The rocking of objects resting on a moving base is an easy mechanics problem to explain, and even each individual contributing element is easy to grasp, but the combination of all of the ingredients lead to some very interesting and highly nonlinear dynamic phenomena.
Together with Manolis Chatzis we have explored the problem to develop analytically based models for 2D and 3D rocking mechanics which need to be solved numerically. So far we have tried to include important ingredients of:
Here's a simple 2D example of the response of a block to one complete cycle of single sine pulse on our shake-table in Columbia's Carleton Laboratory.
We have written a paper which models the 2D rocking mechanics with the key ingredients outlined above:
More recently we have gone on to consider the modeling of the rocking problem in 3-dimensions. With the same block and same single axis base motion, the 3-dimensionality is quickly observed by simply rotating the block slightly so that the axis of base motion is no longer in one of the principal axes.
We have gone on to develop a set of models (depending on the type of base support conditions) with which we can simulate the response of a block of desired dimensions to a triaxial base motion, with selected interface friction behavior and where the base stiffness and damping can be specified.
Here is the type of response the model produces (for an earthquake record):