Modeling the dynamics of a wedge pair under the action of a constant force

The subject of research is the dynamics of a wedge pair under the influence of a constant force. The aim of the article is to derive a differential equation of longitudinal vibrations of a wedge pair; a partial solution to this equation of longitudinal vibrations of a wedge pair under the influence of a constant force corresponding to the given initial and boundary conditions; a general solution of the differential equation of longitudinal vibrations of a wedge pair under the action of a constant force. Research methods are based on the d’Alembert principle, which is a method for solving problems of classical mechanics; on the method of mathematical modeling and the analytical method for their solution. The following aspects were obtained in the article for the longitudinal vibrations of a wedge pair: the differential equation of the longitudinal vibrations of a wedge pair by the method of force addition between two infinitesimal sections of the rod in accordance with the d’Alembert principle; a partial solution of the differential equation of longitudinal vibrations of a wedge pair under the action of a constant force corresponding to the given initial and boundary conditions; a general solution of the differential equation of longitudinal vibrations of a wedge pair under the action of a constant force.

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