Design of damping layer by topology optimization and Non-Negative Intensity

Non-Negative Intensity (NNI) is a quantity which could avoid the near-field cancellation effects in sound intensity and provide direct visualization of surface contributions to sound power. Hence, the NNI and its variants are implemented to be the objective function of topology optimization for damping layer design. Regarding vibro-acoustic systems, the structural vibrations are analyzed by the finite element method (FEM), and fast multipole boundary element method (FMBEM) is used for the acoustic analysis. A two-way coupling is established between the structural and the acoustic domains. By using the FMBEM and the implicitly restarted Arnoldi method (IRAM), the eigenvalue analysis for the symmetrized acoustic impedance matrix is performed with efficiency. Then, the NNI can be easily computed based on the eigen-solutions and the FEM-FMBEM analysis. Further, these eigen-solutions can be recycled in the optimization iterations since they are independent of the solutions of the coupled system. This reduces the computational efforts. For calculating the gradients of the objective function, the adjoint variable method is applied. With the evaluated gradients, the optimization problem is solved by the method of moving asymptotes (MMA) and the optimized distribution of damping layer is obtained.