Base excitation of rigid bodies. II: periodic slide-rock response

An approximate closed-form solution is developed for a single-mode, steady-state slide-rock response resulting from a harmonic ground acceleration. The approximate solution is developed using the method of slowly varying parameters and is valid for a rectangular block undergoing small angles of rotation at the frequency of base excitation. Impacts with the foundation are assumed to be perfectly plastic and frictional impulses are included. Periodic solutions are found to exist in general only for relatively high amplitudes of ground acceleration and friction less than the inverse aspect ratio of the block. The rock component of the response is sensitive to changes in aspect ratio and friction and insensitive to changes in ground acceleration. The slide component of response is approximately equal to the amplitude of ground displacement and is insensitive to changes in friction and aspect ratio. Results compare favorably to those obtained by numerical integration. The accuracy of the approximate solution is shown to depend heavily on the magnitude of impulse applied during impact.