DYNAMIC RESPONSE OF A FRACTAL CUSHIONING PACKAGING SYSTEM

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

FRACTALS (fractals), 2022, vol. 30, issue 07, 1-9

Abstract: This paper focuses on predicting the shape, duration, and peak magnitude of the displacement, velocity, and acceleration curves while dropping weight over a viscoelastic fractal cushioning packaging system. Furthermore, to capture high-frequency harmonic components observed during the impact time span, the approximate frequency–amplitude expression of the governing equation of motion will be obtained via an ancient Chinese algorithm and He’s formulation by assuming initial trial solutions based on Jacobi elliptic functions. Numerical simulations confirmed the ability of the Jacobi elliptic functions to capture high-frequency harmonics observed during the cushioning packaging system dynamic response with a root mean square error (RMSE) value that does not exceed 0.0218, which is an indication of the great accuracy attained from our derived solution when compared to the exact numerical one. Furthermore, our derived approximate solution predicts that when a weight is dropped over the cushioning packaging, the cushion material with smaller porosity will absorb the produced kinetic energy faster.

Keywords: Fractal Cushioning-Packaging Model; Two-Scale Fractal Dimension Transform; He’s Formulation; Jacobi Elliptic Functions (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1142/S0218348X22501481

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