Modal Characteristics of Swept Cantilevered Plates

The aim of this paper is to produce modal data which can be used to synthesise assumed shapes for use in Rayleigh-Ritz approximations of the free vibrations of cantilevered swept plates. The modal data is generated via the use of the FEA technique to predict the natural frequencies and mode shapes of aluminium alloy plates of aspect ratio 2.0 and of swept angles varying from 0° to 20° in steps of 2°. The first fifty natural frequencies and mode shapes of swept cantilevered plates were calculated using ABAQUS FE programme which includes the ABAQUS/CAE pre-and post-processor. To classify each mode shape, the number of nodal lines i along the x-axis and the number of nodal lines j along the y-axis were defined. This definition worked fine for uniform rectangular plates of zero swept angles and also for the first few modes of the swept plates. But as the number of modes of the swept plates increased, this definition became difficult to apply. Similar mode shapes of the various swept angles were put into families and groups headed by the i and j definition of the uniform rectangular plate design. From this modal data, frequency charts, which showed the variation of the dimensionless natural frequencies of the swept plates with swept angle, were constructed. These charts can be used to deduce the types of modes of vibration, whether bending or torsion, of a vibrating swept plate and to synthesis accurately the assumed shapes for use in the prediction of the vibration characteristics of swept plates using the Rayleigh-Ritz approach.