NONLINEAR RESONANCES IN A FLEXIBLE CANTILEVER BEAM

An experimental investigation into the response of a nonlinear continu ous systems with many natural frequencies in the range of interest is presented. The system is a flexible cantilever beam whose first four n atural frequencies are 0.65 Hz, 5.65 Hz, 16.19 Hz, and 31.91 Hz, respe ctively. The four natural frequencies correspond to the first four fle xural modes. The fourth natural frequency is about fifty times the fir st natural frequency. Three cases were considered with this beam. For the first case, the beam was excited with a periodic base motion along its axis. The excitation frequency f(e) was near twice the third natu ral frequency f3, which for a uniform isotropic beam corresponds to ap proximately the fourth natural frequency f4. Thus the third mode was e xcited by a principal parametric resonance (i.e., f(e) almost-equal-to 2f3) and the fourth mode was excited by an external resonance (i.e., f(e) almost-equal-to f4) due to a slight curvature in the beam. Modal interactions were observed involving the first, third, and fourth mode s. For the second case, the beam was excited with a band-limited rando m base motion transverse to the axis of the beam. The first and second modes were excited through nonlinear interactions. For the third case , the beam was excited with a base excitation along the axis of the be am at 138 Hz. The corresponding response was dominated by the second m ode. The tools used to analyze the motions include Fourier spectra, Po incare sections, and dimension calculations.