A New Model for the Sliding Flexible Rocking Oscillator

ABSTRACT A new analytical model called the sliding flexible rocking model (SFRM) is developed to describe the dynamic behaviour of laterally flexible oscillators subjected to earthquakes. The model considers sliding and free flight, that is, complete separation between the structure and the rigid support medium. Phases of motion are defined and the equations of motion for each phase are derived. A hierarchical scheme for transitions between different motion phases is developed. This involves impact‐momentum analyses, which are used to determine the post‐impact states. Simulations show that the new model agrees with authors' earlier flexible rocking model (FRM) when sliding is not present. SFRM also agrees with rigid body rocking models (RSM) allowed to experience sliding and free flight. Comparison between the SFRM and the FRM for slender bodies on low‐grip surfaces show that the sliding in SFRM models greatly affects the overturning stability of the structure. Contrary to what would be expected for rigid rocking bodies, flexible structures can overturn even after experiencing pure sliding. Potential failures due to excessive sliding is also examined. Finally, a new procedure is developed to define the post‐impact phase when the originally chosen impact parameters do not yield an admissible solution. The procedure seeks an admissible solution that minimises the distance of the impulse locus from the impacting corner and respects the hierarchical treatment of phases.