Forced vibration of cylindrical helical rods subjected to impulsive loads

In this study, the forced vibration of cylindrical helical rods subjected to impulsive loads is theoretically investigated in the Laplace domain. The free vibration is then taken into account as a special case of forced vibration. The governing equations for naturally twisted and curved space rods obtained using Timoshenko beam theory are rewritten for cylindrical helical rods. The material of the rod is assumed to be homogeneous, linear elastic, and isotropic. The axial and shear deformations are also taken into account in the formulation. Ordinary differential equations in scalar form obtained in the Laplace domain are solved numerically using the complementary functions method to calculate exactly the dynamic stiffness matrix of the problem. The desired accuracy is obtained by taking only a few elements. The solutions obtained are transformed to the real space using the Durbin's numerical inverse Laplace transform method. The free and forced vibrations of cylindrical helical rods are analyzed through various example. The results obtained in this study are found to be in a good agreement with those available in the literature

Quasi-static and dynamic response of viscoelastic helical rods

In this study, the dynamic behaviour of cylindrical helical rods made of linear viscoelastic materials are investigated in the Laplace domain. The governing equations for naturally twisted and curved spatial rods obtained using the Timoshenko beam theory are rewritten for cylindrical helical rods. The curvature of the rod axis, effect of rotary inertia, and shear and axial deformations are considered in the formulation. The material of the rod is assumed to be homogeneous, isotropic and linear viscoelastic. In the viscoelastic material case, according to the correspondence principle, the material constants are replaced with their complex counterparts in the Laplace domain. Ordinary differential equations in scalar form obtained in the Laplace domain are solved numerically using the complementary functions method to calculate the dynamic stiffness matrix of the problem. In the solutions, the Kelvin model is employed. The solutions obtained are transformed to the real space using the Durbin's numerical inverse Laplace transform method. Numerical results for quasi-static and dynamic response of viscoelastic models are presented in the form of graphics. © 2003 Elsevier Ltd. All rights reserved

Forced vibration of composite cylindrical helical rods

The dynamic behavior of composite cylindrical helical rods subjected to time-dependent loads is theoretically investigated in the Laplace domain. The governing equations for naturally twisted and curved spatial laminated rods obtained using Timoshenko beam theory are rewritten for cylindrical helical rods. The curvature of the rod axis, the anisotropy of the rod material, effect of the rotary inertia, axial and shear deformations are considered in the formulations. The material of the rod is assumed to be homogeneous, linear elastic and anisotropic. Ordinary differential equations in scalar form obtained in the Laplace domain are solved numerically using the complementary functions method to calculate the dynamic stiffness matrix of the problem accurately. The solutions obtained are transformed to the time domain using an appropriate numerical inverse Laplace transform method. The free vibration is then taken into account as a special case of forced vibration. The results obtained in this study are found to be in a good agreement with those available in the literature. © 2005 Elsevier Ltd. All rights reserved

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

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 Durbins 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. © 2014 Elsevier Ltd.36130 National Council for Scientific Research: 111M308This research is supported by the Scientific and Technological Research Council of Turkey under Project no. 111M308 and by the Research Foundation of ITU under Project no. 36130 . These supports are gratefully acknowledged by the authors