The rolling and sliding motions of a rigid body subject to gravity and supported by a plane surface are treated in elementary texts on dynamics. Rocking of a riding body supported by a horizontal surface which experiences oscillatory accelerations due to an earthquake has been discussed by Housner. If the body is deformable there is a potential for the dynamics of the body deformations to couple with the rocking mode; in particular, resonances in the deformation response can develop sufficient reaction moment at the base to cause base uplift which would not occur if the body were rigid. The paper presents a model suitable for studying this phenomena including the magnitude of the uplift, impacts occurring during stable rocking motions, and overturning. The equations governing the plane motion of a deformable body with rocking boundary conditions supported by a horizontal flat surface subject to vertical and horizontal accelerations are derived. These equations depend on dynamic parameters of the body which are defined in terms of integrals of assumed modes of deformation. The number of assumed modes is arbitrary. Motions which involve uplift but not overturning are termed rocking motions and are characterized by impacts with the supporting plane. Integration of these equations requires care in dealing with high frequency rocking motions may occur.
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