A multi-frequency interpolation method for bi-material topology optimization of vibro-acoustic problems

In practical vibro-acoustic problems, external excitation normally contains a certain frequency band structure, and system optimization needs to be performed through frequency band analysis. To reduce the high computation burden in frequency band optimization, we propose a multi-frequency interpolation method for bi-material topology optimization of the vibro-acoustic interaction system. A highly accurate solution of the vibro-acoustic interaction problem is achieved by combining the advantages of the structural finite element method and the acoustic boundary element method. A structural material interpolation model is established using the solid isotropic material with penalization method, and the topological sensitivity formulation is derived based on the adjoint variable method. On the basis of the smoothness property of the radiation impedance matrix, the matrix interpolation method is adopted to obtain the objective function at the frequency points in the frequency band of interest, thus improving the computational efficiency of frequency band topology optimization. The zero points of the Chebyshev polynomial are selected as the interpolation nodes to improve calculation accuracy. The effectiveness of the proposed multi-frequency interpolation method is verified by several numerical tests, and the radiated sound power is reduced considerably after the developed bi-material topology optimization. © 2024 Elsevier Ltd