Exact Parametric Study Giving Insight into Dome Vibrations

Abstract

A parametric study is presented of the undamped free vibration of a one layer truss type circular dome, with terrestrial proportions. The dome is composed of 36 identical portions, but is supported at only 4, 6, 9, 12, 18 or 36 uniformly spaced points. Only one of the 36 portions is needed in the analysis, using the large space frame computer program BUNVIS-RG, which can analyse linearly repetitive or rotationally periodic structures ‘exactly’, e.g. without the usual finite element discretisation approximations. The study includes changing: the height to diameter ratio; the number of supports; the type of supports; and the type of joint from rigid to pinned connections. In addition, modal densities are found for a near optimum dome. The method used gives valuable insights into the exact mode shapes by showing that they are always composed entirely of a (usually short) finite series of circumferential sine waves.

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