Analytical modeling of vibrations in a damaged beam using Green-Volterra formalism

Abstract

Structural Health Monitoring of aeronautic composite structures through Lamb waves can advantageously exploit the fact that Lamb wave damage interaction is nonlinear. However, one di culty in this context is to be able to distinguish between nonlinearities due to the propagation (i.e. ma- terial or geometrical nonlinearities) and those due to the damage itself that are of main interest here. This work proposes to use the Green-Volterra formal- ism to build up a model for Lamb Wave propagation and damage interaction that is complex enough to represent both types of nonlinearities, and simple enough to be used for simulation and estimation purposes. This approach is presented for the low frequency S0 mode nonlinear propagation in a dam- aged beam. An analytical model of the nonlinear wave propagation is rst derived, where the damage is represented with a polynomial sti ness char- acteristic acting via boundary conditions. This model is then used to derive the Green-Volterra series describing the nonlinear input-output relationship of the system. A modal decomposition of the Green-Volterra series is also pro- vided. Simulations are presented, and the proposed approach is successfully compared to state-of-the-art methods based on nite-elements models.