Nihal Eratli

Parametric analysis of viscoelastic hyperboloidal helical rod

The objective of this study is to perform a pioneering research about a viscoelastic hyperboloidal helical rod having a standard type of distortional behavior and a Kelvin type of bulk compressibility. Field equations are based on the Timoshenko beam theory, and the exact curvatures of the hyperboloidal geometry are considered through the formulation. The numerical analysis is carried out by the mixed finite element method, considering the rotary inertia, in the Laplace space, and the results are transformed back to time space numerically using the modified Durbin’s algorithm. A cantilevered hyperboloidal helical rod having solid circular, hollow circular, and thin-walled hollow circular cross sections is handled, and the rod is loaded by rectangular and triangular impulsive types of point load at the tip. Through the analysis, different values of retardation time, three different relaxation functions associated with shear modulus, and three different creep functions associated with bulk modulus are handled. Finally, a benchmark example is presented, and the influence of the loading and the material parameters on the helix geometry is discussed.

The influence of the rotary inertia on the dynamic behavior of viscoelastic non-cylindrical helicoidal bars

The objective of this study is to investigate the influence of the rotary inertia on the dynamic behavior of linear viscoelastic non-cylindrical helicoidal bars due to variation of the active turns. Dynamic analysis is performed in the Laplace space by using the mixed finite element method. The standard model is used for defining the viscoelastic material behavior and by using the correspondence principle, the material constants are replaced with their complex counterparts in the Laplace space. The solution under the rectangular impulsive type loading is carried out in the Laplace space and then the results are transformed back to time domain numerically by the Modified Durbin’s transformation algorithm. Some original numerical results for the dynamic behavior of linear viscoelastic non-cylindrical helices with rectangular cross-section are presented.