Numerische Simulationen des Wellenausbreitungsverhaltens in phononischen Zick-Zack-Gitterstrukturen mittels Spektrale-Elemente-Methoden

In recent decades, the field of structural dynamics has become increasingly important in engineering. For example, in the design of buildings and structures, the stability must be ensured not only with respect to static but also dynamic effects. In particular, there are increasing requirements for new types of buildings and structures in engineering. The limits are particularly strict in the field of micro- and nanotechnology, where vibration amplitudes of just a few μm and even nm can be problematic. Due to these increasing requirements, research is being conducted on the development of novel materials and structures with outstanding elastodynamic properties. In particular, phononic materials and structures are very promising, which are characterized by a periodic arrangement of different materials or geometries. These periodic materials or structures have certain frequency ranges, often referred to in the literature as band-gaps or stop-bands, where acoustic or elastic waves cannot propagate.
The present work addresses the efficient numerical simulation of elastic wave propagation problems in two-dimensional (2D) phononic structures using spectral element methods (SEM). In particular, this work aims to investigate how the wave propagation properties of phononic materials and structures can be specifically tuned to meet given requirements, such as optimal vibration isolation or damping. Both slender and thick-walled 2D phononic zig-zag lattice structures are investigated, which exhibit low self-weight, high mechanical load-carrying capacity, and exceptional wave propagation properties. In this work, the wave propagation characteristics are mainly affected by passive and active measures. The passive measures are mainly based on the variations or combinations of geometrical and material parameters, with the position of the kinks, the deflection, the lattice constant, the arrangement of perforations and the stiffness and mass ratios being the main influencing factors. Distributed single masses, local resonators and external loads can be used selectively as active measures, taking advantage of the geometric nonlinearity.