Abstract
This paper is concerned with qualitative properties of the natural frequencies and principal modes of some basic vibrating systems: the taut, non-uniform string; slender non-uniform rods in longitudinal and torsional vibration; the slender beam in flexural vibration; the circular membrane. These systems may be modelled by lumped-mass systems, finite elements, or by differential equations. The paper summarizes results on the distinctness of natural frequencies, interlacing of frequencies corresponding to different end conditions, nodal patterns for modes, etc. It also briefly describes research on the reconstruction of such systems from natural frequency or principal mode data.
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