THERMAL SCIENCE

International Scientific Journal

Authors of this Paper

External Links

Jun-Feng Lu

,

Li Ma

ANALYSIS OF A FRACTAL MODIFICATION OF ATTACHMENT OSCILLATOR

ABSTRACT
In this paper, we consider a combined technique for a fractal modification of the attachment oscillator arising from nanotechnology. This technique is called as TSFT-GRHBM by coupling the two-scale fractal transformation and the global residue harmonic balance method. The approximations and frequencies of this fractal attachment oscillator are given without linearization. Numerical results are provided to confirm its efficiency.
KEYWORDS
attachment oscillator, fractional complex transformation, global residue harmonic balance method
PAPER SUBMITTED: 2022-11-14
PAPER REVISED: 2023-05-01
PAPER ACCEPTED: 2023-05-19
PUBLISHED ONLINE: 2024-05-18
DOI REFERENCE: https://doi.org/10.2298/TSCI2403153L
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2024, VOLUME 28, ISSUE Issue 3, PAGES [2153 - 2163]
REFERENCES
  1. Liu, F. J., et al., Thermal Oscillation Arising in a Heat Shock of a Porous Hierarchy and Its Application, Facta Universitatis Series: Mechanical Engineering, 20 (2022), 3, pp. 633-645
  2. Lin, L., et al., Release Oscillation in a Hollow Fiber - Part 2: The Effect of Its Frequency on Ions Release and Experimental Verification, Journal of Low Frequency Noise Vibration and Active Control, 40 (2021), 2, pp. 1067-1071
  3. He, C. H., et al., Controlling the Kinematics of a Spring-Pendulum System Using an Energy Harvesting Device, Journal of Low Frequency Noise, Vibration & Active Control, 41 (2022), 3, pp. 1234-1257
  4. He, C. H., et al., Hybrid Rayleigh -Van der Pol-Duffing Oscillator (HRVD): Stability Analysis and Controller, Journal of Low Frequency Noise, Vibration & Active Control, 41 (2022), 1 pp. 244-268
  5. Faghidian, S. A., Tounsi, A., Dynamic Characteristics of Mixture Unified Gradient Elastic Nanobeams, Facta Universitatis Series: Mechanical Engineering, 20 (2022), 3, pp. 539-552
  6. He, J.-H., et al., Pull-in Stability of a Fractal System and Its Pull-in Plateau, Fractals, 30 (2022), 9, 2250185
  7. Tian, D., et al., Fractal N/MEMS: from Pull-in Instability to Pull-in Stability, Fractals, 29 (2021), 2, 2150030
  8. Tian, D., He, C. H., A Fractal Micro-Electromechanical System and Its Pull-in Stability, Journal of Low Frequency Noise Vibration and Active Control, 40 (2021), 3, pp. 1380-1386
  9. He, C. H., A Variational Principle for a Fractal Nano/Microelectromechanical (N/MEMS) System, International Journal of Numerical Methods for Heat & Fluid Flow, 33 (2023), 1, pp. 351-359
  10. He, J.-H., Fast Identification of the Pull-in Voltage of a Nano/Micro-Electromechanical System, Journal of Low Frequency Noise Vibration and Active Control, 41 (2022), 2, pp. 566-571
  11. Ali, M., et al., Homotopy Perturbation Method for the Attachment Oscillator Arising in Nanotechnology, Fibers and Polymers, 22 (2021), 6, pp. 1601-1606
  12. Li, X. X., He, J.-H., Nanoscale Adhesion and Attachment Oscillation under the Geometric Potential. Part 1: The Formation Mechanism of Nanofiber Membrane in the Electrospinning, Results in Physics, 12 (2019), Mar., pp. 1405-1410
  13. Li, X. X., He, J.-H. Bubble Electrospinning with an Auxiliary Electrode and an Auxiliary Air Flow, Recent Patents on Nanotechnology, 14 (2020), 1, pp. 45-42
