Wave-based analysis of jointed elastic bars: nonlinear periodic response

In this paper, we develop two wave-based approaches for predicting the nonlinear periodic response of jointed elastic bars. First, present a vibration approach (WBVA) studying systems informed by re-usable, perturbation-derived scattering functions. This analytical can be used to predict steady-state, forced bar structures incorporating any number and variety joints. As second method, Plane-Wave Expansion (PWE) analyzing in same structures. Both have advantages disadvantages when compared side-by-side. The WBVA results minimal set equations is re-usable following determination reflection transmission functions, while PWE formulation easily applied new joint models maintains solution accuracy higher levels nonlinearity. For example cases three bars connected linearly damped joints with linear cubic stiffness, accurately expected Duffing-like behavior which multiple responses occur near-resonant regime, close agreement reference finite element simulations. Lastly, discuss extensions work composed beam-like members, propose follow-on studies addressing opportunities identified application methods presented.