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A novel frequency formula and its application for a bead sliding on a wire in fractal space | ||
Journal of Computational Applied Mechanics | ||
دوره 56، شماره 3، مهر 2025، صفحه 627-640 اصل مقاله (673 K) | ||
نوع مقاله: Research Paper | ||
شناسه دیجیتال (DOI): 10.22059/jcamech.2025.396203.1494 | ||
نویسندگان | ||
Guang-Qing Feng* 1؛ Abdulrahman Ali Alsolami2 | ||
1School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo, 454003, China | ||
2Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, 21589, Saudi Arabia | ||
چکیده | ||
The present study investigates the frequency-amplitude relationship of a nonlinear oscillator in fractal space, focusing on the dynamics of a bead sliding along a rotating wire with inhomogeneous angular velocity. Utilizing the two-scale fractal theory, the original fractal differential equation is transformed into an equivalent linear damped system in continuous space, thereby enabling the derivation of an exact analytical solution that does not rely on perturbation methods. A novel frequency formula is proposed that integrates fractal parameters and system constants. The establishment of these expressions is achieved through the application of energy conservation principles and Taylor series approximations, thereby providing explicit expressions for the fractal parameters. Numerical simulations were conducted to verify the analytical results and to demonstrate the influence of the parameters on damping behavior and oscillation profiles. The proposed framework is a versatile analytical tool for the study of fractal-mediated dynamics in mechanical systems, with potential applications in resonant engineering and multiscale materials design. | ||
کلیدواژهها | ||
Fractal space mechanics؛ nonlinear oscillator؛ two-scale fractal theory؛ frequency-amplitude relationship؛ numerical simulation؛ Multiscale system response؛ Bead-on-wire dynamics؛ Nonlinear frequency analysis | ||
مراجع | ||
[1] G. Y. Zhang, J. Gao, B. Q. Xiao, L. Chen, J. Y. Cao, G. B. Long, H. R. Hu, Fractal study on the permeability of power-law fluid in a rough and damaged tree-like branching network, Phys. Fluids, Vol. 36, 2024.
[2] M. X. Liu, J. Gao, B. Q. Xiao, P. L. Wang, H. Z. Y. Li, S. F. Li, G. B. Long, Y. Xu, Fractal model for effective thermal conductivity of composite materials embedded with a damaged tree-like bifurcation network, Fractals, Vol. 32, 2024.
[3] P. Zhang, J. Y. Ding, J. J. Guo, F. Wang, Fractal analysis of cement-based composite microstructure and its application in evaluation of macroscopic performance of cement-based composites: a review, Fractal Fract, Vol. 8, 2024.
[4] M. Ungarish, Self-similar flow of Newtonian and power-law viscous gravity currents in a confining gap in rectangular and axisymmetric geometries, J. Fluid Mech, Vol. 1007, 2025.
[5] N. Anjum, C. H. He, J. H. He, Two-scale fractal theory for the population dynamics Fractals, Vol. 29, 2021.
[6] N. Anjum, Q. T. Ain, X. X. Li, Two-scale mathematical model for tsunami wave, Gem-Int. J. Geomat, Vol. 12, pp. 1-12, 2021.
[7] Y. R. Zhang, N. Anjum, D. Tian, A. A. Alsolami, Fast and accurate population forecasting with two-scale fractal population dynamics and its application to population economics, Fractals, Vol. 32, 2024.
[8] J. H. He, Y. O. El-Dib, A tutorial introduction to the two-scale fractal calculus and its application to the fractal Zhiber-Shabat oscillator, Fractals, Vol. 29, 2021.
[9] A. Elias-Zuniga, O. Martinez-Romero, D. O. Trejo, L. M. Palacios-Pineda, Fractal equation of motion of a non-Gaussian polymer chain: investigating its dynamic fractal response using an ancient Chinese algorithm, J. Math. Chem, Vol. 60, pp. 461-473, 2022.
[10] H. Y. Song, A thermodynamic model for a packing dynamical system, Thermal Science, Vol. 24, pp. 2331-2335, 2020.
[11] M. Bayat, I. Pakar, M. Bayat, M. Bayat, I. Pakar, M. Bayat, Recent developments of some asymptotic methods and their applications for nonlinear vibration equations in engineering problems: a review, Lat. Am. J. Solids Struct, Vol. 9, pp. 145-234, 2012.
[12] B. Moussa, M. Youssouf, N. A. Wassiha, P. Youssouf, Homotopy perturbation method to solve Duffing-Van der Pol equation, Adv. Differ. Equ. Control Process, Vol. 31, pp. 299-315, 2024.
[13] G. Q. Feng, Higher-order homotopy perturbation method for the fractal rotational pendulum oscillator, J. Vib. Eng. Technol, Vol. 12, pp. 2829-2834, 2024.
[14] J. H. He, C. H. He, A. A. Alsolami, A good initial guess for approximating nonlinear oscillators by the homotopy perturbation method, Facta Univ. Ser. Mech. Eng, Vol. 21, No. 1, pp. 21-29, 2023.
