Homotopy Analysis Method for Nonlinear Dynamical System of an Electrostatically Actuated Microcantilever

Homotopy Analysis Method for Nonlinear Dynamical System of an Electrostatically Actuated Microcantilever

The homotopy analysis method (HAM) is employed to propose an approach for solving the nonlinear dynamical system of an electrostatically actuated micro-cantilever in MEMS. There are two relative merits of the presented HAM compared with some usual procedures of the HAM. First, a new auxiliary linear...

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Main Authors: Y. M. Chen, G. Meng, J. K. Liu, J. P. Jing
Format: Article
Language:English
Published: Hindawi Limited 2011-01-01
Series:Mathematical Problems in Engineering
Online Access:http://dx.doi.org/10.1155/2011/173459
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spelling doaj-9d10e2c4f2b546a98d517b40d1e3827f2020-11-24T23:55:33ZengHindawi LimitedMathematical Problems in Engineering1024-123X1563-51472011-01-01201110.1155/2011/173459173459Homotopy Analysis Method for Nonlinear Dynamical System of an Electrostatically Actuated MicrocantileverY. M. Chen0G. Meng1J. K. Liu2J. P. Jing3State Key Laboratory of Mechanical System and Vibration, Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai 200240, ChinaState Key Laboratory of Mechanical System and Vibration, Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai 200240, ChinaDepartment of Mechanics, Sun Yat-Sen University, Guangzhou 510275, ChinaState Key Laboratory of Mechanical System and Vibration, Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai 200240, ChinaThe homotopy analysis method (HAM) is employed to propose an approach for solving the nonlinear dynamical system of an electrostatically actuated micro-cantilever in MEMS. There are two relative merits of the presented HAM compared with some usual procedures of the HAM. First, a new auxiliary linear operator is constructed. This operator makes it unnecessary to eliminate any secular terms. Furthermore, all the deformation equations are purely linear. Numerical examples show the excellent agreement of the attained solutions with numerical ones. The respective effects of applied voltage, cubic nonlinear stiffness, gap distance, and squeeze film damping on vibration responses are analyzed detailedly.http://dx.doi.org/10.1155/2011/173459
collection DOAJ
language English
format Article
sources DOAJ
author Y. M. Chen
G. Meng
J. K. Liu
J. P. Jing
spellingShingle Y. M. Chen
G. Meng
J. K. Liu
J. P. Jing
Homotopy Analysis Method for Nonlinear Dynamical System of an Electrostatically Actuated Microcantilever
Mathematical Problems in Engineering
author_facet Y. M. Chen
G. Meng
J. K. Liu
J. P. Jing
author_sort Y. M. Chen
title Homotopy Analysis Method for Nonlinear Dynamical System of an Electrostatically Actuated Microcantilever
title_short Homotopy Analysis Method for Nonlinear Dynamical System of an Electrostatically Actuated Microcantilever
title_full Homotopy Analysis Method for Nonlinear Dynamical System of an Electrostatically Actuated Microcantilever
title_fullStr Homotopy Analysis Method for Nonlinear Dynamical System of an Electrostatically Actuated Microcantilever
title_full_unstemmed Homotopy Analysis Method for Nonlinear Dynamical System of an Electrostatically Actuated Microcantilever
title_sort homotopy analysis method for nonlinear dynamical system of an electrostatically actuated microcantilever
publisher Hindawi Limited
series Mathematical Problems in Engineering
issn 1024-123X
1563-5147
publishDate 2011-01-01
description The homotopy analysis method (HAM) is employed to propose an approach for solving the nonlinear dynamical system of an electrostatically actuated micro-cantilever in MEMS. There are two relative merits of the presented HAM compared with some usual procedures of the HAM. First, a new auxiliary linear operator is constructed. This operator makes it unnecessary to eliminate any secular terms. Furthermore, all the deformation equations are purely linear. Numerical examples show the excellent agreement of the attained solutions with numerical ones. The respective effects of applied voltage, cubic nonlinear stiffness, gap distance, and squeeze film damping on vibration responses are analyzed detailedly.
url http://dx.doi.org/10.1155/2011/173459
work_keys_str_mv AT ymchen homotopyanalysismethodfornonlineardynamicalsystemofanelectrostaticallyactuatedmicrocantilever
AT gmeng homotopyanalysismethodfornonlineardynamicalsystemofanelectrostaticallyactuatedmicrocantilever
AT jkliu homotopyanalysismethodfornonlineardynamicalsystemofanelectrostaticallyactuatedmicrocantilever
AT jpjing homotopyanalysismethodfornonlineardynamicalsystemofanelectrostaticallyactuatedmicrocantilever
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