Theoretical and Numerical Study of Flexural Cloaking ; Theoretische und numerische Untersuchung des Flexural Cloakings

Cloaking is a special case of wave manipulation, where waves are guided around a space by engineering material properties. In the terminology of cloaking, the middle space is called the core, whereas the material matrix around it is called the cloak. Cloaking was first introduced in electromagnetism but was soon adopted for manipulating flexural waves in thin plates. In this regard, the term flexural cloaking is used to refer specifically to the cloaking of flexural waves in thin plates. The design process of a cloak is an inverse problem, where the required material properties for a desired physical field are searched. The transformation method is one of the few techniques to solve such an inverse problem. In this method, the desired physical field, for example, the guidance of the waves around the core, is described with a coordinate transformation. Flexural cloaking has to overcome different challenges to become integrated into real applications. Further studies are required to better understand flexural cloaking and its contributing parameters and accordingly realize it in simpler ways. This thesis is a contribution to this goal. Different aspects of flexural cloaking are investigated theoretically and numerically concerning different parameters, which have not yet been examined thoroughly. This thesis deepens on one hand the investigation of reducing wave scattering through flexural cloaking, which is the main focus of the present related literature; and examines the capability of isolating the core space through flexural cloaking on the other hand, which is mainly disregarded on the literature. The numerical study of this dissertation indicates a strong potential of the cloak to isolate the core, especially at lower frequencies. Regarding the great influence of the underlying transformation on the performance of the cloak, the thesis compares two different transformations, namely polynomial transformations of order 1 and 2. The numerical results of this thesis indicate a better more consistent performance ...