Search

In this paper, the ancient Chinese algorithm is applied to derive fractal microgravity forced oscillator's frequency–amplitude response curves using the two-scale fractal transform derivative. Depending on the fractal parameter values, it is shown that the system restoring forces exhibit hardening or softening behavior. Furthermore, the proposed solution approach is simple, efficient, and accurate for obtaining the approximate steady-state solution of a fractal microgravity nonlinear oscillator with a purely nonlinear power-form restoring force. [ABSTRACT FROM AUTHOR]

In this paper, the steady-state solution of Duffing-type oscillators with fractal-order derivative is obtained. First, the two-scale fractal-order derivative transform is used to write the fractal differential equation of motion as an ordinary differential non-homogenous equation of motion. Then the ancient Chinese algorithm and He's formulation are used to find the approximate frequency-amplitude response curve. The results show that the steady-state response diagrams exhibit hardening or softening behavior depending on the fractal parameter value. [ABSTRACT FROM AUTHOR]

This paper aims to study the dynamic response of the fractal Fangzhu's forced device to elucidate how the harvester device's surface fractal patterned influences water molecules' motion due to the increase or reduction of the wave velocity. It is also investigated under which conditions the oscillation amplitude favors the complete water removal from Fangzhu fractal surface device. Based on the approximate fractal frequency–amplitude relation derived using an ancient Chinese algorithm, and by varying the value of the fractal dimension parameter linked to the material surface morphology, it was found that the Fangzhu water harvester device can efficiently capture microscopic water droplets if the surface morphology is such that the fractal dimension α is less than one. This condition can be used to develop superhydrophobic surfaces mimicking fractal patterned surface structures. [ABSTRACT FROM AUTHOR]