https://users.monash.edu.au/~lyeo/Dr_Leslie_Yeo/Publications_files/sdarticle_3.pdf

The axial–torsional vibration of pretwisted beams

The application of a Dynamic Finite Element (DFE) technique to the extensional-torsional free vibration analysis of nonuniform composite beams, in the absence of flexural coupling, is presented. The proposed method is a fusion of the Galerkin weighted residual formulation and the Dynamic Stiffness Matrix (DSM) method, where the basis functions of approximation space are assumed to be the closed form solutions of the differential equations governing uncoupled extensional and torsional vibrations of the beam. The use of resulting dynamic trigonometric interpolation (shape) functions leads to a frequency dependent stiffness matrix, representing both mass and stiffness properties of the beam element. Assembly of the element matrices and the application of the boundary conditions then leads to a frequency dependent nonlinear eigenproblem, which is solved to evaluate the system natural frequencies and modes. Two illustrative examples of uniform and tapered cantilevered, Circumferentially Uniform Stiffness (CUS), hollow, composite beams are presented. The influence of ply fibre-angle on the natural frequencies is also studied. The correctness of the theory and the superiority of the proposed DFE over the contrasting DSM and conventional FEM methods are confirmed by the published results and numerical checks. The discussion of results is followed by some concluding remarks.

Dynamic Finite Element Analysis of Extensional-Torsional Coupled Vibration in Nonuniform Composite Beams

This chapter focuses on wind power generation, the components of a typical horizontal axis wind turbine, basics of wind power generation, the wind field, its characteristics and spectrum as well as the dynamics and aeroelasticity of the rotor and the tower and the dynamics and hydrodynamics of the floater and the supporting structure.

Wind Power Generation and Control

A new design for hybrid axial-torsional transducers using pretwisted beams requires the resonance frequencies of the torsional and axial vibration modes to be matched. To aid in designing such transducers, the effects of increasing pretwist and changing the cross-section geometry on the resonance frequencies are investigated analytically. The governing equations and boundary conditions for extension, torsion, and cross-sectional warping are derived using the semi-inverse method and Hamilton's principle. A general set of differential equations for the cross-sectional warping of pretwisted beams is derived. Through scaling, the warping function is shown to be locally similar to the Saint-Venant warping function when the beam is slender, low in pretwist, and torsional deformation is dominant. Using this approach, geometric and material limitations in the use of the Saint-Venant's warping function are illustrated, beyond which the simpler form may no longer be used. The simplified equations of motion are solved under the free-free boundary condition for resonance frequencies and mode shapes, and a comparison with finite element analysis illustrates the limitations

Vibration analysis of pretwisted beams for the design of hybrid axial-torsional transducers

In a previous paper concerning the determination of angular frequencies of a twisted straigth bar of constant section, only three simple constraint conditions at the ends had been considered (free end, constrained end). In the present paper the other seven possible (asymmetric) constraint conditions are considered and the corresponding frequency equations are found. A final numerical example with several increasing twisting degrees shows the different influence of this increase upon the frequencies having axial or torsional origin.

Longitudinal vibrations of pre-twisted bars with “asymmetric” boundary conditions

The present paper deals with the calculation of natural frequencies in a pre-twisted solid with constant cross-section.

A. Risitano

Papers

Coupled free, torsional and axial vibration of pre-twisted bars