Oscillation of Massif, Located on the Elastic Foundation (Winkler Model)

Abstract

Oscillation of Massif, Located on the Elastic Foundation (Winkler Model)

Karnilov D.A., Litikov A.P., Mumortsev A.N.

Incoming article date: 08.12.2014

The article deals with self-induced and forced oscillations of the solid core massif on the elastic (Winkler) foundation. Perturbing forces are “inertial forces” of unstable equipment, established on the foundation-like massif. Taking into account some hypothesis, minor oscillations (reciprocal and torsion) across and relative to chief central inertion axis that are represented by the system of six differential equations. In the most general case natural vibration frequencies are regarded as solutions of septic determinants. The authors have worked out two particular cases that allow decreasing the order of determinants. In order to determine the frequency of oscillation of an external force “the disturbation forces” are represented in Fourier series. The article shows the results of numerical calculations for the simplest particular case of massif geometry.

Keywords: "massif, Winkler foundation, inertia weight and inertia moments, elastic foundation response, internal forces system, differential equations of motion, Fourier series, differential equations system determinants, natural vibration frequencies, resonance c