PROPAGATING WAVES AND END MODES IN PRETWISTED BEAMS

Abstract A method is presented for studying propagating waves and end modes in a uniformly pretwisted beam. The variationally derived equations of motion are based on three-dimensional elasticity and finite element modelling of the cross-section. This discretization procedure accommodates arbitrarily shaped cross-sections of inhomogeneous anisotropic material properties that follow the pretwist rotation rate. An harmonic solution form in both timetand axial co-ordinate ζ is introduced, i.e., exp {i(kζ−οt)}, resulting in a two parameter algebraic eigensystem. By specifying the axial wavenumberk, the eigenproblem permits real frequencies of propagating modes to be determined. By specifying real frequency ο, both real and complex axial wavenumbers can be extracted, where real values pertain to propagating modes and the complex ones to edge vibrations or end modes. Due to pretwist, the effect of extension, torsion and flexural are coupled. Examples of homogeneous, isotropic beams with rectangular and square cross-sections are given to illustrate the method of analysis and the physical behavior.