IDENTIFICATION OF THE LENGTH OF THE LONGITUDINAL NOTCH OF THE ROD BY THE NATURAL FREQUENCIES OF BENDING VIBRATIONS

Abstract

Разработанный метод позволяет решить задачу идентификации геометрических параметров различных деталей и конструкций, моделируемых стержнями. Objectives of the work: to consider the direct and inverse problem of vibration of a rectangular rod with a longitudinal notch; to study the patterns of behavior of natural frequencies of bending vibrations when changing the location and size of the notch; to develop a method that makes it possible to uniquely identify the parameters of a longitudinal notch using the natural frequencies of the bending vibrations of the rod. A bar with a longitudinal notch is modeled as two bars, where the first one does not have a notch, and the second one does. For connection, conjugation conditions are used, in which bending vibrations and deformations are equated. The solution of the inverse problem is based on the construction of a frequency equation under the assumption that the desired parameters are included in the equation. By substituting natural frequencies into this equation, we obtain a nonlinear system with respect to unknown parameters. The solution of the latter is the desired notch parameters. Results. Tables of natural frequencies for different parameters of the notch start point are given. Graphs of dependence of natural frequencies on notch parameters are constructed. A method for identifying notch parameters by a finite number of natural frequencies is presented. It is shown that the inverse problem has an exact solution. For an unambiguous solution, one natural frequency is sufficient. The developed method allows to solve the problem of identification of geometric parameters of various parts and structures modeled by rods.