Simulation of Wave Propagation in Complex Structures with the Spectral Element Method

In nondestructive testing, the use of ultrasonic elastic waves has proven as one of the most successful principles to detect structural damage like cracks, delaminations etc. Especially, Structural Health Monitoring (SHM) is characterized by permanently installed embedded or surface–mounted actuators and sensors (e.g. piezoelectric patches). The capability of most approaches strongly depends on adequate choice of parameters like excitation signals and actuator/sensor positions. For this reason there is a growing interest in efficient and accurate simulation tools to shorten time and cost of the necessary pretests. With respect to high frequency excitation a computationally efficient method is required. This contribution presents the theoretical background of the spectral element method including the electro–mechanical coupling of piezo elements. The spectral element method generates a diagonal mass matrix leading to significant savings of memory and to a crucial reduction of complexity of the time integration algorithm. Both in–plane and out–of–plane waves can be handled. Numerical examples for the propagation of waves in stiffened structures are presented. The effect of improper placement of actuators/sensors is shown. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)