Collective and localized modes of mono-coupled multi-span beams with large deterministic disorders

Abstract

Natural frequencies of two-span beams have been studied in the presence of different amounts of deterministic disorder (mistuning) arising from displacement of the intermediate simple support (prop) to different locations away from its tuned (periodic) position. The two beam-segments are assumed to be fully (strongly) coupled in the absence of any torsional constraint offered by the prop. Conditions under which the beam systems with different end conditions and support locations have the same natural frequencies have been identified and explained. Unlike the tuned multi-span beams, the natural frequencies of disordered beams with extreme ends simply supported and clamped have been found to coincide even when they do not belong to the same group(s) of natural frequencies. The deflection mode shapes and the phenomenon of normal mode localization have been presented and discussed for some specific prop locations. Conditions have been identified under which the disordered beams can behave as ordered (tuned, periodic) beams and their normal modes become perfectly collective with peak deflections exactly the same in both spans. Normal modes of fully coupled multi-span beams can become and appear to be strongly localized only if they are strongly disordered. Just as in the case of periodic beams, study of natural modes of two-span disordered beams is also helpful in understanding the natural modes of disordered beams having more than two spans.