Abstract: “The scope of this study is to investigate linear viscoelastic vibration response of conical and hyperboloidal helices having an elliptical hollow section. A mixed finite element formulation based on the Timoshenko beam theory is implemented, where the numerical analysis are performed in the Laplace domain. Noncylindrical helix geometry is spatially discretized by the finite elements where nodes are placed on the exact geometry. The curvatures are approximated by shape functions over each element. The material constants are replaced with their complex counterparts in the Laplace domain in accordance to the correspondence principle. For the step type loading, results from the solutions performed in the Laplace domain are transformed back to the time domain numerically by employing the Modified Durbin’s transformation procedure. Numerical results are presented as benchmark examples investigating the viscolelastic dynamic behavior of noncylindrical helices with elliptical hollow sections.”

Keywords: viscoelasticity, noncylindrical helix, mixed finite element method, free vibration, Laplace space