A level set based topology optimization for finite unidirectional acoustic phononic structures using boundary element method

Abstract

The paper presents a level set based topology optimization method for unidirectional phononic structures with finite layers of lattice cells. Boundary element method(BEM) is employed as the numerical approach to solve the acoustic problems governed by Helmholtz equation. A sized reduced coefficient matrix is derived due to the iteration forms for input and output quantities on the periodic boundary of unit cells. Topological derivatives are formulated by boundary integral equation combined with adjoint variable method and computed for each layer. An average topological sensitivity of a single design domain is proposed for the updating of the level set function(LSF) governed by an evolution equation. Numerical models with different number of layers are considered and several optimized structures of unit cells are obtained in concerned frequencies. A further investigation into the transmission of acoustic waves is carried out by employing more layers of the periodic structures between the input and output domains. The results demonstrate the effectiveness of the proposed optimization method for the finite unidirectional phononic structures.