C5.4 - Application of the Scaled Boundary Finite Element Method (SBFEM) for a numerical simulation of ultrasonic guided waves

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The application of waveguides for acoustic measuring technologies and the development of non-destructive evaluation techniques with guided ultrasonic waves for plate like materials like carbon fiber reinforced plastic shells and layered structures require a good understanding of acoustic wave propagation inside the material. The well-known Finite Element Method can be used for simulations, however at least for higher frequencies, the ratio of wavelength and geometrical dimension demands a time-consuming fine grid. Using commercial simulation tools the computational costs increase considerably for ultrasonic frequencies. In the recent years, the Federal Institute for Materials Research and Testing has developed a very efficient alternative for simulating acoustic wave propagation particularly in wave guides by extending the Scaled Boundary Finite Element Method (SBFEM). The SBFEM as a semi-analytical method has one main advantage over the classical Finite Element Method: It only demands a discretization of the boundary instead of the whole domain. This is pictured in the figures below. The method is still related to the Finite Element Method and uses their well-known solving strategies. SBFEM is shown to be highly efficient, especially in the frequency domain. Additionally, the efficiency can be increased by using higher-order spectral elements. In plates and cylinders, the SBFEM can be used to animate propagating modes and computes their wavenumber. In this contribution, we present a short introduction into the basics of SBFEM formulation of the dynamic elastic wave equation. The applicability and efficiency of the approach is demonstrated by applying the method to layered structures and different wave guide geometries. As one example we present the wave propagation in a typical adhesive joint of different metal sheets as common in new designs in automotive industry. The analysis comprises the computation of dispersion curves as starting point of every development of non-destructive testing techniques for inspecting such structures as well as the analysis of the propagating modes. Additional examples presented handle special cases for axis-symmetric geometries, such as pipes and cylindrical rods which are common in various acoustic measurement applications.