Optimization of natural frequencies for periodic structures

The bi-directional topology optimization method (BESO) is used to maximise the natural frequencies of periodic structures. In this approach, the design domain is divided into a user-defined number of unit cells in order to satisfy the periodic topology constraint. The BESO sensitivity for maximizing the natural frequencies is presented considering the periodic contraint. Following the BESO strategy, material is gradually removed from or added to the design domain to make the structure evolve towards an optimal solution. To demonstrate the capability and effectiveness of the present approach, several numerical examples are presented. Results indicate that the BESO method is capable of solving the natural frequency maximization problem for periodic structures.