Article
Thermodynamics
Shuxian Deng, Xinxin Ge
Summary: This paper introduces a new Laplace-like integral transform named He-Laplace transform, and explains its effectiveness in solving fractal differential equations. An example involving the Phi-four equation with He's derivative is used to demonstrate the main advantages of this technology.
Article
Engineering, Mechanical
Ji-Huan He, Chun-Hui He, Abdulrahman Ali Alsolami
Summary: A good initial guess and an appropriate homotopy equation are the two main factors in the applications of the homotopy perturbation method. In this article, a cosine function is used as an initial guess for a nonlinear oscillator. A general approach to construct the initial guess and the homotopy equation is recommended. The effectiveness of the method is demonstrated using the Duffing oscillator as an example.
FACTA UNIVERSITATIS-SERIES MECHANICAL ENGINEERING
(2023)
Article
Mathematics, Applied
Yusry O. El-Dib
Summary: This study derived an improved frequency formula for immediate frequency estimation of a damped nonlinear oscillator and compared the analytical solution with a numerical solution, showing high accuracy in the estimated frequency.
ZAMM-ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK
(2021)
Article
Engineering, Mechanical
Guang-qing Feng
Summary: This study aims to quickly understand a fractal nonlinear system by obtaining an analytical solution through a simple calculation. The focus is on a fractal model of a simple pendulum connected to a rotating rigid frame.
JOURNAL OF VIBRATION ENGINEERING & TECHNOLOGIES
(2023)
Article
Acoustics
Guang-Qing Feng
Summary: This article discusses the increasing importance of nonlinear oscillation in engineering and introduces a simple method proposed by Ji-Huan He to establish a fractal undamped Duffing equation. The two-scale transform method and the fractal frequency formula are used to find the approximate frequency of the fractal oscillator, showing that He's frequency formula is a unique tool for fractal equations.
JOURNAL OF LOW FREQUENCY NOISE VIBRATION AND ACTIVE CONTROL
(2021)
Article
Acoustics
Qiu-Ping Ji, Jun Wang, Li-Xin Lu, Chang-Feng Ge
Summary: This paper combines Li-He's homotopy perturbation method with the energy method to propose an approximate solution for a tangent nonlinear packaging system. By constructing a higher order homotopy equation and utilizing the energy method, the maximal displacement and frequency of the system are improved with higher accuracy. A comparison with the numerical solution obtained by the Runge-Kutta method shows that the shock responses of the system solved by the new method are more effective with a relative error of 0.15%.
JOURNAL OF LOW FREQUENCY NOISE VIBRATION AND ACTIVE CONTROL
(2021)
Article
Engineering, Mechanical
Ji-Huan He, Galal M. Moatimid, Marwa H. Zekry
Summary: This paper establishes a fractal-differential model for a nonlinear vibration system in a fractal space. The basic properties of a fractal oscillator are revealed using the fractal Duffing-Van der Pol oscillator as an example. The stability criteria are obtained through analytic approximate solutions and nonlinear frequency analysis. Linearized stability theory and multiple time scales technique are utilized for stability analysis.
FACTA UNIVERSITATIS-SERIES MECHANICAL ENGINEERING
(2022)
Article
Mathematics, Applied
KangLe Wang
Summary: This study proposes a fractal vibration model to investigate the effect of microgravity on vibration properties, utilizing fractal derivative, He's frequency formula, and fractal semi-inverse method to establish the model and obtain frequency. The research demonstrates that the method is simple, efficient, and precise, clarifying the relationship between frequency and amplitude, and discussing the impact of microgravity conditions on vibration properties.
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS
(2021)
Article
Mathematics, Interdisciplinary Applications
Ji-Huan He, Yusry O. El-Dib, Amal A. Mady
Summary: This paper demonstrates the basic properties of a fractal oscillator using fractal variational theory and introduces a new form of the Toda oscillator free of the exponential nonlinear term through the homotopy perturbation method. The analytical solution is validated through numerical tests, showing excellent agreement, and the graphical illustration further elucidates the effect of the order of the fractal derivative on the vibration property.
FRACTAL AND FRACTIONAL
(2021)
Article
Multidisciplinary Sciences
Jiahua Fang, Muhammad Nadeem, Mustafa Habib, Ali Akgul
Summary: In this paper, a scheme using the Mohand transform and the homotopy perturbation method is developed to handle fractional-order shock wave equations and wave equations. The approach allows for obtaining series solutions from the recurrence relation after only a few iterations and presents approximate and precise solutions in the form of convergent results.
