Ray Tracing Methodology for Elastic Wave Propagation Improve Simulation Applied to Aeronautic Composite Structures

Abstract

Data processing and simulations for guided wave based Structural Health Monitoring (SHM) systems can be extremely challenging, especially in complex geometries. Aerospace structures, specifically, may contain integrated stiffeners, thickness changes and other structural details, which will result in a very complex signal on the sensor network due to the multiple reflection of the multiple modes on the structural elements. Currently, the most common methodologies to simulate Lamb waves are generally based in the finite element method (FEM), spectral element method (SEM). FEM models require a large amount of computational resources and therefore are limited in the size and number of cases that could be calculated, and SEM present some difficulties to implement out of plane reinforcements and to modelize structural details. For this reason, being able to perform a fast and efficient assessment of the propagation of elastic waves can be very helpful to reduce the need of physical tests, and could be used to identify the critical cases to run with a more detailed numerical simulation or to perform an stochastic analysis. In an attempt to solve this problem, this study presents an analytical methodology based on the ray tracing method, able to solve the propagation of symmetric and anti-symmetric elastic waves on a 2D space and able to take into account different material characteristics, propagation velocities and simple boundaries; the methodology considers different propagation modes independently and takes into account the splitting of rays and possible mode changes when encountering a boundary during the propagation. The capabilities of this method are demonstrated on a series of analytical study cases and compared against physical tests, presenting an equivalent or better correlation than the finite element method, with a substantial reduction in the computational cost.