Natural Frequencies and Mode Shapes of a Nonlinear, Uniform Cantilevered Beam

A series of experiments in 1975, referred to as the Princeton Beam Experiments, were performed to measure natural frequencies and create a nonlinear elastic deformationmodel to improve helicopter main beam designs. These experiments used a uniform, homogeneous 7075 aluminum beam and have been referenced as a baseline for the pastthirty years to validate computer models and theories in an effort to build beams capableof withstanding aero elastic, static, and dynamic loading.The purpose of this study is to measure the dynamic nonlinear bending andtorsion response of a cantilever beam. The natural frequencies are measured in theflatwise and edgewise directions at different static root pitch angles with varying levels oftip weights. The measured natural frequencies were compared to linear equations ofmotion, a nonlinear computer model and previous experiments to verify the nonlineareffects of root pitch angle and tip weights.The experiment produced promising results in that the first mode in the edgewiseand flatwise directions were within the error bands of the Princeton Beam Experiment forall weights and that the linear model matched the experimental case with no tip weights.Further experimentation is needed in order to properly calculate the edgewise frequenciesand estimate mode shapes.

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