About the continuous spectrum of vibrations of beam construction elements under high-frequency effects

In this paper the high-frequency vibrations of beam structural elements on the example of cantilever rod are analyzed. The purpose of this article is to show the existence of the boundary frequency, above which the structure behaves as a system with a continuous spectrum, on elementary examples and to demonstrate the possibility of using this fact during engineering calculations performing. With the help of mathematical transformations and numerical experiments the existence of simple beam structures mixed spectrum, formed by the discrete and continuous parts, is shown. It is also shown that there is a boundary frequency that separates the portions of the spectrum and determines the upper frequency limit of the external effects, for which it is necessary to conduct dynamic account of structures. In this case the amplitude of the vibrations with a frequency exceeding the boundary one does not depend on the dynamic characteristics of the rod, but it is mostly determined by the static characteristics of the rod and the load.