Identification of the rod end fixing by natural frequencies of transverse vibration

Abstract

The acoustic diagnostics actively develops nowadays, it solves the problems of operational control of technical systems by natural frequencies. Scientists actively works on acoustic methods for detecting cracks, determining the shape and size of the object. Nevertheless, the acoustic method in diagnosing the state of fastening of rods and beams started to be applied not long ago. This article presents problem that determines the type of boundary condition at the right end of the rod from the natural frequencies of its vibrations. Transverse vibrations of the rod are also considered. It is assumed that the left end of the rod is clamped, and the right end of the rod is not available for visual inspection. At the right end of the rod, one of ten types of boundary conditions can be presented: clamped, fixed, free end, roller, five types of elastic fastening, and an inertial element at the end of the rod. The boundary conditions at the right end of the rod can be determined from three natural vibration frequencies. The advantage and novelty of this work is in the use of the minimum number of natural frequencies to solve the problem. The error of the result is also estimated. The identification of the boundary conditions by the natural frequencies of vibration of the rod is carried out in connection with the tasks of non-destructive diagnostics, as well as while creating vibration-proof and health-friendly technical systems.