Efficient topology optimization for maximizing fundamental frequency with design-dependent inertial loads

Purpose In this study, a fast algorithm is proposed to obtain topologically optimized beams with maximized fundamental natural frequency by avoiding computationally costly eigenvalue calculations in every iteration step. Design/methodology/approach Structures with better vibration characteristics can be obtained by employing dynamic topology optimization methods. However, these methods involve computationally costly eigenvalue calculations in every iteration step. Hence, a fast algorithm is proposed to obtain topologically optimized beams with maximized fundamental natural frequency. The method takes advantage of the time-efficient static topology optimization methods. By utilizing Rayleigh’s principle together with design-dependent inertial loads, the dynamic topology optimization problem is turned into two sequential static topology optimization problems. As a result, a structure’s fundamental natural frequency is maximized via maximization of the structural stiffness while taking into account the mass distribution. Findings The proposed method’s performance and computational efficiency are verified by comparative numerical studies. It is found that, when compared to the standard dynamic topology optimization approach, run times and memory usage can be significantly reduced. Research limitations/implications The method can be used when preliminary topologically optimized designs with maximized fundamental frequencies are required in a fast manner. Originality/value The proposed method utilizes the compliance minimization topology optimization problem by taking into consideration of design-dependent inertial loads, which are not considered in the literature so far.