Abstract
In this paper, the effect of shear deformation is considered into flexural deflection of the geometrically nonlinear deformation of a flexible beam. Then, considering the coupling effect of deformation in to the extensional and flexural deflection, the second-order coupling terms of deformation in two displacement fields are developed and the axial inertial force and transverse distributed force are considered. The finite element method is used for the system discretization and the coupling dynamic equations of flexible beam are obtained by Lagrange’s equations. In this way, the new governing differential equations of the beam in the geometrically non-linear kinematics of deformation are derived. Numerical examples of a flexible beam are studied to analyze the effect of shear deformation on the dynamic character and to investigate the coupling effect. Furthermore, from this present method, a moving Timoshenko beam can also produce the dynamic stiffening phenomenon and some new properties can be shown.
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