Vibration of a Long, Tip Pulled Deflected Beam

摘要

The static baseline curve of the deflected beam is calculated from the proposed polynomial approximation of the nonlinear relation between the force application angle and cable length. Comparison between the approximated results and the exact deformation solution shows a good agreement between the two strategies. A low-order finite element mesh is superimposed to the deflected baseline of the beam to yield a useful dynamic model of the system. When the beam is subject to small pulling forces and deformations, the polynomial approximation strategy does not yield an accurate representation of the beam's static deflection, as seen in Figs, 4 and 5. However, the eigenfrequency results displayed in Figs. 6 and 7 show that, in spite of the differences in the prediction of the beam's static deformed configuration, the dynamic behavior results are always in good agreement between the exact and approximated solutions. The comparison of results indicate that the strategy of obtaining an approximated analytical expression for the baseline static deformation of the beam, followed by adaptation of a model of low-order finite elements, is an efficient way to obtain a fast and convenient dynamic description of the structure.