The response of a rectangular micro-plate to mechanical shocks considering modified couple stress theory ISAV2012_2162 Kaveh Rashvand, Ghader Rezazadeh, Mehrdad Sheikhlou, Siavash Kazemirad Presenter Kaveh Rashvand Urmia University / Mechanical Engineering Department
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The response of a rectangular micro-plate to me-chanical shocks considering modified couple stress theory
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The response of a rectangular micro-plate to mechanical shocks considering modified couple stress theory
Urmia University / Mechanical Engineering Department
Outlines
Introduction Research Background Assumptions and Formulations Numerical Solution Results Conclusions
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Introduction
• RF MEMS• Capacitive Rectangular Micro-plate• Pull-in Voltage• Modified Couple Stress Theory (MCT) • Material Length-scale parameter
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Research Background of MCT
• Cosserat brothers (1909) The Cosserat theory of elasticity incorporates the local rotation of points as well as
the translation allowed in CT. Moreover, there is a torque per unit area, or couple stress, as well as the usual force per unit area, or stress.
• Yang et al. (2002) The symmetric part of curvature tensor is an additional measure of deformation
that conjugates to the couple stress. This means that the number of required material length scale parameters is only one in the modified couple stress theory (MCT) instead of two in the classical couple stress theory (CCT).
• Tsiatas (2009) A Kirchhoff plate model for the static analysis of isotropic micro-plates with
arbitrary shapes were derived based on MCT.
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Research Background of RF MEMS
• Français and Dufour (1999) proposed a complete normalized study of a diaphragm's behavior in MEMS and
compared the results with measurements made on silicon plates under electrostatic actuation.
• Younis et al. (2007) studied the dynamic response of an electrostatically deflected microbeam under
different shock types with different shock durations and amplitudes based on CT.
• Kimberley et al. (2009) investigated failure of Au RF MEMS beam subjected to dynamic loading
experimentally.
• Rashvand et al. (2012) studied an isotropic rectangular micro-plate statically via MCT without considering
the effect of the axial stress generated by the micro-plate stretching.
ResultsShape functions satisfy the boundary conditions for the rectangular micro-plate:
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m n2 2ˆ ˆsin (m x)siˆ ˆx n (ny y)
Results
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Static pull-in voltage Dynamic response and dynamic pull-in voltage
Results
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Applied voltage 0V for shock duration d=0.1ms in two gaps.
Difference between the linear and nonlinear model of the micro-plate based on MCT
Results
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Applied voltage 1V and as=100g for shock duration d=0.5ms.
Dynamic response of the micro-plate based on MCT
shock amplitude as=100g shock amplitude as=1000gApplied voltage 1V and d=0.1 ms Applied voltage 1V and d=0.1 ms
Conclusions
• The numerical results revealed that the intrinsic size dependence of materials affects the stability region and the dynamic response.
• The results obtained from MCT showed that CT overestimates the deflection of the micro-plate in smaller thicknesses.
• Changes of the pulse duration cause the dynamic response to become similar to the quasi-static one; while changing the amplitude of the acceleration pulse moves the stable region of the micro-plate.
• In small shock amplitudes, the effect of stretching is negligible but in higher shocks this effect is considerable.
• The pulse duration and the amplitude of the acceleration pulse should be considered together with the pull-in voltage to prevent the failure of MEMS devices under mechanical shocks.
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Thank you for your attention
The response of a rectangular micro-plate to mechanical shocks considering modified couple stress theory
Kaveh Rashvand, Ghader Rezazadeh, Mehrdad Sheikhlou, Siavash KazemiradMechanical Engineering Department