Dynamic analysis of viscoelastic, anisotropic curved spatial rod systems

ABSTRACT Ph. D. THESIS DYNAMIC ANALYSIS OF VISCOELASTIC, ANISOTROPIC CURVED SPATIAL ROD SYSTEMS Faruk Fırat ÇALIM DEPARTMENT OF CIVIL ENGINEERING INSTITUTE OF NATURAL AND APPLIED SCIENCES UNIVERSITY OF ÇUKUROVA Supervisor : Assist. Prof. Dr. Beytullah TEMEL Year : 2003, Pages: 160 Jury : Assist. Prof. Dr. Beytullah TEMEL : Prof. Dr. A. Kamil TANRIKULU : Prof. Dr. Naki TÜTÜNCÜ : Assist. Prof. Dr. Hüseyin R. YERLİ : Assist. Prof. Dr. Ali Osman ATAHAN In this thesis, the dynamic behaviour of cylindrical helical rods made of isotropic, anisotropic and elastic, viscoelastic materials under time dependent loads is theoretically 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. Ordinary differential equations in scalar form obtained in the Laplace domain are solved numerically with the help of the complementary functions method to calculate the dynamic stiffness matrix of the problem. In the viscoelastic material case, with the help of elastic-viscoelastic anology, the material constants are replaced with their complex counterparts in the Laplace domain. In the solutions, Kelvin model is employed. The solutions obtained are transformed to the real space using the Durbin's numerical inverse Laplace transform method. The results obtained in this study are found to be in good agreement with those available in the literature and ANSYS. Keywords : Cylindrical Helical Rods, Viscoelastic Solids, Composite Materials, Inverse Laplace Transforms, Complementary Functions Method. II