Authors : E. Ghandi and A. Ali Akbari Rasa
Abstract: The objective of the present study is to analyze dynamic response of the Timoshenko thin-walled beam with coupled bending and torsional vibrations under deterministic loads. The governing differential equations is obtained by using Hamilton’s principle. The Timoshenko beam theory is employed and the effects of shear deformations, rotary inertia and warping stiffness are included in the present formulations. Dynamic features of underlined beam are obtained using free vibration analysis. For this purpose, the dynamic stiffness matrix method is used. Applying exact dynamic stiffness matrix method on the movement differential equations leads to the issue of nonlinear eigenvalue problem that Wittrick-Williams algorithm is used to solve it. Orthogonality property of vibrational modes are extracted by applying differential equations of motion. The theoretical expressions for the displacement response of thin-walled beams subjected to concentrated or distributed loads are presented. The numerical results for dynamic flexural displacements, rotational displacements and torsional displacements are given. The proposed theory is fairly general and can be used for thin-walled beam assemblage of arbitrary boundary conditions subjected to various kinds of deterministic loads.
E. Ghandi and A. Ali Akbari Rasa, 2017. Analytical Investigation of the Dynamic Response of a Timoshenko Thin-Walled Beam with Asymmetric Cross Section under Deterministic Loads. Journal of Engineering and Applied Sciences, 12: 8066-8076.