Influence of beam butt face nonparallelism on free damped vibration spectrum of the beam

Abstract

Introduction. The free vibration method is widely applied to detecting internal defects in rod and lamellar structural elements. In this work, it is used to diagnose a rod sample defect consisting in nonparallelism of the rod ends. The possibility of identifying a defect in the form of a bevel of one of the rod butts by the frequency spectrum of free damped longitudinal and transverse vibration after impact actions to the rod side or butt face is considered. Materials and methods. An experimental facility and a method of contact-free recording of the frequency spectrum of the rod natural vibration by its acoustic radiation spectrum are presented. Signs of a defect in the form of a split frequency of the rod transverse vibration are detected. At the same time, the maximum amplitudes of the split frequencies correspond to higher or lower frequencies depending on the face to which the impact is applied. This allows not only determining the presence of a defect in the form of the bevelled butt face, but also establishing its orientation relative to the side rod faces. Results. An approximate theoretical model is suggested. It explains the effect of frequency splitting in the presence of nonparallelism of the rod butts. For this, the frequency spectra of transverse vibration of two rods with lengths equal to the lengths of the smaller and the larger faces of the original rod with the bevel edge are considered. Experiments show that the differences in the natural frequencies of the bending vibration of these rods, which correspond to the same eigenmodes, are consistent with the differences in the split frequencies of the free damped transverse vibrations of the bevelled-face rod. At this, relationship between the split frequency amplitudes allows determining not only the presence of bevelled face, but also its location. Conclusions. The application and development of the method through the analysis of the natural vibration spectrum can lead to creation of remote quality control equipment for rod structural elements.