

Due to the inevitable imbalance of rotating machinery, resonance occurs when the rotational speed is in the vicinity of the critical speed. A rotor system supported by a single-row deep groove ball bearing shows nonlinear spring characteristics due to the clearance of bearings. In this article, passive vibration control of nonlinear rotor systems using a dynamic damper is studied. Theoretical analysis is performed to investigate the influence of nonlinearity on the vibration characteristics of controlled rotor systems, and the theoretical results obtained are confirmed by experiments. An example shows that the fixed-point theorem for optimization of the dynamic damper cannot be used when the rotor system has an isotropic symmetrical nonlinearity. The Newton-Raphson method is used to determine the optimal parameters of the dynamic damper for the nonlinear rotor, and passive vibration control utilizing the dynamic damper is achieved in the nonlinear rotor system.

Detection of a rotor crack based on the nonlinear vibration diagnosis using harmonic excitation force is investigated. The open-close mechanism of crack is firstly modeled by a piecewise linear function. In addition, another approximation crack model using a power series function that is convenient for the theoretical analysis is used. When the power series function crack model is used, the equations of motion of a cracked rotor have linear and nonlinear parametric terms. In this paper, a harmonic excitation force is applied to the cracked rotor and its excitation frequency is swept, and the nonlinear resonances due to crack are investigated. The occurrence of various types of nonlinear resonances due to crack are clarified, and types of these resonances, their resonance points, and dominant frequency component of these resonances are clarified numerically and experimentally. Furthermore, nonlinear theoretical analyses are performed for these nonlinear resonances, and it is clarified that the amplitudes of these nonlinear resonances depend on the nonlinear parametric characteristics of rotor crack. These results enable us to detect a rotor crack without stopping the system during on-line operation.