Scattering of structural waves by nonlinear elastic joints

An analytic study of the scattering of structural waves by nonlinear elastic joints is presented. Under the assumption of small nonlinearities and/or amplitudes of motion, an averaging methodology is implemented for analyzing the interaction between an incident wave and a nonlinear joint with symmetric stiffness. It is found that, contrary to the predictions of existing linear theories, a single incident wave gives rise to an infinity of reflected waves with frequencies equal to odd multiples of the frequency of the incident wave. The orders of magnitude of the amplitudes of the various reflected waves are considered, and an application of the theory is made by considering the wave scattering from a joint with cubic stiffness nonlinearity. In addition, it is shown that the wave propagation approach presented in this work can be effectively used for predicting nonlinear free oscillations (standing waves) in finite waveguides with nonlinear joints.