Oscillations of an elastic system with dry friction during a mechanical shock

Abstract

Damped oscillations of an elastic system with dry friction caused by a mechanical im-pact on it by a solid body are described. The technical theory of shock is used, according to which it is considered instantaneous. Two variants of a one-act shock are considered: imper-fectly elastic horizontal and absolutely inelastic vertical, when also the action of the instantly applied weight of the body, which strikes, is additionally taken into account. By the method of joining solutions, compact analytical expressions are constructed for calculating the amplitudes of displacements and the maxima of elastic restoring forces in the oscillator. Formulas are also derived for calculating the time when extremes of displacement and elastic force are reached after impact. It is shown that from the theoretical results obtained, as a special case, Cox's formula, known in the technical impact theory for perfectly elastic systems, follows. Examples of calculations are given where a limited number of swings of the oscillatory dissipative system after impact is shown. The consistency of the computation results for the derived formulas with the results of numerical integration of the differential equation of motion on a computer is established.