[15] N. A. M. Alshomrani, W. G. Alharbi, I. M. A. Alanazi, L. S. M. Alyasi, G. N. M. Alrefaei, S. A. Al'Amri, A. H. Q. Alanzi, Homotopy perturbation method for solving a nonlinear system for an epidemic, Adv. Differ. Equ. Control Process, Vol. 31, pp. 347-355, 2024.
[16] N. Anjum, A. Rasheed, J. H. He, A. A. Alsolami, Free vibration of a tapered beam by the Aboodh transformbased variational iteration method, J. Comput. Appl. Mech, Vol. 55, pp. 440-450, 2024.
[17] X. Wang, T. A. Elgohary, Z. Zhang, T. H. Tasif, H. Y. Feng, S. N. Atluri, An adaptive local variational iteration method for orbit propagation in astrodynamics problems, J. Astronaut. Sci, Vol. 70, 2023.
[18] A. A. Rossikhin, V. I. Mileshin, Application of the harmonic balance method to calculate the first booster stage tonal noise, Math. Model. Comput. Simul, Vol. 16, pp. 63-75, 2024.
[19] Q. S. Wang, Z. P. Yan, H. H. Da, An efficient multiple harmonic balance method for computing quasi-periodic responses of nonlinear systems, J. Sound Vib, Vol. 554, 2023.
[20] J. Li, Y. F. Xin, T. T. Murmy, Exploring comfort and vibration dampening in fashion design in fabrics with innovative use of nanoparticle additives, Adv. Nano Res, Vol. 17, pp. 465-471, 2024.
[21] Y. Zhang, Q. H. Guo, X. H. Wan, L. Y. Zheng, Subwavelength topological edge states in a mechanical analogy of nanoparticle chain, New J. Phys, Vol. 27, 2025.
[22] D. Arifin, S. Mcwilliam, Negating self-induced parametric excitation in capacitive ring-based MEMS Coriolis vibrating gyroscopes, J. Sound Vib, Vol. 607, 2025.
[23] C. H. He, A variational principle for a fractal nano/microelectromechanical (N/MEMS) system, Int. J. Numer. Methods Heat Fluid Flow, Vol. 33, pp. 351-359, 2023.
[24] J. H. He, C. H. He, A. A. Alsolami, Periodic solution of a micro-electromechanical system, Facta Univ. Ser. Mech. Eng, Vol. 22, pp. 187-198, 2024.
[25] J. Song, C. Xia, G. S. Shan, Z. Q. Wang, T. Ono, G. G. Cheng, D. F. Wang, Temperature sensing and energy harvesting with a MEMS parametric coupling device under low frequency vibrations, J. Sound Vib, Vol. 585, 2024.
[26] Y. O. El-Dib, Stability analysis of a time-delayed Van der Pol-Helmholtz-Duffing oscillator in fractal space with a non-perturbative approach, Commun. Theor. Phys, Vol. 76, 2024.
[27] Y. O. El-Dib, N. S. Elgazery, Y. M. Khattab, H. A. Alyousef, An innovative technique to solve a fractal damping Duffing-jerk oscillator, Commun. Theor. Phys, Vol. 75, 2023.
[28] G. M. Ismail, G.M. Moatimid, M. I. Yamani, Periodic solutions of strongly nonlinear oscillators using He’s frequency formulation, Eur. J. Pure Appl. Math, Vol. 17, pp. 2155-2172, 2024.
[29] G. Hashemi, A novel analytical approximation approach for strongly nonlinear oscillation systems based on the energy balance method and He’s frequency-amplitude formulation, Comput. Methods Differ. Equ, Vol. 11, pp. 464-477, 2023.
[30] J. H. He, The simpler, the better: Analytical methods for nonlinear oscillators and fractional oscillators, J. Low Freq. Noise Vib. Act. Control, Vol. 38, pp. 1252-1260, 2019.
[31] M. A. Kawser, M. A. Alim, N. Sharif, Analyzing nonlinear oscillations with He’s frequency-amplitude method and numerical comparison in jet engine vibration system, Heliyon, Vol. 10, 2024.
[32] K. Tsaltas, An improved one-step amplitude-frequency relation for nonlinear oscillators, Results Phys, Vol. 54, 2023.
[33] J. H. He, Frequency-amplitude relationship in nonlinear oscillators with irrational nonlinearities, Spectr. Mech. Eng. Oper. Res, Vol. 2, pp. 121-129, 2025.
[34] J. H. He, The simplest approach to nonlinear oscillators, Results Phys, Vol. 15, 2019.
[35] Y. O. El-Dib, N. S. Elgazery, A novel pattern in a class of fractal models with the non-perturbative approach, Chaos Solitons Fractals, Vol. 164, 2022.
[36] Y. O. El-Dib, N. S. Elgazery, An efficient approach to converting the damping fractal models to the traditional system, Commun. Nonlinear Sci. Numer. Simul, Vol. 118, 2023.
[37] Y. O. El-Dib, A dynamic study of a bead sliding on a wire in fractal space with the non-perturbative technique, Arch. Appl. Mech, Vol. 94, pp. 571-588, 2024.
[38] G. M. Moatimid, Sliding bead on a smooth vertical rotated parabola: stability configuration, Kuwait J. Sci, Vol. 47, pp. 6-21, 2020. | ||
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