Comparative study on sensitivity analysis of transient vibration response in topology optimization

This paper investigates and summarizes the sensitivity analysis of transient vibration response in topological optimization problems. Firstly, the finite element calculation process of the transient vibration response based on the Newmark method is given. On this basis, the sensitivity formulae of the vibration response objective function to the element pseudo-density are derived using the finite difference method (FDM), the direct differential method (DDM), and the adjoint variable method (AVM). Numerical examples show that AVM has the same calculation accuracy as the DDM, while the precision of the FDM is affected by the perturbation step length. The calculation time of AVM is only about 0.5% of that of FDM. The conclusions of this study can provide a reference for topology optimization.