Abstract：Pentamode Materials are novel artificial acoustic metamaterials. And they are usually designed by using solid materials, which microstructures are micro truss structures. However, the structures constructed by Pentamode Materials are theoretically unstable. From the perspective of global analysis of the entire structure, this paper proposes a method by employing preloads to insure the stability of the designed structures with Pentamode Materials, and a sufficient condition for the stability of structures with Pentamode Materials is presented. Meanwhile, two numerical examples of typical microstructures of Pentamode Materials are offered to verify the condition. Furthermore, in order to apply and implement the stability condition of structures in the structural design procedure, an optimization model of structures is established to describe the design problem, which views the structure design with Pentamode Materials as the transformation procedure of Pentamode Materials. As a result, if the unit cells of Pentamode Materials are constructed by micro trusses the optimization model is simple, both of the structure stability constraints and the characteristic constraints of Pentamode Materials are linear.
2016, Vol. 37 
