Mathematical modeling of forced oscillations of semidefinite vibro-impact system sliding along rough horizontal surface

Abstract

The paper considers the motion conditions of a semidefinite vibratory system placed upon a rough horizontal surface. Such systems are sometimes called unrestrained or degenerate ones, and are usually used in various vibration-driven robots and capsules. Unlike the numerous existent investigations dedicated to a similar subject, the novelty of the present paper consists in the implementation of a crank mechanism for exciting oscillations of a double-mass vibro-impact system setting into planar locomotion a robot’s movable body. A general design diagram of the improved semidefinite vibro-impact system is proposed, and the corresponding mechanical diagram is considered. The differential equations describing the system sliding (planar locomotion) along a rough horizontal surface are derived. A thorough analysis of the main inertia-stiffness, design, and excitation parameters influencing the system motion conditions is carried out. Performing the numerical modeling in MathCad software, the dynamic behavior of the robot’s movable body is studied under the specified system’s parameters and operational conditions.