THERMAL SCIENCE
International Scientific Journal
SOLITARY WAVE SOLUTION FOR THE NON-LINEAR BENDING WAVE EQUATION BASED ON HE'S VARIATIONAL METHOD
ABSTRACT
A beam vibration originating in the beam porous structure or on a non-smooth boundary might make its vibrating energy concentrated on a single wave, leading to a solitary wave. This paper applies the variational approach to analysis of the soliton basic property, and the effect of the fractal dimensions on the solitary wave is elucidated. This paper is to draw attention the beam soliton property be-yond its widely known resonance and periodic and chaotic properties.
KEYWORDS
PAPER SUBMITTED: 2022-11-23
PAPER REVISED: 2023-05-25
PAPER ACCEPTED: 2023-05-27
PUBLISHED ONLINE: 2024-05-18
THERMAL SCIENCE YEAR
2024, VOLUME
28, ISSUE
Issue 3, PAGES [1983 - 1991]
- Limkatanyu, S., et al., Bending, Bucking and Free Vibration Analyses of Nanobeam-Substrate Medium Systems, Facta Universitatis Series: Mechanical Engineering, 20 (2022), 3, pp. 561-587
- Hoang, L. T. T., A New C0 Third-Order Shear Deformation Theory for the Non-linear Free Vibration Analysis of Stiffened Functionally Graded Plates, Facta Universitatis Series: Mechanical Engineering, 19 (2021), 2, pp. 285-305
- Jankowski, P., Detection of Non-Local Calibration Parameters and Range Interaction for Dynamics of FGM Porous Nanobeams Under Electro-Mechanical Loads, Facta Universitatis Series: Mechanical Engineering, 20 (2022), 3, pp. 457-478
- Faghidian, S. A., Tounsi, A., Dynamic Characteristics of Mixture Unified Gradient Elastic Nanobeams, Facta Universitatis Series: Mechanical Engineering, 20 (2022), 3, pp. 539-552
- 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
- He, J.-H., et al., Pull-in Stability of a Fractal System and Its Pull-In Plateau, Fractals, 30 (2022), 9, 2250185
- He, J.-H., et al., Periodic Property and Instability of a Rotating Pendulum System, Axioms, 10 (2021), 3, 191
- Tian, D., et al., Fractal N/MEMS: From Pull-in Instability to Pull-in Stability, Fractals, 29 (2021), 2, 2150030
- 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
- 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
- Li, S. Q., Zhou, L. Q., Chaos Analysis for a Class of Impulse Duffing van der Pol System, Zeitschrift fur Naturforschung Section A, 78 (2023), 5, pp. 395-403
- Zhang, J. L., et al., Resonance and Bifurcation of Fractional Quintic Mathieu-Duffing System, Chaos, 33 (2023), 2, 023131
- Kim, J. J., Hong, W. P., New Solitary-Wave Solutions for the Generalized Reaction Duffing Model and Their Dynamics, Zeitschrift fur Naturforschung Section A, 59 ( 2004),11, pp. 721-728
- He, J.-H., et al., Forced Non-linear Oscillator in a Fractal Space, Facta Universitatis Series: Mechanical Engineering, 20 (2022), 1, pp. 1-20
- Sawada, K., Kotera, T., Method for Finding N-Soliton Solutions of KdV Equation and Kdv-like Equation, Progress of Theoretical Physics, 51 (1974), 5, pp. 1355-1367
- Wang, K. L., et al., Physical Insight of Local Fractional Calculus and Its Application to Fractional KdV-Burgers-Kuramoto Equation, Fractals, 27 (2019), 7, 1950122
- Wang, K. L., He, C. H., A Remark on Wang's Fractal Variational Principle, Fractals, 27 (2019), 8, 1950134
- He, J.-H., et al., Solitary Waves Travelling Along an Unsmooth Boundary, Results in Physics, 24 (2021), 104104
- Ji, F. Y., et al., A Fractal Boussinesq Equation for Non-linear Transverse Vibration of a Nanofiber-Reinforced Concrete Pillar, Applied Mathematical Modelling, 82 (2020), June, pp. 437-448
- 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
- Kuo, P.-H., et al., A Thermal Displacement Prediction System with an Automatic LRGTVAC-PSO Optimized Branch Structured Bidirectional GRU Neural Network, IEEE Sensors Journal, 23 (2023), 12, pp. 12574-12586
- 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
- He, J.-H., et al., Hamiltonian-Based Frequency-Amplitude Formulation for Non-linear Oscillators, Facta Universitatis-Series Mechanical Engineering, 19 (2021), 2, pp. 199-208
- Harada, Y., Asakura, T., Radiation Forces on a Dielectric Sphere in the Rayleigh Scattering Regime, Optics Communications, 124 (1996), 5-6, pp. 529-541
- Liu, Z. F., et al., Study on the Propagation Characteristics of Non-linear Bending Wave Propagation in Beams (in Chinese), Theoretical and Applied Mechanics, 39 (2007), 2, pp. 238-244
- 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
- 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
- He, J.-H., et al., Homotopy Perturbation Method for Strongly Non-linear Oscillators, Mathematics and Computers in Simulation, 204 (2023), Feb., pp. 243-258
- 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
- He, J.-H., et al., Stability of Three Degrees-Of-Freedom Auto-Parametric System, Alexandria Engineering Journal, 61 (2022), 11, pp. 8393-8415
