Sliding-Rocking Vibration of Body on Elastic Medium

The dynamic response in coupled horizontal translation and rocking rotation of a rigid mass with circular base attached to the top of a homogeneous, isotropic, linearly elastic half-space medium is investigated analytically when the mass is excited harmonically by a horizontal force anywhere on the vertical axis of symmetry. Two coupled differential equations of motion of the vibrating mass are written with constant masses and frequency-dependent velocity and displacement coefficients, based upon the works of Bycroft and Hsieh. Amplitude versus frequency and phase-angle versus frequency relations are derived and given in nondimensional forms. Certain physical characteristics of the system are exposed and discussed, and illustrated by curves. The effects of coupling the two modes of vibration are shown to be important. Similarities and applications of the elastic half-space model to the vibration of rigid structures on soil are pointed out.