Vibration of Multi-span Thin Walled Beam Due to Torque and Bending Moment

Abstract

In this paper, the flexural torsional vibration of a thin walled beam due to combined action of bending moment and torque has been analyzed to calculate the natural frequencies and corresponding eigenvectors under different combination of bending moment and torque. The aim is to account the effect of intermediate support on the dynamic behavior of beam compared to single span beam. Also, the interaction formula has been derived for axial force, bending moment and torque for single span and multiple span beams. In the case of lateral buckling of beams, the critical bending moment is inversely proportional to length, which is the condition of zero natural frequency. Therefore, the lowering of natural frequency due to increased length is expected. However, the effect of length on the ratio of torsional and flexural component of vibration is not so obvious in spite of the fact that a phenomenon of flexural torsional vibration is important in long span beam only. The calculation shows that as the length increases, given the bending moment, the torsional component increases as the length increases. This fact is important in case of long span bridges to show that in-plane flexural vibration will trigger the flexural torsional vibration. The problem of multi-span beam is also important in hydropower plants where due to large length of turbo generator shaft, to control the lateral vibration of shaft several intermediate guide bearings are provided to latterly support the shaft. This is a case of multi-span shaft with lateral constraint but torsionally unrestrained at intermediate support. The impact of intermediate support on the on the torsional component of flexural torsional vibration may warrant the consideration of flexural torsional vibration in the design of intermediate support.