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Mechanical investigations of local fractional magnetorheological elastomers model on Cantor sets

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  • Feng, Yi-Ying
  • Yang, Xiao-Jun
  • Liu, Jian-Gen
  • Chen, Zhan-Qing

Abstract

The local fractional magnetorheological elastomers (MREs) model proposed in this work is extremely helpful in understanding how MREs behave mechanically when they exhibit nonlinear self-similarity on fractal sets. By replacing the integral order dashpot in the prestigious Li four parameter model to the local fractional dashpot, we put forward this novel and efficient model to analyze the stress response with constant strain, dynamic behavior under harmonic loads and complex modulus that consists of the storage modulus and the loss modulus of MREs, respectively. The adoption of the local fractional Laplace transform and the local fractional Fourier transform on Cantor sets are the underpinning to solve these non-differentiable problems. The local fractional MREs model is heuristically compared with the known Li model since the fractal MREs element is suitable for the description of the fractal magnetorheological effect with self-organizing phenomenon.

Suggested Citation

  • Feng, Yi-Ying & Yang, Xiao-Jun & Liu, Jian-Gen & Chen, Zhan-Qing, 2023. "Mechanical investigations of local fractional magnetorheological elastomers model on Cantor sets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 621(C).
    • Handle: RePEc:eee:phsmap:v:621:y:2023:i:c:s0378437123003448
    DOI: 10.1016/j.physa.2023.128789
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    References listed on IDEAS

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    1. H. M. Srivastava & Alireza Khalili Golmankhaneh & Dumitru Baleanu & Xiao-Jun Yang, 2014. "Local Fractional Sumudu Transform with Application to IVPs on Cantor Sets," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-7, May.
    2. Kumar, Sunil & Kumar, Ranbir & Cattani, Carlo & Samet, Bessem, 2020. "Chaotic behaviour of fractional predator-prey dynamical system," Chaos, Solitons & Fractals, Elsevier, vol. 135(C).
    3. Kai Liu & Ren-Jie Hu & Carlo Cattani & Gong-Nan Xie & Xiao-Jun Yang & Yang Zhao, 2014. "Local Fractional -Transforms with Applications to Signals on Cantor Sets," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-6, March.
    4. Mohammadi, Hakimeh & Kumar, Sunil & Rezapour, Shahram & Etemad, Sina, 2021. "A theoretical study of the Caputo–Fabrizio fractional modeling for hearing loss due to Mumps virus with optimal control," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    5. Yi-Ying Feng & Xiao-Jun Yang & Jian-Gen Liu & Zhan-Qing Chen, 2021. "New Perspective Aimed At Local Fractional Order Memristor Model On Cantor Sets," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 29(01), pages 1-6, February.
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