Theoretical Foundations for Modeling Elastic Interaction Modes of Elements of Vibration Technological Machines Taking into Account Unilateral Ties

A systematic approach is being developed to assess, form and correct the dynamic states of technical objects under vibration loading conditions, taking into account unilateral connections. The problem of constructing periodic modes of elastic interactions of elements of mechanical oscillatory systems with a vibrating surface is considered. Methods of the theory of oscillations, Laplace integral transforms, and the theory of functions of a complex variable are used. Within the framework of operational calculus, ideas are developed about the conditions for realizing the separation of a mass-inertial element from the vibration surface based on a generalized gap function. A theorem on necessary and sufficient conditions for breaking contact is proved using the concept of separation order. Analytical conditions are formulated to characterize the multiple tossing regimes taking into account elastic interactions. Forms of movements with continuous tossing are constructed in analytical form. The role of the frequency ratio in the formation of the characteristics of the gap between the mass-inertial element of the system and the vibrating surface is determined. Asymptotic estimates of the characteristics of modes with multiple tossing are constructed depending on the frequency and amplitude dimensionless parameters. The results of computational experiments are presented.