The vertical, horizontal and rocking vibrations of a body on the surface of an otherwise unloaded half plane are studied. The problems are formulated so that one stress vanishes over the entire surface, and an oscillating displacement is prescribed in the loaded region. The problems are mixed with respect to the prescribed displacement and the remaining stress. Each case leads to a mixed boundary value problem represented by dual integral equations which are reduced to a single Fredholm integral equation. Although numerical methods are used to solve the integral equation, the contact stresses are found to be presentable in closed form to good accuracy. An estimate of the stiffnesses for coupled horizontal and rocking vibration is also suggested and it is found that the coupling effect is significant.

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