Nonlinear rocking of rigid blocks on flexible foundation: Analysis and experiments

Primarily, two models are commonly used to describe rocking of rigid bodies; the Housner model, and the Winkler foundation model. The first deals with the motion of a rigid block rocking about its base corners on a rigid foundation. The second deals with the motion of a rigid block rocking and bouncing on a flexible foundation of distributed linear springs and dashpots (Winkler foundation). These models are two-dimensional and can capture some of the features of the physics of the problem. Clearly, there are additional aspects of the problem which may be captured by an enhanced nonlinear model for the base-foundation interaction. In this regard, what it is adopted in this paper is the Hunt-Crossley nonlinear impact force model in which the impact/contact force is represented by springs in parallel with nonlinear dampers. In this regard, a proper mathematical formulation is developed and the governing equations of motion are derived taking into account the possibility of uplifting in the case of strong excitation. The analytical study is supplemented by experimental tests conducted in the Laboratory of Experimental Dynamics at the University of Palermo, Italy. In this context, due to their obvious relevance for historical monuments, free-rocking tests are presented for several marble-block geometries on both rigid and flexible foundations. Numerical vis-à-vis experimental data are reported, supporting the usefulness and reliability of the proposed approach.