zbMATH — the first resource for mathematics

Oscillations of a solid parallelepiped on a supported base. (Russian. English summary) Zbl 1372.70022
Summary: An analytical solution of the problem of forced oscillation of the solid parallelepiped on a horizontal base is presented. It is assumed that the slippage between the body and the base is absent, and the base moves harmonically in a horizontal direction. It is also assumed that the height of the box is much larger than the width. The dissipation of impact is taken into account in the framework of Newton’s hypothesis. The forced oscillation modes of parallelepiped corresponding to the main and two subharmonic resonances are found by using the averaging method. The results are shown in the form of amplitude-frequency characteristics.
70E18 Motion of a rigid body in contact with a solid surface
70F40 Problems involving a system of particles with friction
Full Text: DOI MNR