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

Author

ELÍAS-ZÚÑIGA, ALEX, MARTÍNEZ-ROMERO, OSCAR, TREJO, DANIEL OLVERA, and PALACIOS-PINEDA, LUIS MANUEL

Subjects
ORDINARY differential equations, EQUATIONS of motion, ALGORITHMS, STEADY-state responses, DUFFING oscillators, DUFFING equations
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. [ABSTRACT FROM AUTHOR]

Published
2021
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