On a Certain Property of the Natural Frequencies in the Lateral Vibration of a Beam Having a Circular Hole

Abstract

It is pointed out that the natural frequencies in the lateral vibration of a beam having a circular hole, irrespective of the modes and its support conditions, vary with the position of the hole. When the center of the hole is positioned near a point where the antinode of the normal mode would appear in the absence of a hole, the natural frequency assumes a local minimum. On the other hand, when the center of the hole is positioned near the inflectinoal point of the normal mode of the beam without a hole, the natural frequency assumes a local maximum. The natural frequencies were computed according to Rayleigh's method using the deflection curves obtained by modifying the normal functions for the beam without a hole, and the above mentioned property was verified analytically. The theoretical results were in good agreement with experimental results up to the first three natural frequencies.