Numerical Study of Flexural Cloaking and its Contributing Factors

Kurzfassung

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 firstly 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 is 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 in real applications. Further studies are required to better understand the 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 with regard to 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 in 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 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 of the nonlinear cloak. The frequency dependency of flexural cloaks is another investigated topic in this thesis, which is not discussed explicitly in the literature despite its importance. The frequency dependency investigation in this thesis is focused on a multilayered flexural cloak and indicates that using finer layers leads to more effective cloaking. As the last contribution, the thesis also proposes a design for fabrication of elastic cloaks and investigates its performance numerically.