Abstract
The object of this investigation was to examine an assumption, commonly used when analysing the coupled vibrations of asymmetric turbine blades and structural members, that the specimen cross-section displacements can be represented by a translation of, and a rotation about, the centre-of-flexure. The specimen examined comprised a cantilever with monosymmetric, thin-walled section of circular arc open profile. By applying a theory of Argyris, which considered the higher order effects of specimen mid-wall shear strain contributions due to non-uniform warping, it was evident that the specimen need not rotate about its centre-of-flexure when subject to torsion moments due to inertia effects during torsional vibration. This led to a comparison being made between two coupled vibration theories. A lower order theory of Gere & Lin and a higher order theory of Tso which was similar to that of Argyris. The differential equations of motion of both theories were solved numerically using a transformation technique and a finite difference method to determine the first: three coupled normal mode frequencies and shapes. The mode frequencies were compared with experimental results while the theoretical modal shapes were used to establish centre-of-rotation axes for each mode, The results indicated that the centre-of-rotation axis did not always coincide with the centre-of-flexure axis but diverged from it in regions of non-uniform warping along the specimen. However, it is not desirable to utilise this curved reference axis in an analysis and it was concluded that a centre-of-flexure axis be taken as the reference axis, providing, the true displacements relative to that axis are known. This is achieved by utilising a higher order theory which takes into account the specimen mid-wall shear strain contributions during non-uniform warping.