A topology optimization for finite 1D phononic structures with objective function involving tangential derivative quantities using TDBIE

The paper proposes a topology optimization method for 1D phononic structures to minimize the tangential component of particle velocity at the objective boundary. The tangential derivative of the boundary integral equation (TDBIE) is employed for the evaluation of the objective function involves the tangential derivative quantities. The topological derivative is derived through the adjoint method and the Neumann boundary condition of the adjoint field is obtained using the TDBIE. The average topological derivative which is obtained by calculating the average value of the topological derivative in each layer of design domains, is employed for the updating of the level set function. Numerical implementations demonstrate the proposed method is effective for the design of the 1D phononic crystals with the objective function involving tangential derivative quantities.