Dynamic analysis of linear viscoelastic cylindrical and conical helicoidal rods using the mixed FEM

• The rotary inertia is more prominent as thickness to width ratio increase.
• Inclusion of rotary inertia is more pronounced in the free vibration zone.
• The retardation time inversely proportional with the influence of rotary inertia.
• As the retardation time increase, stress resultants and displacements decrease.
• As the taper ratio of conical helix increases, the displacements increase.

The objective of this study is to investigate the influence of the rotary inertia on dynamic behavior of linear viscoelastic cylindrical and conical helixes by means of the Laplace transform-mixed finite element formulation and solution. The element matrix is based on the Timoshenko beam theory. The influence of rotary inertias is considered in the dynamic analysis, which is original in the literature. Rectangular, sine and step type of impulsive loads are applied on helices having rectangular cross-sections with various aspect ratios. The Kelvin and standard models are used for defining the linear viscoelastic material behavior; and by means of the correspondence principle (the elastic-viscoelastic analogy), the material parameters are replaced with their complex counterparts in the Laplace domain. The analysis is carried out in the Laplace domain and the results are transformed back to time space numerically by modified Durbin׳s algorithm. First, the solution algorithm is verified using the existing open sources in the literature and afterwards some benchmark examples such as conical viscoelastic rods are handled.