Wave Modeling and Propagation in Aerospace Structures

Abstract

Guided wave-based nondestructive evaluation (NDE)/structural health monitoring (SHM) methods have been developed in an effort to examine integrity and predict remaining useful life of structural systems through the detection of existing damage. If damage is to be effectively and accurately detected, a strong and deep understanding of wave propagation in structures must be developed. Complexities associated with guided waves interacting with structural boundaries, transducers, and various damage scenarios must be considered. The problem, therefore, requires tools more powerful and flexible than analytic methods. Rapid advances in computational resources enable the ability to perform elaborate numerical simulations. Numerical methods allow for a practical solution of wave propagation problems that are close to realistic scenarios and within a prescribed accuracy. However, the state of the art in numerical simulation is mostly limited to finite element analyses that are either unable to handle the fine spatial-temporal resolutions required by guided-wave simulation, or are computationally inefficient. The finite difference-based Local Interaction Simulation Approach (LISA) offers an effective solution by exploiting the massive parallelization capabilities of the algorithm and the capability to incorporate sophisticated local mechanisms that allow for the coupled modeling of transducers and damage.

This dissertation presents the developments of the multi-GPU enabled UM-LISA numerical framework for guided-wave modeling and propagation simulation and several applications in SHM and elastic metamaterials. The coupled piezoelectric-mechanical physics is considered and the derivation of the LISA formulation is presented. Multiple formulation features are developed and numerically implemented that enable versatile simulation of wave propagation in finite damped mediums with various damage scenarios. The features and enhancements achieved in the framework include:

1. the development of conventional and hybrid non-reflective boundary (NRB) techniques with non-uniform grids to reduce wave reflections from structural boundaries and minimize model dimensions to achieve efficient simulation;

2. the development of piezoelectric coupled elastodynamic formulation in both 2-D and 3-D UM-LISA, considering anisotropic material properties and providing an accurate mechanism of modeling wave generation;

3. the implementation of linear and nonlinear damage modeling strategies in UM-LISA for capturing various complex wave-damage interactions;

4. the implementation of a selection of time integration schemes, including central finite difference, low-storage Runge-Kutta and generalized-alpha schemes, extending the numerical accuracy and stability of UM-LISA;

5. the implementation of UM-LISA on a multi-GPU environment through the Compute Unified Device Architecture (CUDA) parallel programming model for faster computations.

The new UM-LISA is then exercised in several problems that demonstrate its versatility and power. These applications include the characterization of fatigue damage in aluminum plates, the investigation of wave fields generated by phased arrays of d31-type and d36-type piezoelectric wafers, and the performance characterization of 3-D printed functionally graded acoustic black hole structures, as well as the modeling of wave propagation in composite plates with delamination. Validation experiments are also conducted and compared with numerical simulations. The agreement between simulation results and experiments demonstrates the effectiveness of utilizing numerical simulation for the investigation of wave propagation in SHM and elastic metamaterial applications.