Guest Editors
Prof. Ji-Huan He, Soochow University, China
Ji-Huan He is an expert in nonlinear science and nanotechnology, he is the owner of some famous analytical methods, such as the semi-inverse method, the variational iteration method, the homotopy perturbation method, the exp-function method, and He’s frequency formulation. He has published more than 400 articles with an h-index of 67, he has been listed as a highly cited researcher by Clarivate Analytics and Elsevier for many years, and was also one of the World's Hottest Researchers. His present interest mainly includes fractal calculus and fractional calculus.
Summary
Due to the last development of nanotechnology, nano/micro devices and systems, e.g., nanotubes, nano/micro structures/systems, and nanofiber fabrication, have been caught much attention, and the era of miniaturized nano devices is approaching. The nonlinear vibration or instability becomes the cutting edge in nanotechnology and nonlinear dynamics. To control the instability becomes the main focus in designing a device or a system. This special issue focuses on analytical, computational, and experimental approaches to nano/micro devices/systems.
Keywords
Nanotube, N/MEMS system, 3D printing technology, nanofiber fabrication, fractional differential equation, nonlinear vibration, optimal control, fractal vibration, analytical method, numerical method
Published Papers
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Open Access
ARTICLE
Damped Mathieu Equation with a Modulation Property of the Homotopy Perturbation Method
Yusry O. El-Dib, Nasser S. Elgazery
Sound & Vibration, Vol.56, No.1, pp. 21-36, 2022, DOI:10.32604/sv.2022.014166
（This article belongs to this Special Issue:
Analytical Methods for Nonlinear Vibration & Active Control in Nano/Micro Devices and Systems)
Abstract In this article, the main objective is to employ the homotopy perturbation method (HPM) as an alternative to classical perturbation methods for solving nonlinear equations having periodic coefficients. As a simple example, the nonlinear damping Mathieu equation has been investigated. In this investigation, two nonlinear solvability conditions are imposed. One of them was imposed in the first-order homotopy perturbation and used to study the stability behavior at resonance and non-resonance cases. The next level of the perturbation approaches another solvability condition and is applied to obtain the unknowns become clear in the solution for the first-order solvability condition. The approach…
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Open Access
ARTICLE
An Alternative Algorithm for the Symmetry Classification of Ordinary Differential Equations
Yi Tian, Jing Pang
Sound & Vibration, Vol.56, No.1, pp. 65-76, 2022, DOI:10.32604/sv.2022.014547
（This article belongs to this Special Issue:
Analytical Methods for Nonlinear Vibration & Active Control in Nano/Micro Devices and Systems)
Abstract This is the first paper on symmetry classification for ordinary differential equations (ODEs) based on Wu’s method. We carry out symmetry classification of two ODEs, named the generalizations of the Kummer-Schwarz equations which involving arbitrary function. First, Lie algorithm is used to give the determining equations of symmetry for the given equations, which involving arbitrary functions. Next, differential form Wu’s method is used to decompose determining equations into a union of a series of zero sets of differential characteristic sets, which are easy to be solved relatively. Each branch of the decomposition yields a class of symmetries and associated parameters.…
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Open Access
ARTICLE
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Open Access
ARTICLE
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Open Access
ARTICLE
Modeling of Dark Solitons for Nonlinear Longitudinal Wave Equation in a Magneto-Electro-Elastic Circular Rod
Hulya Durur, Asıf Yokuş, Doğan Kaya, Hijaz Ahmad
Sound & Vibration, Vol.55, No.3, pp. 241-251, 2021, DOI:10.32604/sv.2021.014157
（This article belongs to this Special Issue:
Analytical Methods for Nonlinear Vibration & Active Control in Nano/Micro Devices and Systems)
Abstract In this paper, sub equation and expansion methods are proposed to construct exact solutions of a nonlinear longitudinal wave equation (LWE) in a magneto-electro-elastic circular rod. The proposed methods have been used to construct hyperbolic, rational, dark soliton and trigonometric solutions of the LWE in the magneto-electro-elastic circular rod. Arbitrary values are given to the parameters in the solutions obtained. 3D, 2D and contour graphs are presented with the help of a computer package program. Solutions attained by symbolic calculations revealed that these methods are effective, reliable and simple mathematical tool for finding solutions of nonlinear evolution equations arising in…
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