Dynamics of Elastic Structures Subjected to Impact Excitations

A collection of results obtained through experimental and analytical investigations into the dynamics of thin-walled structures subjected to impact excitations is presented. A stainless steel cantilever beam with a tip mass is considered and this elastic structure is impacted close to the free end. The considered excitations include harmonic excitations and periodic excitations of the form Dcos(Ωt). The excitation amplitude and excitation frequency are used as control parameters. The experimental results are presented in the form of bifurcation diagrams and phase portraits. During harmonic impact excitations, period-doubled motions, incomplete perioddoubling sequences, and aperiodic motions are observed. In addition to these responses, the responses observed during half-sine impact excitations 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 by using this model. The analytical results show many qualitative similarities with the experimental results. In the considered parameter ranges, nonlinear interactions are not observed. Some of the observed experimental responses appear to suggest the presence of grazing impacts. The implications of the current study for workpiece-tool interactions during milling of thin-walled structures are discussed.