关键词: 振动与波, 薄壁Timoshenko梁, 翘曲刚度, 弯扭耦合振动, 动态有限元法

Abstract:

The dynamic stiffness matrix for a uniform and straight thinwalled Timoshenko beam element is derived by directly solving the governing differential equations of coupled bendingtorsional vibration of beam element. The effects of bendingtorsion coupling, warping stiffness, shear deformation and rotary inertia are taken into account in the present formulations. An illustrative example on the application of the dynamic finite element method is given for a bendingtorsion coupled channel section thinwalled beam In order to obtain the natural frequencies and normal modes, the automated Muller root search method and the bisection method ombined with frequency sweep method are used to solve the frequency characteristics equation. The effects of warping stiffness, shear deformation and rotary inertia on the natural frequencies and mode shapes of the particular thinwalled beam are discussed. Numerical results demonstrate the accuracy and effectiveness of the proposed method and show the warping stiffness, shear deformation and rotary inertia can change the natural frequencies and mode shapes of the open thinwalled beam substantially.

Key words: vibration and wave, thinwalled Timoshenko beam, warping stiffness, bendingtorsion coupled vibration, dynamic finite element method