基于变换方法的索网结构波传播控制研究

Wave control in net structure based on transformation method

索网结构具有尺寸大、质量轻、可展开等特点,已应用于大型空间展开天线等结构中.本文开展了基于变换方法的索网结构波传播控制研究.首先将索网均匀化为等效薄膜,建立了可描述索网结构波传播规律的均匀化等效波动方程.等效波动方程的形式与薄膜波动方程的形式相同,等效质量和刚度由网格构型、几何参数和材料参数决定.对于张紧力均匀分布的正三角形、正方形和正六边形网格,等效质量和刚度均为各向同性.根据该波动方程,利用坐标变换方法给出预定波传播方式下所需的材料参数空间分布.将所得连续材料参数分布离散化,设计相应的索网微结构,从而实现索网中可控的波传播形式.基于压缩变换、白洞变换和鱼眼透镜等功能化设计,数值验证了方法的有效性.本文所提出的索网结构的变换方法,为大型空间索网结构的振动控制提供了一定的理论指导.

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.