Wave Propagation Analysis using High-Order Finite Element Methods: Spurious Oscillations excited by Internal Element Eigenfrequencies

f ultrasonic guided waves is still a very demanding task. Because of the high-frequency regime both a fine spatia l and temporal discretization is required. To minimize the numerical costs, efficient and robust algorithms ought t o be developed. One promising idea is therefore to focus on high-order finite element methods (ho-FEM). The current article investigates the behavior of thep-version of the finite element method (p-FEM) and the spectral element method (SEM) with respect to the existence of spurio us oscillations in the solution. Convergence studies have shown that it is possible to observe non-physical os cillations under certain conditions. These parasitic vibrations, however, significantly deteriorate the accura cy of the simulation. For this reason, we analyse this phenomenon in detail and propose solutions to avoid its occurre nce. Without loss of generality, we employ a two-dimensional pla ne strain model to derive a guideline as to how to avoid these spurious oscillations, placing a special empha sis on the relation between the element size, the polynomial degree of the high-order shape functions and the excita tion frequency. Our results show that accurate simulations are possible if t he model is generated according to the proposed methodology. Moreover, the implementation of the guidelin e into an existing finite element software is straightforward; these properties turn the method into a useful tool forpractical wave propagation analyses.