Mathematical simulation of elastic systems with unilateral external interaction

We consider the behavior of elastic systems with external unilateral interaction (friction, recovering forces, forces of relay type), which are given as functions defined by inequalities relative to unknown variables. The investigation is based on application of the concept of motion separation (coupled application of methods of motion decomposition with respect to normal modes of oscillations, asymptotic methods of nonlinear mechanics and frequency separation of motions). This approach makes it possible to construct a discrete nonlinear model of the investigated system and the analytical-numerical method for its investigation. The transient modes of the system motion were studied. Peculiarities of manifestation of nonlinear properties of the system are discussed. We consider also the case of oscillations of elastic systems with variable stiffness coupled with unilateral interaction. The results of numerical simulation were presented. It was shown that the unilateral interaction generates conditions for prevention of the resonant development of oscillations and can be considered as a means for active suppression of oscillations.