Abstract
A refined mathematical dynamic model of a rigid body with a gravity–friction seismic damper moving inside a movable hemispherical rough depression is set up. This model describe the frequency and decrement properties of a rigid body undergoing translational vibrations on a gravity–friction seismic-isolation mechanism. The mechanism consists of two platforms. The lower (supporting) platform has spherical supports that contact with the upper (supported) platform within its hemispherical depressions. The equations of motion incorporate the nonideality of the unilateral constraints and the shock interaction of a material point with the sphere. It is shown how to join the models describing the free motion and the sliding motion of the point over a spherical surface
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