Waves in pretwisted rods of arbitrary cross sections

A semi-analytical method is presented for studying the natural vibrations and waves in pretwisted rods. The analysis is based on three-dimensional elasticity using a non-orthogonal curvilinear coordinate system that rotates with the cross section. The cross section is modeled using finite elements to enable the analysis of arbitrary geometries, and material inhomogeneities including anisotropy. While the behavior in the long direction of the rod is modeled analytically using a complex exponential function. This allows for the analysis of either propagating (sinusoidal) or decaying (exponential) waves. If the center of rotation and the origin of the coordinate system coincide allowing for pretwist about any point in or out of the cross section. The equations of motion take into account both the in-plane and warping of the cross section. Specifying the solution in a harmonic wave form leads to an eigensystem from which the natural frequencies, mode shapes and stress distribution can be obtained. By specifying the solution in an exponential decay form the resulting eigensystem yields the inverse characteristic decay lengths. For bending behavior along the whole length of the beam/rod the rate of pretwist (α) has to be included in the solution form. For local bending extensional or torsional deformations including the pretwist term is not required. The method agrees with solutions of cases without pretwist when the angle of pretwist is set to zero and the method also agrees with the solution of a circular rod with or without pretwist. With a non-zero pretwist rate specified the method shows coupling of bending about both axis (for symmetric cross sections) and the extension-torsion coupling behavior found in pretwisted rods. The elastic behavior of both propagating and decaying waves are studied.