Abstract: This paper investigates the optimal distribution of damping material in thin-plate structures considering transient response by using structural topology optimization method. Therein, an artificial damping penalty model similar to the SIMP model is adopted. In the topology optimization model, the relative densities of the damping material are taken as design variables and the volume constraint of damping material is considered. The design objective is to minimize the time integration of the structural transient response at specified positions. Since the structure exhibits a non-proportional damping effect, the vibration equations of the structure are solved by the time integration method. The design sensitivities of the vibrating structure under applied loads are calculated using the adjoint variable method. Then the topology optimization problem is solved with the method of moving asymptote algorithm, which is a gradient-based method. Numerical examples are presented for demonstrating the validity and effectiveness of the proposed optimization model and numerical techniques.