Numerical simulation and experimental investigation for the dynamic rocking response of two stacked rigid blocks

Abstract

A system of two stacked rigid blocks (TSRBs), such as a statue on a pedestal, is extensively constructed and utilized. However, the numerical simulation of its dynamic response has been a crucial and challenging problem due to the diversity of motion patterns and the nonlinearity in the impacts. Therefore, a high-accuracy and appropriate numerical simulation approach for solving the rocking response of TSRBs was proposed in this paper. First, their rocking patterns were presented, and the judgment diagram of their transitions was defined. Then, the rocking equations of the motion and the formulas of the post-impact angular velocities were introduced. Next, to solve the rocking response of TSRBs, a novel numerical method stemming from the Rosenbrock method and the substep-two-step method was proposed and preliminarily verified. Moreover, free and forced vibration experiments were conducted to verify its accuracy further, and the regularity of the motion was summarized. Finally, parametric analyses of the applications was performed on statue-pedestal systems to investigate the influence of the wall thicknesses and height-to-width ratios of the pedestals on the dynamic response. The results indicate that the proposed method has favorable stability, acceptable accuracy, and high computational efficiency due to its accurate impact point identification and rocking pattern determination. In practice, to reduce the dynamic response of statues, it is preferred to place pedestals with smaller wall thicknesses and larger height-to-width ratios under statues.