Topology optimization of proportionally damped structures under harmonic excitations: Analysis of velocity and acceleration responses

Topology optimization of proportionally damped structures subjected to harmonic excitations within a frequency interval is a challenging task. In this work, we consider the structural velocity and acceleration responses in a frequency interval as the optimization objectives. The optimized structures will be significantly different from those with the displacement response only due to the influence of excitation frequencies. In particular, if the acceleration amplitude of structural frequency responses in a frequency interval is considered, the optimization process usually converges to a configuration that is unable to ensure engineering feasibility. An optimization model that takes the structural static response of the structure as a weighted part of the objective function is proposed, it can make the optimized configuration more applicable for engineering design. An efficient method for calculating frequency responses over a frequency interval is also introduced. The derivatives of the objective function are derived by the adjoint method and can be calculated in a manner similar to the frequency response. Two illustrative examples are given to examine the accuracy and validity of the proposed method.