The purpose of this study is to understand the main differences between deterministic and randorm response characteristics of a cantilever beam in the neighborhood of combination parametric resonance. The beam orientation with respect to the excitation is made in such a way that the bending and torsion modes are in cross coupling through the excitation. In the absence of excitation the two modes are also coupled due to nonlinear inertia forces. This measn that both linear generalized and normal coordinates are the same. For sinusoidal parametric excitation the beam experiences instability in the neighborhood of the combination parametric resonance #OMEGA# = #omega#_u + #omega#_o, where #OMEGA# is the excitation frequency, #omega#_u and #omega#_o are the bending and torsion first mode natural frequencies, respectively. The dependence of the response amplitude on the excitation level reveals three distinct regions which include linear behavior, jump phenomena, and energy transfer. Under random excitation, with center frequency close to the sum of the bending and torsion mode frequencies, the system may experience a single response, two possible responses or nonstationary responses depending on the excitation level. The response may also be Gaussian or non-Gaussian depending on the excitation level as well. Experimentally, it is possible to obtain two different responses for the same excitation level by providing some perturbation to the system.
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