Linear Versus Nonlinear Response of a Cantilevered Beam Under Harmonic Base Excitation: Theory and Experiment

A computational and experimental study of a uniform cantilever beam with a tip mass under base excitation was performed. The beam was excited at various levels of base displacement to provoke tip displacements greater than 15% of the beam length. Damping and yield stress of the beam were both considered. It was found that a large tip displacement causes nonlinear inertial (NLI) and structural (NLS) effects to arise. Each of the structural and inertial nonlinearities has an opposite effect on the resulting resonance frequency, which are nearly mutually canceling. The result was that resonant frequency calculated using the full nonlinear (FNL) model was essentially equal to the value calculated by linear (LIN) theory, and the tip displacement amplitude varied only modestly from the LIN value. It was also observed that the damping in this system is likely nonlinear, and depends on tip displacement amplitude. A theoretical model for fluid damping is suggested. Initial investigation shows encouraging agreement between the theoretical fluid damping and the measured values.