Sensitivity analysis on dynamic responses of geometrically imperfect base excited cantilevered beams

The non-linear non-planar dynamic responses of a near-square cantilevered geometrically imperfect (i.e., slightly curved) beam under harmonic primary resonant base excitation with a one-to-one internal resonance is investigated. By assuming two different geometric imperfection shapes, the sensitivity of the perfect beam model predicted limit-cycles to small geometric imperfections is analyzed by continuing them versus the imperfection parameter incorporating the imperfect beam model. This was carried out by assuming that the corresponding frequency detuning parameter associated with each limit-cycle is fixed. Also, other possible branches of dynamic solutions for the corresponding fixed detuning parameter within the interval of the imperfection amplitude are determined and the importance of accounting for the small geometric imperfections is discussed.