Large-Amplitude Vibrations of a Slender Cantilevered Beam

We present a geometrically exact beam model for a cantilevered beam undergoing large-amplitude motions, motivated by recent wind-energy capture systems that exploit vortex-induced vibrations. The derivation of this model leads to a single nonlinear 2nd-order ordinary differential equation that appears similar to a Duffing oscillator with additional nonlinear acceleration terms. For prismatic configurations, the formulation is characterized by its linear natural frequency and a normalization constant of the shape-function. A brief parametric study is conducted to demonstrate the softening effects of the nonlinear acceleration terms. Continuation methods are used to construct the amplitude versus forcing frequency plots to capture the nonlinear response.