Natural Frequency Control Using Simulated Annealing-Based Binary Topology Optimization

Control of natural frequencies in structural design is a challenging issue for engineers. Local modes can prevent the solution from reaching the optimum point, especially in discrete problems. This paper presents a topology optimization method with simulated annealing to minimize and control the first natural frequency of a structure with binary elements. The algorithm generates new solutions by adding or removing solid elements in a design domain and evaluates the new solutions by the Metropolis-Hastings algorithm. The algorithm was applied successfully to a clamped square plate as the design domain and with solid mass at the center. The results show a smooth convergence to the optimum solution with reasonable computational costs. The design reaches a specific small first natural frequency in the non-convex topology optimization problem. The algorithm can be used efficiently in the design of structures with specific natural frequencies and constraints.