Base Excitation of Rigid Bodies. I: Formulation

Abstract

This paper presents the general, two‐dimensional formulation for the response of free‐standing rigid bodies to base excitation. The formulation assumes rigid body, rigid foundation, and Coulomb friction. The behavior is described in terms of the five possible modes of response (rest, slide, rock, slide‐rock, and free‐flight) and impact between the body and foundation. The governing equations of motion are summarized for the modes: slide, rock, and slide‐rock. Approximate equations are outlined for the rock and slide‐rock modes that are valid for small angles of rotation. A model governing impact from a rock, slide‐rock or free‐flight mode is derived from first principles using classical impact theory. This model assumes a point‐impact, nonzero coefficient of restitution and finite value of friction. The paper presents a complete and consistent formulation, which can be used in its entirety or in part, for investigation of the generalized response using suitable analytical or numerical techniques.