On the Stability of an Electrostatically-Actuated Functionally Graded Magneto-Electro-Elastic Micro-Beams Under Magneto-Electric Conditions

Journal of Solid Mechanics

مقاله 6، دوره 8، شماره 4، اسفند 2016، صفحه 756-772   

نوع مقاله: Research Paper

نویسندگان

A Amiri^* ؛ G Rezazadeh؛ R Shabani؛ A Khanchehgardan

Mechanical Engineering Department, Urmia University, Urmia, Iran

چکیده

In this paper, the stability of a functionally graded magneto-electro-elastic (FG-MEE) micro-beam under actuation of electrostatic pressure is studied. For this purpose Euler-Bernoulli beam theory and constitutive relations for magneto-electro-elastic (MEE) materials have been used. We have supposed that material properties vary exponentially along the thickness direction of the micro-beam. Governing motion equations of the micro-beam are derived by using of Hamilton’s principle. Maxwell’s equation and magneto-electric boundary conditions are used in order to determine and formulate magnetic and electric potentials distribution along the thickness direction of the micro-beam. By using of magneto-electric potential distribution, effective axial forces induced by external magneto-electric potential are formulated and then the governing motion equation of the micro-beam under electrostatic actuation is obtained. A Galerkin-based step by step linearization method (SSLM) has been used for static analysis. For dynamic analysis, the Galerkin reduced order model has been used. Static pull-in instability for 5 types of MEE micro-beam with different gradient indexes has been investigated. Furthermore, the effects of external magneto-electric potential on the static and dynamic stability of the micro-beam are discussed in    detail.

کلیدواژه‌ها

Functionally graded؛ MEE؛ MEMS؛ Maxwell’s Equation؛ Pull-in instability

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