MODEL OF MECHANISM OF CONVERSION OF EXTERNAL ACTION INTO NATURAL OSCILLATIONS

Abstract

The work presents a geometrical interpretation of a mathematical model intended to give a specific description of the process of conversion of external dynamic action into natural oscillations of a part. Besides geometrical constructions, the essence of the model stems from the strict logic as well, following which the model does not have a tangible embodiment. Nonetheless, it is a function space, in which the process is being generated and energy of natural oscillations is getting accumulated, i.e. the model is an non-material carrier of free energy of elastic oscillations. Material carrier is the very part. The model is represented as the Riemannian space, in which all dynamic parameters are constant and set to zero, therefore, on the one side, it appears as if it does not have any tangible embodiment. On the other side, by nature, the model is a necessary expansion of the function space, which, on the qualitative level, allows to obtain explanation of a number of processes, which are observed experimentally, but to this day were not provided with a specific substantiation from a physics perspective. The proposed model can be an effective tool for analysis of processes, occurring in the course of non-destructive testing and vibration-based diagnostics. For example, the Article presents a theoretical justification of the process of modelling of cracks in the non-destructive testing methods, using natural oscillations of the item being checked. On top of that, it gives a derivation of the formula determining amount of the crack detected through these methods.