The eigenfrequencies and shapes of longitudinal vibrations of rods that have defects of various kinds (inertial, geometric, stiffness, etc.) are studied with the aim of detecting these defects. This study is based on the direct Sturm-Liouville problem and an accelerated convergence method for obtaining a high-accuracy solution to it. Numerous computational (numerical- analytical) and physical experiments are analyzed for defects of various types, places of their localization, and vibration modes. On the basis of this analysis, an effective criterion for detecting a damaged state was introduced. Qualitative features of the defects and the possibilities for identifying them on the basis of solving the inverse problem were established. It was shown that the vibrations become substantially more complex for several defects. The solution of the inverse problem by means of conventional methods is complicated
|
