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ON TWO-SCALE DIMENSION AND ITS APPLICATION FOR DERIVING A NEW ANALYTICAL SOLUTION FOR THE FRACTAL DUFFING’S EQUATION

ALEX ELÍAS-ZÚÑIGA

Mechanical Engineering and Advanced Materials Department, School of Engineering and Science, Tecnológico de Monterrey, Avenue Eugenio Garza Sada 2501, Monterrey 64849, Mexico

E-mail Address: aelias@itesm.mx

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https://doi.org/10.1142/S0218348X2250061XCited by:5 (Source: Crossref)

Abstract

In this paper, the analytical solution that describes the evolution in time of the fractal damped Duffing equation subjected to external forces of elliptic type is derived using He’s two-scale fractal transform and the elliptic balance method (EBM). This solution predicts the evolution in time of the Duffing equation and unveils qualitative and quantitative system behavior when the values of the fractal parameter varies, and how these affect the frequency, the wavelength, and the oscillation amplitude from the start of the motion. Comparison of the amplitude–time response curves over the selected time-interval with those obtained from numerical simulations confirms the accuracy of the derived analytical solution.

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