IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v164y2022ics0960077922008736.html
   My bibliography  Save this article

A novel pattern in a class of fractal models with the non-perturbative approach

Author

Listed:
  • El-Dib, Yusry O.
  • Elgazery, Nasser S.

Abstract

This paper provides evidence on how the fractal vibration system can be converted into a damping system in a continuous space. The fractal Duffing vibration is considered an example. It is shown that the inertia force in the fractal space can be transformed into a combination of the inertia force and the damping force in a continuum space employing the fractional parameter. In addition, the velocity force can be converted to both the damping force and the stiffness force in the smooth space. The nonlinear system is solved using the non-perturbation method. The calculations showed that the approximate solution agrees with the corresponding numerical one when the fraction parameter becomes the unity value. The new approach is represented as the best one because it highlights the damping influence of fraction derivatives. This approach can help a large number of researchers interested in studying nonlinear fractal oscillations.

Suggested Citation

  • El-Dib, Yusry O. & Elgazery, Nasser S., 2022. "A novel pattern in a class of fractal models with the non-perturbative approach," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    • Handle: RePEc:eee:chsofr:v:164:y:2022:i:c:s0960077922008736
    DOI: 10.1016/j.chaos.2022.112694
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077922008736
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2022.112694?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Alex Elã As-Zãšã‘Iga & Oscar Martã Nez-Romero & Daniel Olvera Trejo & Luis Manuel Palacios-Pineda, 2021. "Investigation Of The Steady-State Solution Of The Fractal Forced Duffing’S Oscillator Using An Ancient Chinese Algorithm," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 29(06), pages 1-9, September.
    2. Chun-Hui He & Chao Liu, 2022. "A Modified Frequency–Amplitude Formulation For Fractal Vibration Systems," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(03), pages 1-8, May.
    3. Chun-Hui He & Chao Liu & Ji-Huan He & Khaled A. Gepreel, 2021. "Low Frequency Property Of A Fractal Vibration Model For A Concrete Beam," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 29(05), pages 1-7, August.
    4. Naveed Anjum & Chun-Hui He & Ji-Huan He, 2021. "Two-Scale Fractal Theory For The Population Dynamics," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 29(07), pages 1-10, November.
    5. El-Dib, Yusry O., 2022. "The damping Helmholtz–Rayleigh–Duffing oscillator with the non-perturbative approach," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 194(C), pages 552-562.
    6. Chen, Mu & Yu, Boming & Xu, Peng & Chen, Jun, 2007. "A new deterministic complex network model with hierarchical structure," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 385(2), pages 707-717.
    7. Ji-Huan He & Shuai-Jia Kou & Chun-Hui He & Zuo-Wei Zhang & Khaled A. Gepreel, 2021. "Fractal Oscillation And Its Frequency-Amplitude Property," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 29(04), pages 1-9, June.
    8. Cao Wang, 2021. "Monte Carlo Simulation," Springer Series in Reliability Engineering, in: Structural Reliability and Time-Dependent Reliability, chapter 0, pages 105-163, Springer.
    9. Yang, Jinghua & Wang, Min & Wu, Lei & Liu, Yanwei & Qiu, Shuxia & Xu, Peng, 2021. "A novel Monte Carlo simulation on gas flow in fractal shale reservoir," Energy, Elsevier, vol. 236(C).
    10. Qi Gao & Yuanfang Cheng & Songcai Han & Yang Li & Chuanliang Yan & Zhongying Han, 2021. "Fractal Analysis Of Shale Gas Transport Through Micropores And Microfractures," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 29(03), pages 1-21, May.
    11. Kang-Le Wang, 2021. "A New Fractal Transform Frequency Formulation For Fractal Nonlinear Oscillators," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 29(03), pages 1-7, May.
    12. Alex Elã As-Zãšã‘Iga & Oscar Martã Nez-Romero & Daniel Olvera Trejo & Luis Manuel Palacios-Pineda, 2021. "An Efficient Ancient Chinese Algorithm To Investigate The Dynamics Response Of A Fractal Microgravity Forced Oscillator," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 29(06), pages 1-7, September.
    13. Ji-Huan He & Yusry O. El-Dib, 2021. "A Tutorial Introduction To The Two-Scale Fractal Calculus And Its Application To The Fractal Zhiber–Shabat Oscillator," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 29(08), pages 1-9, December.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Bukhari, Ayaz Hussain & Raja, Muhammad Asif Zahoor & Alquhayz, Hani & Abdalla, Manal Z.M. & Alhagyan, Mohammed & Gargouri, Ameni & Shoaib, Muhammad, 2023. "Design of intelligent hybrid NAR-GRNN paradigm for fractional order VDP chaotic system in cardiac pacemaker with relaxation oscillator," Chaos, Solitons & Fractals, Elsevier, vol. 175(P2).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Li, Jing & Xie, Yetong & Liu, Huimin & Zhang, Xuecai & Li, Chuanhua & Zhang, Lisong, 2023. "Combining macro and micro experiments to reveal the real-time evolution of permeability of shale," Energy, Elsevier, vol. 262(PB).
