The Two-dimensional Elastic Cloaking Theory And The Design Of Medium Parameters

Cloaking has been one of the most interesting phenomena. In order to achieveit, scientists have tried various ways and made a lot of research work. The theory ofelectromagnetic cloaking is already good, while the corresponding theory of elasticwave that is an important medium expressing the information of formation is stillnot very mature. The elastic cloaking theory based on the transformation method intwo dimension plane has been rarely carried out. At the same time, the shape ofelastic cloak is circular. Based on the transformation method, this paper designed alot of elastic cloaks. There are finite element method examples such as the circularelastic cloak, elliptic elastic cloak, elastic cloak in irregular shape, rectangularelastic cloak.Using transformation method can solve medium parameters with the constraintof prescribed wave propagation path. Transformation method is used to determinethe parameters based on the form invariance of the equation under coordinatetransformation. Here, the paper using transformation method has determined theparameters of elastic cloak.Firstly the paper has designed the circular elastic cloak. The first step using thetransformation method is to deduce parameters of circular elastic cloak. Then thecloak medium parameters designed are used to construct the finite element methodexample of circular elastic cloak. At last, we solve this example. In addition, theanalytical solution of displacement field excited by point force form source isdeduced.Secondly the elliptic elastic cloak is designed. The first step using thetransformation method is to deduce parameters of elliptic elastic cloak..Then withdifferent medium parameters on cloaking region, the paper created different finiteelement method examples of elliptical elastic cloak and solved them.To speak of,the elastic wave displacement field is discussed with different source position.Finally the elastic cloak of the irregular shape is designed.The first step is tosolve the new coordinates after coordinate transformation by solving Laplace’sequation.Then the paper created elastic cloak of arbitrary shape with different medium parameters on cloaking region and solved these finite element methodnumerical examples. Finally the square elastic cloak is designed according to thedesign method of irregular shape cloak.In addition, based on the calculation method of ray tracing the elastic wavepropagation path is calculated with elliptical elastic cloak.