Lie group analysis of non-linear dynamic of micro structures under electrostatic field
| Autor: | Ion Stiharu, M. Amin Changizi |
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| Rok vydání: | 2015 |
| Předmět: | |
| Zdroj: | Journal of Computational Methods in Sciences and Engineering. 15:327-338 |
| ISSN: | 1875-8983 1472-7978 |
| DOI: | 10.3233/jcm-150546 |
| Popis: | This paper presents an analytical solution of nonlinear differential equation of micro-structures subjected to electro- static fields. The constitutive equation of such a model is a second order differential equation (ODE). The problem is solved when the assumption of linear deflection is considered. However, deflection of micro cantilevers in practical applications is non- linear. Moreover, the constitutive ODE is stiff and various numerical algorithms used to solve it yield non-consistent numerical solutions. A deduction order method - Lie group symmetry is employed to reduce the order of the ODE. Although the resulting first order ODE has no symmetry that would guarantee an explicit close form solution, it enables an analytical formulation for the no-damping assumption only. The restoring force term in the first order ODE reveals the pull-in voltage as expressed in classical MEMS textbooks. It is shown that the numerical solution for the second order ODE and the reduced first order ODE are same. Finding any symmetry other than translation, scaling or rotation will enable the reduction of the first order ODE and thus, the formulation of an analytical solution to this highly non-linear problem. |
| Databáze: | OpenAIRE |
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