Nonlinear parametric amplification and attenuation in a base-excited cantilever beam

This work investigates the nonlinear behavior of a representative parametrically amplified macroscale structure. Specifically, the effort examines the effects of structural and inertial nonlinearities on the near-resonant response of a base-excited, flexible cantilever beam driven by a combined (simultaneously parametric and direct) excitation. The prototypical structure is modeled using classical energy methods and key response metrics are analyzed through the use of the method of averaging. A series of experimental investigations are performed to validate analytically predicted behaviors. The work demonstrates that with the proper selection of various system parameters, both vibration amplification and attenuation can be efficiently achieved. This work provides a baseline understanding of the effect of nonlinearities on parametrically excited systems and is expected to guide future work on micro/nanoscale systems, where parametric excitations arise quite naturally.