Natural flexural waves and the normal modes of periodically-supported beams and plates

Abstract

The free vibration of beams and plates over supports at regular intervals has been analysed using the knowledge of natural flexural waves and the associated propagation constants. It has been shown that the conditions at the extreme ends of a finite, periodic structure, permit only certain discrete values of the propagation constant. These, in turn, dictate the distribution of natural frequencies in the frequency spectrum. The whole analysis, when compared to the conventional methods, simplifies the problem of determination of natural frequencies of such structures. In addition, it gives a better physical understanding of the phenomenon involved, and a simple graphical method of determination of natural frequencies of periodically-supported beams and plates.