While stacked objects are ubiquitous, there are few works devoted to modeling their dynamics. In a new paper “On the Dynamics of a Collapsing Stack of Blocks”, coauthored with Theresa Honein we use a generalized alpha numerical method developed by Capobianco et al [1] to simulate the collapse. The examples we consider include the Leaning Tower of Lyre and the collapse of a stack of blocks that is produced by harmonic excitation of a foundation.
A graphical summary of the paper can be found here:
Our primary result show that an abundance of solutions are possible for the collapsing stack of blocks. As a result, predicting the dynamics is particularly challenging. The results have application to the challenges controllers for robotic manipulators will face when trying to transport stacked objects.
My own interest in these types of problems can be traced to the influence of my PhD advisor Phil Holmes. His seminal work on the dynamics of a bouncing ball [2] illuminated the complexity one can expect from mechanical systems with impact phenomena. I was thrilled to see his recent, well-deserved election to the National Academy of Engineering.
References
[1] Capobianco, G., Harsch, J., Eugster, S.R., Leine, R.I.: A nonsmooth generalized-alpha method for mechanical systems with frictional contact. Int. J. Numer. Methods Eng. 122(22), 6497–6526 (2021). https://doi.org/10.1002/nme.6801
[2] Holmes, P.J.: The dynamics of repeated impacts with a sinusoidally vibrating table. J. Sound Vibration 84(2), 173–189 (1982). https://doi.org/10.1016/S0022-460X(82)80002-3