The dynamic behaviour of flexible oscillators rocking and sliding on concentrated springs

This study presents the Flexible Rocking Model on Concentrated Springs (FRMCS), developed to investigate 2D laterally flexible oscillators rocking and sliding on deformable support media during ground excitations. In this model, concentrated vertical springs and viscous dampers simulate the contact forces from support medium at the corners of the body; the tensionless vertical contact element is linear in compression. Horizontal concentrated springs and linear viscous dampers simulate the frictional behaviour at the corners; the constitutive law for the springs models elastic deformations and sliding (according to Coulomb's friction law). With these elements, FRMCS can model the response of a rocking body which can experience sliding and free-flight phases of motion. The consideration of the flexibility of the support medium enables the evaluation of the forces exerted by the support medium on the structure during an impact. In this study, the FRMCS response is first compared to a previous model where the support medium deformability and the effects of sliding and free-flight are ignored. Then, the responses of four configurations, which feature either stiff or soft lateral springs and stiff or soft high-grip support media, are examined under the influence of pulse excitations. Finally, to understand the potential influence of sliding, a configuration with a low-grip support medium is explored. The comparative influence of lateral flexibility and support medium deformability and sliding is quantified with stability diagrams and various response spectra, describing structural force and moment demands.