Rolling-induced flexural vibration

Flexural vibration can be triggered by rolling, an unusual way that has never been studied. Being a planar motion triggered from another motion, it integrates structural dynamics, flexural vibration and contact mechanics. I coin the term “rolling-induced flexural vibration” for this new problem, which is valuable not only to the fundamental theory of structural dynamics but also to various rolling mechanical systems like rolling soft robots. The developed wheels-on-a-string rolling beam that extends the Euler–Bernoulli theory overcomes numerical challenges in contact mechanics by removing inequalities in boundary conditions. An analysis of energy transport and dissipation highlights an unusual rolling beam system. Comparisons are conducted among 3D contact finite element analysis, the rolling beam model and a few analytic solutions. Despite ignoring certain aspect ratio dependence in 3D contact finite elements, the rolling beam model serves as a tool for assessing the efficiency and quality of 3D contact solutions to determine whether switching to alternative contact solvers is necessary. The computational efficiency of the rolling beam model can be up to hundreds of thousands of times higher than that of 3D contact finite elements.