Determination of the variable density of the rod from natural frequencies of longitudinal vibrations

Abstract

Abstract Rods of various configurations are elements of many structures and machines. Therefore, the acoustic and vibration diagnostics of such parts has been widely developed. The paper considers the problem of determining the variable density of the rod from the natural frequencies of longitudinal vibrations. It is assumed that the density changes along the axis and is described by a polynomial function. This approach allows one to determine the law of density variation from a finite set of eigenvalues. The results of the study can find applications for finding hidden defects in steel and composite rods, which arise during the production process or due to corrosion.