Simulation Model of Propagation of Vibrations in a System of Connected Bodies for the Solution of Problems of Vibration Diagnostics

Abstract

An approach to the construction of a mathematical model of the process of propagation of acoustic vibrations in equipment that is in the form of a system of connected bodies is considered. The proposed structure of the mathematical model is implemented as a graph whose edges are links between the elements of a system of connected bodies formalized by nonhomogeneous wave equations that take into account dissipative losses. Through the use of the mathematical model together with the introduction of sources of an external disturbance in any node of the graph, it becomes possible to describe a variation in the vibration signal at a contact point, estimate its properties, and select on a well-defined basis the point of attachment of the vibration signal sensor. The mathematical model is tested to assure it corresponds qualitatively to the actual processes in the propagation of vibration signals by means of test disturbances, and it is shown that it may be used to evaluate the selection of the points of attachment of the vibration signal sensors in problems of vibration diagnostics of equipment.