Dynamics of an Elastic Structure Excited by Harmonic and Aharmonic Impactor Motions

In this paper, we study the dynamics of a thin-walled structure subjected to impact excitations with the help of experimental and numerical investigations. A stainless-steel cantilever beam with a tip mass is considered, and this elastic structure is impacted close to the free end with an impactor. The impactor motions are prescribed in the form of harmonic functions and aharmonic functions of the form D¦cos(Ωt)¦. A finite time of contact between the structure and the impactor is considered. The excitation amplitude and the excitation frequency associated with the impactor motions are used as control parameters, and the results obtained are presented in the form of bifurcation diagrams and phase portraits. During harmonic impactor motions, period-doubled motions, incomplete period-doubling sequences, aperiodic motions, and multiple responses are observed. In addition to these responses, the responses observed during half-sine impactor motions include period-three motions and modulated motions. A finite-dimensional model is developed in the analytical efforts through a Galerkin projection and numerical studies are conducted using this model. The numerical results show many qualitative similarities with the experimental results, and they also show the importance of considering finite-time duration of the loading.