Longitudinal and Transverse Coupling Dynamic Properties of a Timoshenko Beam with Mass Eccentricity

Non-uniform mass distribution on a beam will lead to the coupling between lateral and axial vibrations of the beam. To simulate the mass eccentricity, a double-layered Timoshenko beam model is developed. Based on Hamilton's principle, the coupled governing equations are derived and mass and stiffness coupling coeffcients are also derived. Moreover, the spectral element method (SEM), with high frequency accuracy by employing the dynamic shape functions, is utilized to study the dynamic properties of the beam. In addition, a corresponding finite element model is established to verify the SEM model. The coupling vibration characteristics are investigated and the coupling mechanism is revealed. Furthermore, the effects of mass non-uniformity on the free vibration and forced vibration of the beam with classical and flexible boundary conditions are analyzed. Finally, an optimal control method for reducing the contributions of bending modes under the axial excitation is presented with the results displayed.