Sliding and rocking response of a flexible structure on a rigid block using floating frame of reference formulation

The assessment of sliding and rocking responses in flexible structures subjected to ground vibrations presents complex challenges due to their high sensitivity to input motion, geometric variations, and dissipation issues. While numerous researchers have focused on studying flexible structures, the rocking response of these structures has often been overlooked, with examinations limited to models involving a single body rather than multiple bodies with intricate connection constraints. Consequently, the aim of this paper is to develop an analysis method capable of comprehensively describing the sliding and rocking motions of structures consisting of a combination of rigid blocks and flexible structures, as well as connection constraints, utilizing the Floating Frame of Reference Formulation (FFRF). The proposed analytical model was evaluated for its ability to predict the sliding and rocking responses of flexible structures laid on rigid blocks under external pulse excitation and initial conditions. By integrating the Finite Element Method into FFRF, the model enables the description of complex systems with diverse shapes and connections. Furthermore, we derive an impact equation that accounts for elastic deformation and develop an equation for calculating the coefficient of restitution, considering the effect of elastic displacement based on FFRF. This integration extends the simulation analysis to encompass flexible multi-body systems, accurately capturing energy dissipation during rocking impacts. To demonstrate and generalize the novel application of FFRF, time histories of sliding and rocking motion under pulse excitation and initial conditions were analyzed and presented. The results showcased the effectiveness and versatility of the proposed approach in capturing the intricate dynamics of sliding and rocking rigid blocks and flexible structures. Overall, this study contributes to the advancement of analytical methods for assessing the sliding and rocking behavior of multibody systems and the coefficient of restitution when elastic displacement was considered, providing valuable insights for design and analysis in various engineering applications.