振子によるオートパラメトリック共振を利用した傾き振動系の制振

Abstract

This paper investigates the vibration control of inclination systems by using pendulum vibration absorbers (PVAs). Two kinds of structures are examined; the first one, named as system A, is an SDOF inclination structure to which a pendulum is attached and is subjected to an external, harmonic moment, and the second one, named as system B, is a 2DOF structure, consisting of the vertical and inclination vibrations, to which two pendula are attached and subjected to an external, harmonic force. In the theoretical analysis, van der Pol's methods are employed to determine the frequency response curves. The response curves are compared with simulation results to verify the validity of the theoretical analysis. The autoparametric resonances in the pendula occur when the natural frequencies of the structures and pendula satisfy the 2:1 tuning conditions, and then the vibrations of the structures can be suppressed. The influence of the position of pendula on the performance of the PVAs is investigated. The influence of the deviation of the tuning conditions on the performance of the PVAs are also investigated. The deviation causes Hopf bifurcation to appear, followed by amplitude modulated motions including chaotic vibrations. In system B, a PVA for the vertical vibration of the structure works more effectively when it is attached near the position of the external force.