Abstract
A rotary machine is a significant component of many mechanical systems and it is important to clarify the dynamic characteristics under many rotational conditions. In this paper, we theoretically and experimentally analyze the steady state responses in a horizontally supported Jeffcott rotor produced in the cases when the rotational speed is in the neighborhood of twice the natural frequencies in the horizontal and vertical directions. First, we derive the equations of motion by considering the effects of gravity and the cubic nonlinearity of restoring force by the support condition. These synergistic effects produce the difference between the linear natural frequencies in the vertical and horizontal directions and make the stiffness in the vertical direction asymmetric. Secondly, we perform nonlinear analysis by the method of multiple scales and derive two unstable regions and frequency response curve. These indicate that the nonlinear resonances can be produced in the neighborhood of twice the natural frequencies in the horizontal and vertical directions and the frequency response curve of the resonance near twice the horizontal natural frequency is hardening-type, while the frequency response curve of the resonance near twice the vertical natural frequency is softening-type.
