This study evaluates the effects of weak harmonic perturbations applied to a mechanical system with dry sliding parts that exhibits both chaotic and periodic stick-slip vibrations. A previously published model of such a system was tested in numerical simulations. Since the trajectories of the stick-slip vibrations in the system include removal discontinuities, we use a technique based on the Poincaré map for analysis. This analysis reveals that weak harmonic perturbations induce a shift of the bifurcation points in agreement with several previous studies, which suggests a mechanism for taming the chaotic behavior of the system. Our results indicate that taming the chaotic behavior in mechanical systems with discontinuities can be addressed with weak harmonic perturbations.

In this paper, we propose a novel gearbox design method called multiple gearbox optimization (MGO), that can simultaneously design multiple patterns of feasible gearboxes. This MGO consists of a penalty handling method and a multimodal optimization method. The handling method converts an existing constrained gearbox design problem into an unconstrained one. The multimodal optimization method is developed by making our previously proposed gravitational particle swarm algorithm (GPSA) to solve mixed-integer optimization problems. As a result, our MGO successfully obtained an average of 14.18 design patterns in a single run that satisfied all design constraints. Statistical tests indicated that the performance of our MGO was significantly superior to some conventional methods in terms of the number of design patterns and the volume/weight of gearboxes.

In this study, we propose a novel optimization method, which can track multiple optimal solutions in dynamic environments. In our previous study, we proposed a gravitational particle swarm algorithm (GPSA), which is able to search for multiple optimal solutions. In this paper, first, we apply the original GPSA to a multi-solution tracking problem and reveal its drawback. Second, we propose a modified GPSA, called τGPSA, by replacing original GPSA's update rule for personal bests with a tolerance update rule. Finally, we demonstrate that τGPSA can track multiple optimal solutions in an one-dimensional shifting sphere function.