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This study aims to investigate the dynamic motion of an ultrasonic machining system comprising two Duffing oscillators, each with a single degree of freedom. After derivation of the differential equations of the system using the Lagrange equations and dimensionless time, numerical analysis was used to observe changes in the system caused by differences in excitation frequency.

To suppress this effect and improve performance, proportional differential (PD) control was used. The integral absolute error was used as the fitness function, and particle swarm optimization was used to find the best value for the gain constant of the PD controller.

The results showed that with specific changes of excitation frequency, the dynamic motion of the system became nonlinear and chaotic behavior resulted. This made the system unstable and affected performance.

A range of methods, including fuzzy control, was used to analyze the results, and exhaustive laboratory work was carried out. Means of control were found that were effective in suppressing the chaotic behavior, and differences in response to control were investigated and verified. The findings of this study can be used as a basis for system parameter settings or control circuit design.

The purpose of this paper is to study the mixing performance of the electrokinetically-driven power-law fluids in a zigzag microchannel.

The Poisson-Boltzmann equation, the Laplace equation, the modified Cauchy momentum equation, and the convection-diffusion equation are solved to describe the flow characteristics and mixing performance of power-law fluids in the zigzag microchannel. A body-fitted grid system and a generalized coordinate transformation method are used to model the grid system and transform the governing equations, respectively. The transformed governing equations are solved numerically using the finite-volume method.

The mixing efficiency of dilatant fluids is higher than that of pseudoplastic fluids. In addition, the mixing efficiency can be improved by increasing the width of the zigzag blocks or extending the total length of the zigzag block region.

The results presented in this study provide a useful insight into potential strategies for enhancing the mixing performance of the power-law fluids in a zigzag microchannel. The results of this study also provide a useful source of reference for the development of efficient and accurate microfluidic systems.