- He, C. H., et al., Low Frequency Property of a Fractal Vibration Model for a Concrete Beam, Fractals, 29 (2021), 5, 2150117
- He, C. H., Liu, C., A Modified Frequency-Amplitude Formulation for Fractal Vibration Systems, Fractals, 30 (2022), 3, 2250046
- He, J.-H., et al., Homotopy Perturbation Method for Fractal Duffing Oscillator with Arbitrary Conditions, Fractals, 30 (2022), 9, 22501651
- He, J.-H., et al., Fractal Oscillation and Its Frequency-Amplitude Property, Fractals, 29 (2021), 4, 2150105
- He, C. H., Liu, C., Fractal Dimensions of a Porous Concrete and Its Effect on the Concrete's Strength, Facta Universitatis Series: Mechanical Engineering, 21 (2023), 1, pp. 137-150
- He, C. H., et al., A Novel Bond Stress-Slip Model for 3-D Printed Concretes, Discrete and Continuous dynamical Systems-Series S, 15 (2022), 7, pp. 1669-1683
- Liu, H., et al., Influence of Pore Defects on the Hardened Properties of 3D Printed Concrete with Coarse Aggregate, Additive Manufacturing, 55 (2022), 102843
- He, C. H., Liu, C., Fractal Approach to the Fluidity of a Cement Mortar, Non-linear Engineering, 11 (2022), 1, pp. 1-5
- He, C. H., et al., A Fractal Model for the Internal Temperature Response of a Porous Concrete, Applied and Computational Mathematics, 21 (2022), 1, pp. 71-77
- He J.-H., et al., A Tutorial Introduction to the Two-Scale Fractal Calculus and Its Application to the Fractal Zhiber-Shabat Oscillator, Fractals, 29 (2021), 8, 2150268
- He, J.-H., Ji, F. Y., Two-Scale Mathematics and Fractional Calculus for Thermodynamics, Thermal Science, 23 (2019), 4, pp. 2131-2133
- 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
- Zhang, P. L., Wang, K. J., A New Fractional Thermal Model for the Cu/low-k Interconnects in Nanometer Integrated Circuit, Thermal Science, 26 (2022), 3B, pp. 2413-2418
- Lv, G. J., Dynamic Behaviors for the Graphene Nano/Microelectromechanical System in a Fractal Space, Journal of Low Frequency Noise, Vibration & Active Control, 42 (2023), 3, pp. 1107-1116
- He, J.-H., Qian, M. Y., A Fractal Approach to the Diffusion Process of Red Ink in a Saline Water, Thermal Science, 26 (2022), 3B, pp. 2447-2451
- He, J.-H., et al., Evans Model for Dynamic Economics Revised, AIMS Mathematics, 6 (2021), 9, pp. 9194-9206
- Anjum, N., et al., Two-Scale Fractal Theory for the Population Dynamics, Fractals, 29 (2021), 7, 2150182
- Kou, S. J., et al., Fractal Boundary Layer and Its Basic Properties, Fractals, 30 (2022), 9, 22501729
- Wu, P. X., et al., Solitary Waves of the Variant Boussinesq-Burgers Equation in a Fractal-Dimensional Space, Fractals, 30 (2022), 3, 2250056
- He, C. H., et al., Taylor Series Solution for Fractal Bratu-Type Equation Arising in Electrospinning Process, Fractals, 28 (2000), 1, 2050011
- Zhang, P. L., Wang, K. J., A New Non-linear Fractal Vibration of the Euler-Bernoulli Beams in a Microgravity Space, Journal of Low Frequency Noise, Vibration & Active Control, 42 (2023),1, pp. 222-230
- Elias-Zuniga, A., et al., Recent Strategy to Study Fractal-Order Viscoelastic Polymer Materials Using an Ancient Chinese Algorithm and He's Formulation, J Journal of Low Frequency Noise, Vibration & Active Control, 41 (2022), 3, pp. 842-851
- He J.-H., Semi-Inverse Method of Establishing Generalized Variational Principles for Fluid Mechanics with Emphasis on Turbomachinery Aerodynamics, International Journal of Turbo & Jet-Engines, 14 (1997), 1, pp. 23-28
- He J.-H., Variational Approach to Impulsive Differential Equations Using the Semi-Inverse Method, Zeitschrift fur Naturforschung Section A, 66 (2011), 10-11, pp. 632-634
- He, J.-H., Variational Principles for Some Non-linear Partial Differential Equations with Variable Coefficients, Chaos Solitons Fractals, 19 (2004), 4, pp. 847-851
- He, C. H., Liu, C., Variational Principle for Singular Waves, Chaos, Solitons & Fractals, 172 (2023), 113566
- Wang, S. Q., A Variational Approach to Non-linear Two-Point Boundary Value Problems, Computers & Mathematics with Applications, 58 (2009), 11, pp. 2452-2455
- Shen, Y. Y., et al., Subcarrier-Pairing-Based Resource Optimization for OFDM Wireless Powered Relay Transmissions with Time Switching Scheme, IEEE Transactions on Signal Processing, 65 (2016), 5, pp. 1130-1145
- Sun, J. S., Variational Principle and Solitary Wave of the Fractal Fourth-Order Non-linear Ablowitz-Kaup-Newell-Segur Water Wave Model, Fractals, 31 (2023), 5, 2350036
- Sun J. S., Approximate Analytic Solution of the Fractal Klein-Gordon Equation, Thermal Science, 25 (2021), 2, pp. 1489-1494
- He J.-H., On the Fractal Variational Principle for the Telegraph Equation, Fractals, 29 (2021), 1, 2150022
- He, J.-H., et al., On a Strong Minimum Condition of a Fractal Variational Principle, Appl. Math. Lett., 119 (2021), 107199