The Nonlinear Dynamic Response and Vibration Transmission Characteristics of an Unloading System with Granular Materials

The aim of this study is to research the flow property of granular materials under nonlinear vibration, which directly affects the stability of the unloading system and the motion state of granules. According to the mechanical constitutive relation, the coupled suspension–tire model with nonlinear ordinary differential equations is established and the kinematic equations of granules are derived. Furthermore, the amplitude–frequency responses of the coupled system and force transmissibility are obtained by the incremental harmonic balance method (IHBM) with high-order approximation, and then the flow characteristics of granular materials are investigated based on the approximate analytic solution under nonlinear vibration. The theoretical analysis and numerical simulation show that the coupled suspension–tire system presents a softening nonlinear feature and the peaks are significantly smaller than that of the linear system, which further affects the motion rules of granular materials. As a result, different sliding states and flow paths are observed under the same operating conditions. This research not only shows the unloading mechanism and vibration transmission characteristics between the continuum structure and granular material but also theoretically explains the control mechanism of the coupled continuum–granular system. The research is instructive in improving the unloading efficiency of granules in practical engineering.