A method for analyzing the interaction of nondispersive structural waves and nonlinear joints

The scattering of nondispersive structural waves by joints with stiffness and damping nonlinearities is examined. The analysis is based on the method of characteristics and the nonlinear scattering is described by a first-order nonlinear ordinary differential equation with constant coefficients. This equation is solved by analytical and numerical techniques, and the nonlinear distortions of the reflected waves are quantified by an FFT analysis. The scattering of periodic and transient incident waves from joints with cubic and clearance nonlinearities is then considered. Generally, it is found that the nonlinear distortions in the power spectrum of the reflected waves become negligible as the frequency increases. Moreover, as the linear stiffness of the joint increases the low-frequency nonlinear distortions in the spectrum become more evident. Based on the present theory, a nonparametric method for identifying the nonlinear stiffness and damping characteristics of nonlinear joints connecting axial members is developed.