Spectral finite element of a helix

Determination of a spectral (i.e. frequency dependent) finite element of a helix is the focus of this communication. The helix is treated as straight, linear elastic element, exhibiting coupling of axial with torsional responses. We derive explicit forms of all the coefficients of the stiffness matrix and plot their dependencies on the frequency and the parameter describing the said coupling. In general, the growth of that parameter leads to a progressively denser occurrence of the resonances of both axial and torsional motions.