Nonlinear characteristics of contact-induced vibrations of the rotating variable thickness plate under large deformations

Abstract A tip-rub model is developed for nonlinear dynamics analysis of contact-induced vibrations of the rotating variable thickness plate under large deformations. Variable thickness, coupled with large deformations, contact-impact and centrifugal stiffening, increases complexity of the nonlinear system. Natural frequencies for different variable thickness are compared to indicate a great precision of the present method. Solution procedure for tip-rub has been proved to be in good agreement with existing experimental results. Numerical simulation for tip-rub reveals the requirement of large deformation analysis. Then special attention is given to nonlinear characteristics of the rotating rubbing plate with variable thickness. Results show that there are very rich and complex nonlinear dynamics of contact-induced vibrations of the rotating variable thickness plate under large deformations such as multi-period, bifurcation and chaotic motions. And effects of thickness strategies of exponential and linear decrease along the span used in engineering on nonlinear characteristics induced by tip-rub are investigated. Numerical results reveal that smaller thickness at the free end used to reduce centrifugal stress should not be too small to avoid aggravation of contact-induced bifurcation and chaos. Moreover, in order to obtain less centrifugal stress and weak chaotic behavior, there is an optimal thickness at the fixed end when the smaller thickness at the free end is unchanged. As the order of thickness function increasing, the trend of bifurcation and chaotic motions is gradually aggravated. It is better to choose a small order of thickness function to ensure stable operation.