Article
Multidisciplinary Sciences
Galal M. Moatimid, A. T. El-Sayed, Hala F. Salman
Summary: In this article, the inverted pendulum is controlled using nonlinear control theory. The equation of motion of its substructure is derived from classical analytical mechanics. The Taylor expansion is employed to analyze the system due to the inclusion of restoring forces. A satisfactory periodic solution is obtained using the modified Homotopy perturbation method and justified using numerical techniques. A positive position feedback control is developed to dampen vibrations in the system.
SCIENTIFIC REPORTS
(2023)
Article
Mathematics, Interdisciplinary Applications
Mohammed Kbiri Alaoui, Rabia Fayyaz, Adnan Khan, Rasool Shah, Mohammed S. Abdo
Summary: In this article, the solution of the time-fractional Belousov-Zhabotinskii reaction is found using modified Adomian decomposition method and homotopy perturbation method with Yang transform. The obtained solution is in series form, which helps in investigating the analytical solution of the system. The proposed methods are verified for accuracy through an illustrative example and comparison with graphs, showing the desired rate of convergence to the exact solution. The technique's primary benefit lies in its low computational requirements and applicability to various domains.
Article
Mathematics, Interdisciplinary Applications
Muhammad Imran Liaqat, Ali Akgul
Summary: This study proposes a novel combined computational approach using conformable natural transform and the homotopy perturbation method for the extraction of analytical and numerical solutions of the time-fractional conformable Schrodinger equation. The method shows high accuracy and convergence rates according to the analysis of relative, recurrence, and absolute errors.
CHAOS SOLITONS & FRACTALS
(2022)
Article
Mathematics
Mohamed M. Mousa, Fahad Alsharari
Summary: This work outlines the main concept of the homotopy perturbation method (HPM) and proves convergence theorems for solving various classes of nonlinear integral, integro-differential, and differential equations. The efficiency of the technique is explored by applying it to solve several classes of equations.
Article
Engineering, Mechanical
Chein-Shan Liu, Chih-Wen Chang
Summary: This paper proposes a new method to enhance the accuracy of analytic solution by using a linearized perturbation method. By linearizing the nonlinear ODE with respect to a zeroth order solution, a series of linear ODEs are solved sequentially to obtain higher order approximate analytic solutions. The method also determines the frequency explicitly by solving a frequency equation. Additionally, the paper develops a novel perturbation method for solving the Mathieu equations with periodic forcing terms and provides accurate formulas for nonlinear oscillators.
MECHANICAL SYSTEMS AND SIGNAL PROCESSING
(2022)
Article
Mathematics, Interdisciplinary Applications
Pin-Xia Wu, Qian Yang, Ji-Huan He
Summary: In this study, we focused on the fractal variant Boussinesq-Burgers equation, which accurately describes the motion of shallow water along an unsmooth boundary. By establishing a fractal variational principle, we obtained two types of soliton solutions and found that the order of the fractal derivative has a significant impact on the wave propagation process.
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY
(2022)
Editorial Material
Materials Science, Multidisciplinary
Ji-Huan He, Man-Yu Qian, Ya Li
Summary: This paper investigates the angle variation of polymer bubbles during bubble electrospinning, and finds that the maximal angle is about 49°, which can be used for the optimal design of nozzle to fabricate nanofibers with specific morphologies.
FRONTIERS IN MATERIALS
(2022)
Article
Chemistry, Physical
Man-Yu Qian, Ji-Huan He
Summary: A novel bubble spinning process was designed to produce nanoscale artificial membranes. By enlarging the bubble size, the thickness of the bubble wall can be reduced to several tens of nanometers, resulting in the formation of nanoscale membranes from the fragments of broken bubbles. This process demonstrates great potential for biomimetic fabrication of nanoscale membranes.
SURFACES AND INTERFACES
(2022)
Article
Engineering, Multidisciplinary
Naveed Anjum, Jamshaid Ul Rahman, Ji-Huan He, Md Nur Alam, Muhammad Suleman
Summary: Periodic behavior analysis of nano/microelectromechanical systems (N/MEMS) is important for their applications in microinstruments. This study explores the periodicity of oscillatory problems in N/MEMS using a coupled approach of variational iteration method and Laplace transform. The results show that this method provides accurate frequency-amplitude relationship and good agreement with observations numerically.
MATHEMATICAL PROBLEMS IN ENGINEERING
(2022)
Article
Engineering, Multidisciplinary
Ji-Huan He, Mahmoud H. Taha, Mohamed A. Ramadan, Galal M. Moatimid
Summary: This paper presents a new numerical technique for solving a system of linear Fredholm integral equations of the second kind. The method introduces a coupling between hybrid Bernstein functions and improved block-pulse functions. Numerical examples demonstrate the promising and efficient nature of this approach.
