Coupled Axial-Torsional Vibration of Thin-Walled Z-Section Beam

The coupled axial-torsional vibration of thin-walled Zsection beam induced by the boundary conditions is considered. The restrained axial displacement of the pin end at centroid of Z-section of a thin-walled beam causes the coupling of the axial and torsional vibration. The bending vibration is not dealt with in this paper, because it is uncoupled from axial and torsional vibration. The object of this paper is to investigate thecoupled axial and torsional vibration of thin-walled Zsection beam induced by the different boundary conditions. The correct governing differential equations for linear axial and torsional vibration of a uniform Zsection beam are derived using the d’Alembert and virtual work principles based on the Vlasov thin-walled theory. Numerical examples are studied to verify the accuracy of the proposed method and to consider the effect of boundary conditions and the value of warping function at centroid of the coupled axial and torsional natural frequency of Z-section beam. It is shown the lowest 10 natural frequency and shape modes in this section and a solving of problem using FEM for a case of boundary condition to verify the method.

کلیدواژه ها:

thin-walled beam ، natural frequency ، axialtorsionalvibration