  14. Lin, L., et al., Fabrication of PVDF/PES Nanofibers with Unsmooth Fractal Surfaces by Electrospinning: A General Strategy and Formation Mechanism, Thermal Science, 25 (2021), 2B, pp. 1287-1294
  15. Li, X. X., et al., Multiple Needle Electrospinning for Fabricating Composite Nanofibers with Hierarchical Structure, Journal of Donghua University (English Edition), 38 (2021), 1, pp. 63-67
  16. Qian, M. Y., He, J.-H., Collection of Polymer Bubble as a Nanoscale Membrane, Surfaces and Interfaces, 28 (2022), 101665
  17. He, J.-H., et al. The Maximal Wrinkle Angle During the Bubble Collapse and Its Application to the Bubble Electrospinning, Frontiers in Materials, 8 (2022), 800567
  18. He, J.-H., A Tutorial Review on Fractal Spacetime and Fractional Calculus, International Journal of Theoretical Physics, 53 (2014), Nov., pp. 3698-3718
  19. He, J.-H., Fractal Calculus and Its Geometrical Explanation, Results in Physics, 10 (2018), Sept., pp. 272-276
  20. Qian, M. Y., He, J.-H., Two-Scale Thermal Science for Modern Life: Making the Impossible Possible, Thermal Science, 26 (2022), 3B, pp. 2409-2412
  21. Anjum, N., et al., Two-Scale Fractal Theory for the Population Dynamics, Fractals, 29 (2021), 7, 2150182
  22. He, J.-H., El-Dib, Y. O., A Tutorial Introduction to the Two-Scale Fractal Calculus and Its Application to the Fractal Zhiber-Shabat Oscillator, Fractals, 29 (2021), 8, 2150268
  23. Tian, D., et al., Fractal Pull-in Stability Theory for Microelectromechanical Systems, Frontiers in Physics, 9 (2021), 606011
  24. Elías-Zuniga, A., et al., Analytical Solution of the Fractal Cubic-quintic Duffing Equation, Fractals, 29 (2020), 4, 2150080
  25. He, C. H., et al., Low Frequency Property of a Fractal Vibration Model for a Concrete Beam, Fractals, 29 (2021), 5, 2150117
  26. He, J. H., et al., Homotopy Perturbation Method for Fractal Duffing Oscillator with Arbitrary Conditions, Fractals, 30 (2022), 9, 22501651
  27. He, J.-H., et al., Forced Non-linear oscillator in a Fractal Space, Facta Universitatis, Series: Mechanical Engineering, 20 (2022), 1, pp. 1-20
  28. He, J.-H., et al., Homotopy Perturbation Method for the Fractal Toda Oscillator, Fractal and Fractional, 5 (2021), 93
  29. Feng, G. Q., Niu, J. Y., An Analytical Solution of the Fractal Toda Oscillator, Results in Physics, 44 (2023), 106208
  30. He, J. H., et al., A Fractal Modification of Chen-Lee-Liu Equation and Its Fractal Variational Principle, International Journal of Modern Physics B, 35 (2021), 2150214
  31. Lu, J., Chen, L., Numerical Analysis of a Fractal Modification of Yao-Cheng Oscillator, Results in Physics, 38 (2022), 105602
  32. He, C. H., El-Dib, Y. O., A Heuristic Review on the Homotopy Perturbation Method for Non-conservative Oscillators, Journal of Low Frequency Noise Vibration and Active Control, 41 (2022), 2, pp. 572-603
  33. He, J.-H., et al., Homotopy Perturbation Method for Strongly Non-linear Oscillators, Mathematics and Computers in Simulation, 204 (2023), Feb., pp. 243-258
  34. He, J.-H., et al., A Good Initial Guess for Approximating Non-linear Oscillators by the Homotopy Perturbation Method, Facta Universitatis, Series: Mechanical Engineering, 21 (2023), 1, pp. 21-29
