INVESTIGATION OF THE STEADY-STATE SOLUTION OF THE FRACTAL FORCED DUFFING’S OSCILLATOR USING AN ANCIENT CHINESE ALGORITHM

ELà AS-ZÚÑIGA Alex, Oscar Martã Nez-Romero (), Daniel Olvera Trejo () and Luis Manuel Palacios-Pineda ()
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ELà AS-ZÚÑIGA Alex: Mechanical Engineering and Advanced Materials Department, School of Engineering and Science, Tecnologico de Monterrey, Ave. Eugenio Garza Sada 2501, Monterrey 64849, Mexico
Oscar Martã Nez-Romero: Mechanical Engineering and Advanced Materials Department, School of Engineering and Science, Tecnologico de Monterrey, Ave. Eugenio Garza Sada 2501, Monterrey 64849, Mexico
Daniel Olvera Trejo: Mechanical Engineering and Advanced Materials Department, School of Engineering and Science, Tecnologico de Monterrey, Ave. Eugenio Garza Sada 2501, Monterrey 64849, Mexico
Luis Manuel Palacios-Pineda: ��Tecnológico Nacional de México/Instituto, Tecnológico de Pachuca, Carr. México-Pachuca, Km 87.5, Pachuca, Hidalgo, Código, Postal 42080, Mexico

FRACTALS (fractals), 2021, vol. 29, issue 06, 1-9

Abstract: 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.

Keywords: Duffing Oscillator; Fractal Oscillator; Two-Scale Fractal Transform; Amplitude-Frequency Response curves; Ancient Chinese Algorithm (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1142/S0218348X21501334

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