QUALITATIVE PROPERTIES OF FREQUENCY SPECTRUM AND MODES OF ARBITRARY SUPPORTED BEAMS IN VIBRATION

Some important qualitative properties of the frequency spectra and modes for Euler beams with arbitrary supports are determined. The case of supports free-pinned, free-sliding, free-free and sliding-slinding are considered, the rigid-body modes occur for beams with such supports. In addition, the sufficient and necessary conditions of a mode of the beams are obtained.