UC San Diego

In this thesis, harmonic wave propagation in pre-twisted beams with arbitrary rate of uniform pre-twist was investigated utilizing the three-dimensional theory of elasto-dynamics expressed in the curvilinear coordinates. Harmonic wave propagation in the axial direction defines an eigen-value problem over the cross-section of the beam. By developing a finite element code to solve generalized eigenvalue problem, the eigenvalues and corresponding eigenmodes were computed to elucidate the effect of pre- twist on phase velocities and mode shapes. Lowest four modes which describe longitudinal, torsional, minor-axis bending and major-axis bending deformations were numerically investigated for two rectangular cross- sections with aspect ratios: 4:1 and 2:1 and an elliptic cross-section with aspect ratio of 5:1. The resulting phase velocity spectra are observed to be affected by the pre-twist and are valuable in the assessment of the accuracy of beam models used for dynamic analysis of pre- twisted beams. In addition, the resulting mode shapes consistently demonstrate the effect of pre-twist on the coupling of torsion-extension and the minor-major bending stiffnesses