  35. He, J.-H., The Simplest Approach to Non-linear Oscillators, Results in Physics, 15 (2019), 102546
  36. Ma, H. J., Simplified Hamiltonian-Based Frequency-Amplitude Formulation for Non-linear Vibration Systems, Facta Universitatis-Series Mechanical Engineering, 20 (2022), 2, pp. 445-455
  37. Tian, Y., Frequency Formula for a Class of Fractal Vibration System, Reports in Mechanical Engineering, 3 (2022), 1, pp. 55-61
  38. Lyu, G. J., et al., Straightforward Method for Non-linear Oscillators, Journal of Donghua University (English Edition), 40 (2023), 1, pp. 105-109
  39. He, J.-H., The Simpler, the Better: Analytical Methods for Non-linear Oscillators and Fractional Oscillators, Journal of Low Frequency Noise Vibration and Active Control, 38 (2019), 3-4, pp. 1252-1260
  40. He, J.-H., et al., Pull-down Instability of the Quadratic Non-linear Oscillators, Facta Universitatis, Series: Mechanical Engineering, 21 (2023), 2, pp. 191-120
  41. He, J.-H., Seeing with a Single Scale is Always Unbelieving: From Magic to Two-scale Fractal, Thermal Science, 25 (2021), 2B, pp. 1217-1219
  42. Ju, P., Xue, X., Global Residue Harmonic Balance Method to Periodic Solutions of a Class of Strongly Non-linear Oscillators, Applied Mathematical Modelling, 38 (2014), 24, pp. 6144-6152
  43. Lu, J., Ma, L., Numerical Analysis of a Fractional Non-linear Oscillator with Coordinate-Dependent Mass, Results in Physics, 43 (2022), 106108
  44. Lu, J., Global Residue Harmonic Balance Method for Strongly Non-linear Oscillator with Cubic and Harmonic Restoring Force. Journal of Low Frequency Noise, Vibration and Active Control, 41 (2022), 4, pp. 1402-1410
  45. Lu, J., Ma, L., Numerical Analysis of Space-time Fractional Benjamin-Bona-Mahony Equation, Thermal Science, 27 (2023), 3A, pp. 1755-1762
  46. He, J.-H., Li, Z. B., Converting Fractional Differential Equations into Partial Differential Equations, Thermal Science, 16 (2012), 2, pp. 331-334
  47. Li, Z. B., He, J.-H., Fractional Complex Transform for Fractional Differential Equations, Mathematical and Computational Applications, 15 (2010), 5, pp. 970-973
  48. Chen, B., et al., Numerical Investigation of the Fractal Capillary Oscillator. Journal of Low Frequency Noise, Vibration and Active Control, 42 (2023), 2, pp. 579-588
  49. Lu, J., Application of Variational Principle and Fractal Complex Transformation to (3+1)-Dimensional Fractal Potential-YTSF Equation, Fractals, 32 (2024), 1, 2450027
  50. Sun, J., Variational Principle and Solitary Wave of the Fractal Fourth-order Nonlinear Ablowitz-Kaup-Newell-Segur Water Wave Model, Fractals, 31 (2023), 5, 2350036
  51. Lu, J., Variational Approach for (3+1)-Dimensional Shallow Water Wave Equation, Results in Physics, 56 (2024), 107290
  52. Kuo, P. H., et al., Novel Fractional-Order Convolutional Neural Network Based Chatter Diagnosis Approach in Turning Process with Chaos Error Mapping, Non-Linear Dynamics, 111 (2023), 8, pp. 7547-7564
  53. Jing, X. B., et al., Stability Analysis in Micro Milling Based on p-Leader Multifractal Method, Journal of Manufacturing Process, 77 (2022), May, pp. 495-507
PDF VERSION [DOWNLOAD]
Analysis of a fractal modification of attachment oscillator

© 2024 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence