Homotopy perturbation method for N/MEMS oscillators

被引：83
作者：
Anjum, Naveed [1 ,2 ,3 ]
He, Ji-Huan [1 ,4 ,5 ]
机构：
[1] Soochow Univ, Coll Text & Engn, Natl Engn Lab Modern Silk, Suzhou, Peoples R China
[2] Soochow Univ, Sch Math Sci, Suzhou, Peoples R China
[3] Govt Coll Univ, Dept Math, Faisalabad, Pakistan
[4] Henan Polytech Univ, Sch Math & Informat Sci, Jiaozuo, Henan, Peoples R China
[5] Xian Univ Architecture & Technol, Sch Sci, Xian, Peoples R China
来源：
MATHEMATICAL METHODS IN THE APPLIED SCIENCES | 2020年
关键词：
amplitude-frequency relationship; He-Laplace method; homotopy perturbation method; Laplace transform; nano; microelectromechanical systems; nonlinear oscillators; PULL-IN INSTABILITY; HE-LAPLACE METHOD; NONLINEAR VIBRATION; PART; MODEL; EQUATION; BEAMS; PROMISES; DESIGN;
D O I：
10.1002/mma.6583
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The nano/microelectromechanical systems (N/MEMS) have caught much attention in the past few decades for their attractive properties such as small size (low mass), high reliability (high thermal conductivity and high Young's modulus), batch fabrication, and low power consumption. The dynamic oscillatory behavior of these systems is very complex due to strong nonlinearities in these systems. The basic aim of this manuscript is to investigate the nonlinear vibration property of N/MEMS oscillators arising in nanotube-based N/MEMS and resonators by the homotopy perturbation method coupled with Laplace transform (also called as He-Laplace method in literature). A generalized N/MEMS oscillator is systematically studied, and a fairly accurate analytic solution is obtained. Three special cases for electrically actuated MEMS, multi-walled carbon nanotubes-based MEMS, and MEMS subjected to van der Waals attraction are considered for comparison, and a good agreement with exact solutions is observed.
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页数：15
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共 69 条
[1]   APPLICATION OF HE'S FRACTIONAL DERIVATIVE AND FRACTIONAL COMPLEX TRANSFORM FOR TIME FRACTIONAL CAMASSA-HOLM EQUATION [J].
Anjum, Naveed ;
Ain, Qura Tul .
THERMAL SCIENCE, 2020, 24 (05) :3023-3030
[2]   The oscillating and electrostatic characteristics of microelectromechanical system cantilever structure analyzed based on the air gap domain [J].
Cheng, Jianlian ;
Li, Kai ;
Zhang, Zhuang ;
Gu, Yufeng .
JOURNAL OF LOW FREQUENCY NOISE VIBRATION AND ACTIVE CONTROL, 2018, 37 (04) :725-747
[3]   Stability Analysis of a Strongly Displacement Time-Delayed Duffing Oscillator Using Multiple Scales Homotopy Perturbation Method [J].
El-Dib, Yusry O. .
JOURNAL OF APPLIED AND COMPUTATIONAL MECHANICS, 2018, 4 (04) :260-274
[4]   Application of the energy balance method to a nonlinear oscillator arising in the microelectromechanical system (MEMS) [J].
Fu, Yiming ;
Zhang, Jin ;
Wan, Liangjiao .
CURRENT APPLIED PHYSICS, 2011, 11 (03) :482-485
[5]   Beyond Adomian polynomials: He polynomials [J].
Ghorbani, Asghar .
CHAOS SOLITONS & FRACTALS, 2009, 39 (03) :1486-1492
[6]  
Gondal MA, 2010, INT J NONLIN SCI NUM, V11, P1145
[7]   Nonlinear vibration control with nanocapacitive sensor for electrostatically actuated nanobeam [J].
Gong, Qingmei ;
Liu, Canchang ;
Xu, Yingzi ;
Ma, Chicheng ;
Zhou, Jilei ;
Jiang, Ruirui ;
Zhou, Changcheng .
JOURNAL OF LOW FREQUENCY NOISE VIBRATION AND ACTIVE CONTROL, 2018, 37 (02) :235-252
[8]   Fangzhu((sic)(sic)): An ancient Chinese nanotechnology for water collection from air: History, mathematical insight, promises, and challenges [J].
He, Chun-Hui ;
He, Ji-Huan ;
Sedighi, Hamid M. .
MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2020,
[9]   TAYLOR SERIES SOLUTION FOR FRACTAL BRATU-TYPE EQUATION ARISING IN ELECTROSPINNING PROCESS [J].
He, Chun-Hui ;
Shen, Yue ;
Ji, Fei-Yu ;
He, Ji-Huan .
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY, 2020, 28 (01)
[10]   Iteration perturbation method for strongly nonlinear oscillations [J].
He, JH .
JOURNAL OF VIBRATION AND CONTROL, 2001, 7 (05) :631-642
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