Unilateral Constraints in Interactions of System Elements: Estimation of Dynamic Constraint Reactions

Abstract

The article considers the features of dynamic interactions of compound solid bodies in the structure of mechanical oscillatory systems at periodical external disturbances. The purpose of research is to develop a method of mathematical model building that could provide an estimation of dynamic conditions of compound solid bodies with unilateral constraints in contacts. The paper uses the approaches of structural mathematical modeling, within which a structural diagram of a dynamically equivalent automatic control system is compared with the design scheme of a technical object in the form of a mechanical oscillatory system. The authors propose and develop a technology of identification of static and dynamic reactions at specific connection points of system elements. The system transfer functions are used to identify constraint reactions. The paper studies possible cases of the system loading at kinematical disturbances from the side of the bearing surface. Analytical ratios for critical or limiting conditions are offered. The possible causes of external vibration loadings, as well as at simultaneous action of two external disturbances, are considered. The concept of receipt of limiting conditions is formed. The parameters of these conditions are identified by the conditions of external disturbances and the introduction of additional constraints.