| Title |
Dynamic Stability of A Structure with Vertical and Rotational DOFs under An Inclined Base Excitation |
| Keywords |
Inclined Base Excitation ; Parametric Stability Index ; Dynamic Stability ; Vertical DOF |
| Abstract |
The structural response to an inclined base excitation is examined. A structure is modeled by the inverted pendulum equipped with the viscoelastic rotational and vertical degrees of freedoms (DOF). Perturbation method and numerical simulation are implemented to investigate the motion under harmonic excitation. The DOFs are interactive to each other; rotational motion influences the vertical by way of centrifugal effect and vertical motion does on the rotational by Coriolis effect. Parametric resonances can occur when the frequency ratio of base excitation to rotational frequency is an half, one or two times. At the parametric resonance, forcing terms consist of parametric excitation from the vertical and forced excitation from the horizontal component of base excitation. The prominent parametric resonance at the two times frequency ratio is controlled by the suggested parametric stability index. The index is proportional to classical static stability index and the base vertical acceleration, but inversely to the rotational viscous damping ratio. The influence of vertical motion must be examined at the state of the resonance by itself and the large rotational motion. |