Nonlinear Parametric Vibration Analysis of Radial Gates

Abstract

In this work, based on dynamic characteristics of radial gates, a nonlinear differential equation of motion for the radial gate arm is established. Excitation conditions of principal parametric resonance and subharmonic parametric resonance are obtained by using multi-scale method and numerical method. The parameter analysis shows that: comparing with traditional calculation method of dynamic instability region division, the presented method is more suitable to analysis of parametric vibration for radial gates as considering the end moment, vibration duration and amplitude. The vibration amplitudes of arm increase with the increase of its length and excitation amplitude, as well as the decrease of arm inclination angle. Moreover, the parametric resonance is easier to be excited and its resonance region become wider with the initial end moment increasing. Since the vibration response of the arm is influenced by the nonlinear term in the equation, the damping effect is limited. Thus, energy transfer method (e.g. tuned mass damper) can be adopted to achieve vibration control.