Free Rocking of Cylindrical Structures

Abstract

Rocking or toppling of a cylindrical structure or object on a shaking foundation is a common occurrence of engineering interest. The behavior is analyzed with a simple three‐dimensional model which has an upright rigid cylinder standing on a rigid foundation. Given an initial side impulse, the cylinder will rock and rotate on the base under the influence of gravity alone. The constraint for the model is that no slipping occurs at the point of contact between the cylinder and the foundation. Otherwise, rolling, rocking, and toppling are not restricted. The governing equations are derived, and the response of the cylinder under free rocking is calculated for various initial conditions. Three types of response are observed: rocking, nutation, and toppling. Rocking is the side‐to‐side motion, while nutation is the wavy precession about the vertical. In addition, rocking and nutation both exhibit a stiff type and a smooth type. The regions for each type of response are mapped out in the domain formed by the initial conditions. From the plots of these regions, one can predict the type of response for a given set of initial conditions.