Structural topology optimization and frequency influence analysis under harmonic force excitations

In this paper, structural topology optimization is studied under harmonic force excitations. The displacement amplitude at the specified location of a structure is defined as the objective function subjected to the volume constraint. The displacement amplitude is calculated based on modal superposition method and the corresponding sensitivity analysis is derived. In order to avoid localized modes, the polynomial interpolation scheme is introduced to relate material properties to pseudo density variables. In the meantime, the influences of the excitation frequency and direction upon the displacement response are investigated and how the eigen-modes vary in the optimization process is highlighted. Topology optimization of structure under harmonic excitation with high frequency is specially analyzed. More constraints on the static displacements are applied to generate clear structural topology. Numerical optimization examples are finally solved to demonstrate the validity of the proposed optimization procedure.