Spectral Element Modelling of Wave Propagation and Impedance Based SHM Systems

Abstract

In recent years many SHM approaches based on elastic waves that are generated and sensed by surface-bonded piezoelectric patches have been developed. Some of those utilize wave propagation phenomena; others use changes in the electromechanical impedance to detect structural damage. The capability of most approaches strongly depends on adequate choice of SHM system parameters like excitation signals and actuator/sensor types and positions. For this reason there is a growing interest in efficient and accurate simulation tools to shorten time and cost of the necessary tedious pretests. To detect small damage generally high frequency excitation signals have to be used. Because of this a very dense finite element mesh is required for an accurate simulation. As a consequence a conventional finite element simulation becomes computationally inefficient. A new approach that seems to be more promising is the time domain spectral element method. This contribution presents the theoretical background and some results of numerical calculations of the propagation of waves. The simulation is performed using the spectral element method (SEM), which leads to a diagonal mass matrix. Besides a significant saving of memory this leads to a crucial reduction of complexity of the time integration algorithm for the wave propagation calculation. A new approach to simulate the E/M impedance using time domain spectral elements is shown. An example demonstrates a good correlation of simulation and measurement data, so that the proposed simulation methodology seems to be a promising tool to make impedance based SHM systems more efficient, especially regarding the necessary parameter studies.