Effect of Temperature Changes on Dynamic Pull-in Phenomenon in a Functionally Graded Capacitive Micro-beam

Document Type : Research Paper


1 Department of Agricultural Machinery Engineering, Bonab Branch, Islamic Azad University

2 Department of Mechanical Engineering, Urmia University


In this paper, dynamic behavior of a functionally graded cantilever micro-beam and its pull-in instability, subjected to simultaneous effects of a thermal moment and nonlinear electrostatic pressure, has been studied. It has been assumed that the top surface is made of pure metal and the bottom surface from a metal–ceramic mixture. The ceramic constituent percent of the bottom surface ranges from 0% to 100%. Along with the Volume Fractional Rule of material, an exponential function has been applied to represent the continuous gradation of the material properties through the micro-beam thickness. Attentions being paid to the ceramic constituent percent of the bottom surface, five different types of FGM micro-beams have been studied.  Nonlinear integro-differential thermo-electro-mechanical equation based on Euler–Bernoulli beam theory has been derived. The governing equation in the static case has been solved using Step-by-Step Linearization Method and Finite Difference Method.  Fixed points or equilibrium positions and singular points of the FGM micro-beam have been determined and shown in the state control space. In order to study stability of the fixed points, beam motion trajectories have been drawn, with different initial conditions, in the phase plane. In order to find the response of the micro-beam to a step DC voltage, the nonlinear equation of motion has been solved using Galerkin-based reduced-order model and time histories and phase portrait for different applied voltages and various primal temperatures have been illustrated. The effects of temperature change and electrostatic pressure on the deflection and stability of FGM micro-beams having various amounts of the ceramic constituent have been studied .


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