    2. Gang Liu & Duo Chen & Bo Li & Changjun Li, 2023. "Primary Growth Behavior of Sulfur Particles through the Throttle Valve in the Transmission System of High Sulfur Content Natural Gas," Energies, MDPI, vol. 16(7), pages 1-31, March.
    3. Qin, Lei & Wang, Ping & Lin, Haifei & Li, Shugang & Zhou, Bin & Bai, Yang & Yan, Dongjie & Ma, Chao, 2023. "Quantitative characterization of the pore volume fractal dimensions for three kinds of liquid nitrogen frozen coal and its enlightenment to coalbed methane exploitation," Energy, Elsevier, vol. 263(PA).
    4. Wei Zhang & Qihong Feng & Sen Wang & Xianmin Zhang & Jiyuan Zhang & Xiaopeng Cao, 2022. "Molecular Simulation Study and Analytical Model for Oil–Water Two-Phase Fluid Transport in Shale Inorganic Nanopores," Energies, MDPI, vol. 15(7), pages 1-20, March.
    5. Liaqat, Muhammad Imran & Akgül, Ali, 2022. "A novel approach for solving linear and nonlinear time-fractional Schrödinger equations," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    6. Guilin Zhu & Linyou Zhang & Zhihui Deng & Qingda Feng & Zhaoxuan Niu & Wenhao Xu, 2023. "Three-Dimensional Geological Modeling and Resource Estimation of Hot Dry Rock in the Gonghe Basin, Qinghai Province," Energies, MDPI, vol. 16(16), pages 1-16, August.
    7. Hollingshad, Nicholas W. & Turalska, Malgorzata & Allegrini, Paolo & West, Bruce J. & Grigolini, Paolo, 2012. "A new measure of network efficiency," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(4), pages 1894-1899.
    8. Rohan Sharma & Bibhas Adhikari & Tyll Krueger, 2019. "Self-Organized Corona Graphs: A Deterministic Complex Network Model With Hierarchical Structure," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 22(06), pages 1-22, December.
    9. Tian, Xin & Duan, Xianggang & Sun, Mengdi & Mohammadian, Erfan & Hu, Qinhong & Ostadhassan, Mehdi & Liu, Bo & Ke, Yubin & Pan, Zhejun, 2024. "Evolution of fractal characteristics in shales with increasing thermal maturity: Evidence from neutron scattering, N2 physisorption, and FE-SEM imaging," Energy, Elsevier, vol. 298(C).
    10. Jiao, Bo & Nie, Yuan-ping & Shi, Jian-mai & Huang, Cheng-dong & Zhou, Ying & Du, Jing & Guo, Rong-hua & Tao, Ye-rong, 2016. "Scaling of weighted spectral distribution in deterministic scale-free networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 451(C), pages 632-645.
    11. Tan, Bo & Cheng, Gang & Fu, Shuhui & Wang, Haiyan & Li, Zixu & Zhang, Xuedong, 2022. "Molecular simulation for physisorption characteristics of O2 in low-rank coals," Energy, Elsevier, vol. 242(C).
    12. He, Ji-Huan & Jiao, Man-Li & Gepreel, Khaled A. & Khan, Yasir, 2023. "Homotopy perturbation method for strongly nonlinear oscillators," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 204(C), pages 243-258.
    13. Tian, Feng & Wang, Junlei & Xu, Zhenhua & Xiong, Fansheng & Xia, Peng, 2023. "A nonlinear model of multifractured horizontal wells in heterogeneous gas reservoirs considering the effect of stress sensitivity," Energy, Elsevier, vol. 263(PD).
    14. Wei, Mengke & Han, Xiujing, 2024. "Fast–slow dynamics related to sharp transition behaviors in the Rayleigh oscillator with two slow square wave excitations," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
    15. He, Chun-Hui & Liu, Chao, 2023. "Variational principle for singular waves," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
    16. Guillem Piris & Ignasi Herms & Albert Griera & Montse Colomer & Georgina Arnó & Enrique Gomez-Rivas, 2021. "3DHIP-Calculator—A New Tool to Stochastically Assess Deep Geothermal Potential Using the Heat-In-Place Method from Voxel-Based 3D Geological Models," Energies, MDPI, vol. 14(21), pages 1-21, November.
    17. Maximilian Frick & Stefan Kranz & Ben Norden & David Bruhn & Sven Fuchs, 2022. "Geothermal Resources and ATES Potential of Mesozoic Reservoirs in the North German Basin," Energies, MDPI, vol. 15(6), pages 1-26, March.
    18. Zheng, Yangfeng & Zhai, Cheng & Chen, Aikun & Yu, Xu & Xu, Jizhao & Sun, Yong & Cong, Yuzhou & Tang, Wei & Zhu, Xinyu & Li, Yujie, 2023. "Microstructure evolution of bituminite and anthracite modified by different fracturing fluids," Energy, Elsevier, vol. 263(PB).
    19. Sivashankar, M. & Sabarinathan, S. & Nisar, Kottakkaran Sooppy & Ravichandran, C. & Kumar, B.V. Senthil, 2023. "Some properties and stability of Helmholtz model involved with nonlinear fractional difference equations and its relevance with quadcopter," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    20. Kasala, Erasto E. & Wang, Jinjie & Lwazi, Hussein M. & Nyakilla, Edwin E. & Kibonye, John S., 2024. "The influence of hydraulic fracture and reservoir parameters on the storage of CO2 and enhancing CH4 recovery in Yanchang formation," Energy, Elsevier, vol. 296(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:164:y:2022:i:c:s0960077922008736. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.