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Fractal model of a Brownian polymer network: investigation of its dynamic fractal response using an ancient Chinese algorithm
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  • Alex Elías-Zúñiga,
  • Oscar Martínez-Romero,
  • Daniel Olvera-Trejo,
  • Luis Palacios-Pineda
Alex Elías-Zúñiga
Tecnológico de Monterrey, Campus Monterrey

Corresponding Author:[email protected]

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Oscar Martínez-Romero
Tecnologico de Monterrey
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Daniel Olvera-Trejo
Tecnologico de Monterrey
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Luis Palacios-Pineda
Tecnologico Nacional de Mexico
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In this paper, a mathematical model that describes polymer chain dynamics considering the Brownian motion of particles, an external driving force, the material fractal structure, and a finite extensibility nonlinear elastic (FENE) spring is investigated. To solve the fractal differential equation of motion, first, a two-scale dimension transform is introduced. Then, an ancient Chinese algorithm is used to derive the approximate steady-state frequency-amplitude response curves. Theoretical predictions show that the response shift from the 2D frequency-amplitude curves for fractal parameter values different from one, which modifies the polymer network oscillation amplitudes.