Stochastic analysis of dynamic characteristics and pull-in instability of FGM micro-switches with uncertain parameters i
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Stochastic analysis of dynamic characteristics and pull-in instability of FGM micro-switches with uncertain parameters in thermal environments Mohsen Mohammadi
. Mohammadi Eghtesad . Hossein Mohammadi
Received: 27 June 2017 / Accepted: 12 July 2017 Springer Science+Business Media B.V. 2017
Abstract In this paper, the stochastic vibration characteristics of a functionally graded material micro-switch with random material properties near the pull-in instability are investigated. The uncertainties of the material properties and randomness of the composition of constituents due to the fabrication process are considered in this study. The micro-switch is modeled as a micro-beam and is under the effects of electrostatic and Casimir forces. The properties of the constituent materials are temperature dependent, and the system undergoes a change in temperature. The governing equations of motion of the Euler–Bernoulli micro-beam are derived based on modified couple stress theory and are solved using the state space form finite difference method. The statistics of the dynamic characteristics are obtained based on Monte Carlo simulation method. The effects of Casimir force, the length scale parameter, temperature dependencies of the material properties, the temperature change, the applied voltage and the volume fraction index on stochastic properties of the first natural frequency, the second natural frequency, the pull-in gap, and the pullin voltage are studied in detail. Keywords Functionally graded materials Stochastic analysis Thermal environment M. Mohammadi (&) M. Eghtesad H. Mohammadi School of Mechanical Engineering, Shiraz University, Shiraz, Iran e-mail: [email protected]
Micro/nano beam Nonlinear vibration Monte Carlo simulation Finite difference method
1 Introduction Functionally graded materials are a class of inhomogeneous composite materials in which the composition change smoothly over the volume. The FGMs are usually composed of two different materials such as ceramics and metals, and as a result, inherit heat and wear resistance, high stiffness and high toughness from each constituent materials. The FGM structures are widely used in various engineering applications such as rocket engine components, nuclear reactor components, thermoelectric generators and solar cells. The FGMs are expected to endure high-temperature gradients; for example, the outer wall of the functionally graded combustion chamber of a space shuttle was at 1376 C, while the inner wall temperature reached 2027 C. No damage to the combustors was reported when a hit gas flow test was performed (Miyamoto et al. 2013). Powder metallurgy, melt processing (Kieback et al. 2003) and layer-by-layer additive manufacturing (Bobbio et al. 2017) are among the typical fabrication processes of FGMs. The common property of the manufacturing processes is the complexity of the method compared to fabrication procedures of pure materials. The complete control of a complex manufacturing process is not economically feasible.
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