Coupled bending-bending vibrations of pre-twisted cantilever blading allowing for shear deflection and rotary inertia by the Reissner method

Finite element model for vibration analysis of pre-twisted Timoshenko beam

“…The second example is concerned with a cantilever pre-twisted beam treated experimentally by Carnegie [2] and by theoretical means by Lin et al [11] and Subrahmanyam et al [7]. The properties of the beam are given in Table 2.…”

“…The properties of the beam are given in Table 2. Although it is well known that shear coefficient depends on the geometry of the cross-section, it is taken the same as in the related references [2,7,11] for comparison purposes. To show efficiency and convergence of the proposed model, the first four frequencies of the second example are calculated.…”

The Forced Vibration and Boundary Control of Pretwisted Timoshenko Beams With General Time Dependent Elastic Boundary Conditions

“…Gupta and Rao [21] and Abbas [22] used the "nite element method to determine the natural frequencies of uniformly pretwisted tapered cantilever blading. Subrahmanyam et al [23] and Subrahmanyam and Rao [24] used the "nite element method and the Reissner method to determine the natural frequencies of uniformly pretwisted tapered cantilever blading respectively. Celep and Turhan [25] used the Galerkin method to investigate the in#uence of non-uniform pretwisting on the natural frequencies of uniform cross-sectional cantilever or simply supported beams.…”

On the vibration and stability of spinning axially loaded pre-twisted Timoshenko beams

“…In comparison with results between linearly and nonlinearly pre-twisted beams, the deviations increased as increasing pretwist angle. By treating the blade as a pre-twisted Timoshenko beam, the vibration equations of motion of the pre-twisted blade were developed using different techniques [6][7][8][9][10][11][12][13] to study the effects of geometric aspects, rotary inertia and shear deformation on the lateral frequencies of the blade. The variational method was utilized by Carnegie [6] to derive the bending-bending-torsion equations of motion for a pre-twisted cantilever blade allowing for the shear deformation and rotary inertia effects.…”