Vibration analysis of multi-supported curved panel using the periodic structure approach

This papers deals with the radial vibration of a row of cylindrical panels of finite length using the concept of wave propagation in periodic structures. For this study, the structure is considered as an assemblage of a number of identical cylindrically curved panels each of which will be referred to as a periodic element. For a given geometry dispersion curves of the propagation constant versus (non-dimensional) natural frequency have been drawn corresponding to the circumferential wave propagation. New conclusions that have emerged from this study are as follows. It is shown that by a proper choice of the periodic element the bounding frequencies and the corresponding modes in all the propagation bands can be determined. These have been shown to correspond to a single curved panel with all its edges simply supported. It is noted that there are no attenuation gaps in the entire frequency spectrum beyond the lowest bounding frequency. This is a unique feature of circumferential wave propagation around circular cylindrical shells and panels, as opposed to the wave propagation of periodically supported beams and rectangular panels without curvature. The natural frequency corresponding to every circumferential mode of the complete shell has been identified on the propagation constant curve. It has been observed that the natural frequencies of a cylindrically curved panel of a given curvature and length but of different circumferential arc length (corresponding to different angles subtended at the centre of any circular cross-section) may also be identified on the same propagation constant curve. Finally, it is shown that the same propagation constant curve may also be used to determine all the natural frequencies of a finite row of curved panels with the extreme edges simply supported. Wherever possible the numerical results have been compared with those obtained independently from finite element analysis and/or results available in the literature. Flutter analysis of multi-span curved panels using a wave approach is the ultimate objective of this work.