Design of phononic-like structures and band gap tuning by concurrent two-scale topology optimization

Phononic crystals have been paid plenty of attention due to the particular characteristics of band gap for elastic wave propagation. Many works have been focused on the design of the phononic crystals materials/structures through different methods including experimental and numerical approaches such as topology optimization. However, most of the works on topological design of the phononic materials/structures are on micro-scale topology optimization of the crystal unit cell based on the assumption of infinite periodicity. Finite design domain and corresponding boundary condition are seldom considered directly in the single micro-scale topology optimization of the crystal unit cell. This paper presents a concurrent two-scale topology optimization framework to design phononic-like structures with respect to the vibro-acoustic criterion, and the finite dimension and the boundary condition of the macro-scale design domain can be fully taken into consideration simultaneously. Accuracy of the proposed model and method to compute the wave band gap property of two-dimensional phononic structures is validated. Then the concurrent two-scale topology optimization approach is employed to design the phononic-like structures and tune the wave band gap property. Numerical examples show the advantage of the concurrent two-scale topology optimization over the single micro-scale design of the crystal unit cell. Many interesting features of the proposed approach are also revealed and discussed. The presented work shows that the concurrent two-scale topology optimization approach is promising to be a powerful tool in the design of vibro-acoustic phononic-like structures for achieving the desired band gap property.