Time-History Analysis of Sliding-Rolling Mechanical Systems

The response of freestanding objects subjected to sliding-rolling induced by dynamic excitations is of interest for several mechanical applications, not least for the stability of museum exhibits of historical and artistic value. A simplest plane geometry for describing pot-like artifacts is the rigid half disc which also provides a basis for understanding more complex mechanical problems, like polygonal-shaped blocks in masonry structures. Besides dependency on excitation frequency, amplitude and phase, the observed response of these objects is also strongly dependent on friction coefficients and finishing of contacting surfaces. Time-history analysis of these systems requires appropriate numerical integration as well as suitable error bounds evaluation. Analytical and numerical analyses are presented in this contribution for the rolling half disc model subjected to an impulsive base excitation. Results are critically examined to appraise the model sensitivity to rolling friction.