Multiscale design and experimental verification of Voronoi graded stochastic lattice structures for the natural frequency maximization problem

Additive manufacturing (AM) has gained popularity for its capacity to produce geometrically complicated structures, such as lattice structures. Lattice structures have great advantages in the lightweight design of the aerospace and automotive field, in which frequent vibration is one of the most concerning problems during the structure design process. Consequently, it is necessary to research structural vibration frequency to avoid dynamic failure, especially the natural vibration frequency of the structure. In this work, a multiscale topology optimization method is proposed to design the Voronoi graded stochastic lattice structures for the first-order frequency maximization problem. Firstly, the generation and analysis of the Voronoi stochastic lattice microstructure are carried out on the microscale. Then, the macroscale structural optimization is conducted with a penalty-free density method. Finally, the full-scale Voronoi graded stochastic lattice structure is reconstructed based on the obtained relative density distribution and mapping relationship. Numerical examples are performed to demonstrate the correctness and validity of the proposed method for designing the Voronoi graded stochastic lattice structure. Several dynamic experiments also verify the effectiveness of the developed multiscale method and the advantage of the optimized graded lattice structure in structural dynamic response.