Examining the Energy Loss in the Inverted Pendulum Model for Rocking Bodies

Abstract

Understanding the mechanisms that may lead to failure of rocking bodies is significantly important in quantifying and minimizing the associated risk. The most common model to describe the rocking problem is the inverted pendulum model (IPM) proposed by George W. Housner, which has been followed by multiple researchers. It is often claimed that the IPM is an acceptable model if behaviors such as sliding, uplifting, deformability, and the three-dimensional nature of the response can be restrained mechanically. However, even in a suitably chosen case in which the previous may indeed have a minimal effect in the response, there are still uncertainties with regard to the assumption introduced in the IPM of how energy is lost during impacts. This paper focuses on this assumption and investigates the effects in the stability of rocking bodies. The effect of this assumption is discussed, showing that the associated uncertainty points to whether a rocking body would survive or fail when subjected to a ground excitation. A method that quantifies this uncertainty by making use of a dynamic property of the rocking system is introduced.