Stochastic analysis of dynamic characteristics and pull-in instability of FGM micro-switches with uncertain parameters in thermal environments

  • Mohsen MohammadiEmail author
  • Mohammadi Eghtesad
  • Hossein Mohammadi


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 pull-in voltage are studied in detail.


Functionally graded materials Stochastic analysis Thermal environment Micro/nano beam Nonlinear vibration Monte Carlo simulation Finite difference method 


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© Springer Science+Business Media B.V. 2017

Authors and Affiliations

  1. 1.School of Mechanical EngineeringShiraz UniversityShirazIran

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