Coupled bending-torsional dynamic behavior of a cantilever beam carrying multiple point masses

In this study, we examine the coupled bending-torsional dynamic behavior of a cantilever beam carrying point masses along the span. The eigenfrequencies were found using the Extended Galerkin Method (EGM) and validated by the finite element analysis software ANSYS®. Mainly, two cases were investigated: (i) a beam carrying a moveable mass along the span and (ii) a beam carrying two masses (one stationary tip mass and one moving along the span). Free vibrational analysis was carried out to demonstrate the effect of the external masses and their location on the natural frequencies. The results were in perfect agreement with the finite element analysis. A coupled bending-torsional behavior is ensured using a kite-type beam cross section. A validation of the methodology to the literature is also present for the uncoupled dynamic behavior. Overall, the results presented in this paper indicate that the dynamical behavior of beams is highly dependent on the location and magnitude of the external mass. A natural frequency decrease was observed as the mass approached the tip of the beam. Moreover, the addition of a tip mass to such system was helpful for dynamic stability. From a practical point of view, this study will be useful in the design of engineering structures that carry external stores.