MATHEMATICAL PROBLEMS IN ENGINEERING
(2022)
Article
Materials Science, Multidisciplinary
Ji-Huan He, T. S. Amer, H. F. El-Kafly, A. A. Galal
Summary: This study demonstrates the 3D motion of a 6-DOF rigid body around a fixed point by examining the influence of the gyrostatic moment vector and magnetic field. The proposed method involves imposing a large value of the projection of the angular velocity to constrain the governing system of motion. The new analytic approximate solutions of the governing equations are achieved using the small parameter technique of Poincare.
RESULTS IN PHYSICS
(2022)
Article
Engineering, Mechanical
Ji-Huan He, Galal M. Moatimid, Marwa H. Zekry
Summary: This paper establishes a fractal-differential model for a nonlinear vibration system in a fractal space. The basic properties of a fractal oscillator are revealed using the fractal Duffing-Van der Pol oscillator as an example. The stability criteria are obtained through analytic approximate solutions and nonlinear frequency analysis. Linearized stability theory and multiple time scales technique are utilized for stability analysis.
FACTA UNIVERSITATIS-SERIES MECHANICAL ENGINEERING
(2022)
Article
Biotechnology & Applied Microbiology
Qingli Wang, Ji-Huan He, Zhi Liu
Summary: Polar bear hairs possess remarkable properties that allow them to survive in extremely cold environments. The micro-structured scales on the hair surface have been found to absorb maximal radiative flux from the Sun, which could inspire the development of intelligent nanomaterials for efficient solar energy absorption.
FRONTIERS IN BIOENGINEERING AND BIOTECHNOLOGY
(2022)
Article
Thermodynamics
Ji-Huan He, Nasser S. Elgazcry, Nader Y. Abd Elazem
Summary: This paper presents a numerical analysis of the flow of unsteady compressible magneto-radiative gas near a vertical wavy wall, considering the effects of nonlinear thermal radiation and fluid properties. The results confirm the importance of considering thermal radiation in heat transfer studies.
INTERNATIONAL JOURNAL OF NUMERICAL METHODS FOR HEAT & FLUID FLOW
(2023)
Article
Engineering, Mechanical
Ji-Huan He, Nader Y. Abd Elazem
Summary: This paper investigates the radiation effects on the flow of carbon nanotube suspended nanofluids in the presence of a magnetic field past a stretched sheet impacted by slip state. The parameters such as radiation parameter, slip parameter, solid volume fraction, magnetic parameter, Eckart and Prandtl numbers are analyzed to demonstrate their impact on velocity, temperature, and heat transfer rate profiles.
FACTA UNIVERSITATIS-SERIES MECHANICAL ENGINEERING
(2022)
Article
Thermodynamics
Ji-Huan He, Man-Yu Qian
Summary: The diffusion of red ink in saline water is stochastic and unpredictable, making it difficult to accurately describe the process with a differential model. This paper explores the diffusion at the molecular scale and highlights the necessity of adopting two-scale fractal calculus to account for particle size and properties of the saline solution. Experimental findings and theoretical explanations shed light on modeling various contamination diffusion in air and water.
Article
Thermodynamics
Man-Yu Qian, Ji-Huan He
Summary: This article discusses the importance of thermal science in simplifying complex problems, particularly in virus prevention where a simple cup of hot water can be sufficient. The article also introduces the emerging field of two-scale thermal science.
Article
Thermodynamics
Dan Tian, Ji-Huan He
Summary: This paper investigates methods to control the structure and properties of nanofibers. By using a rotary blowing air, the radial topological structure of nanofibers can be manipulated and a macromolecule-scale inner structure can be designed. The influence of flow properties on the mechanical properties of nanofibers is experimentally studied.
Article
Engineering, Multidisciplinary
Ji-Huan He, T. S. Amer, A. F. Abolila, A. A. Galal
Summary: This paper focuses on studying the dynamical response of a vibrating three degrees-of-freedom auto-parametric system near resonance. The stability and instability regions are examined, and the significance impact of this work is its great engineering applications in high towers, buildings, and bridges.
ALEXANDRIA ENGINEERING JOURNAL
(2022)
Article
Mechanics
Naveed Anjum, Ji-Huan He, Chun-Hui He, Alina Ashiq
Summary: This study provides an overview of current asymptotic approaches and novel innovations in the field of microelectromechanical systems (MEMS), offering effective methods for obtaining approximate solutions to both weakly and highly nonlinear equations derived from MEMS models. The study also discusses the limitations of traditional methods and presents modified approaches to overcome these limitations. The concept of two-scale idea in MEMS technology is described, and examples are given to demonstrate the effectiveness and convenience of these methodologies.
JOURNAL OF APPLIED AND COMPUTATIONAL MECHANICS
(2022)
