Topology optimization for harmonic vibration problems using a density-weighted norm objective function

The optimized design of structures subjected to harmonic excitation is of great interest, for both the suppression of the oscillatory response (minimization) and the design of resonant structures (maximization). This work proposes an objective function which can be used for both goals, can properly locate resonance even for large damping ratios, and can be tuned to avoid the presence of non-physical modes in regions with void or intermediate relative densities. The properties of the proposed formulation are shown using a traditional benchmark case and the formulation is compared with other two formulations presented in the literature: dynamic compliance and active power. The results show that the proposed formulation is simple to use, leading to well-defined topologies with extreme harmonic behavior, although not solving the well-known problem of discontinuous topologies.