Wave control in net structure based on transformation method

Due to the features of large size, light weight, and highly deployable capacity, the net structure has been successfully used in large space developable antennas. Here we explore the possibility of wave control in net structure by utilizing coordinate transformation method. For low-frequency flexural wave, the net structure can be homogenized as a thin membrane with effective mass and stiffness. For the net structures with regular triangle, regular square and regular hexagon lattices, their effective mass matrix and stiffness matrix can be simplified to isotropic forms. The homogenized continuous model is verified by the comparison of natural frequencies with the corresponding net structures. As the homogenized governing wave equation keeps form invariance, the coordinate transformation method can be used to control the wave propagation in the net structure. Based on the compression, “white hole” and Maxwell fisheye transformation, the required effective material parameters distributions are obtained. According to the expression of the effective mass and stiffness, the distributions of geometry and material parameters are realized. Finally, wave propagations in the designed net structures are validated numerically by using finite element method. Our work provides a novel concept to the vibration suppression on net structure in engineering applications.