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In this work effect of mass diffusion on the damping ratio in micro-beam resonators is investigated based on modified couple stress theory and the Euler-Bernoulli beam assumptions. The couple stress theory is a non-classical elasticity theory which is capable to capture size effects in small-scale structures. The governing equation of a micro-beam deflection is obtained using Hamilton’s principle and also the governing equations of thermo-diffusive elastic damping are established using two dimensional non-Fourier heat conduction and non-Fickian mass diffusion models. Free vibration of the micro-beam resonators is analyzed using Galerkin reduced order model formulation for the first mode of vibration. A clamped-clamped micro-beam with isothermal boundary conditions at both ends is studied. The obtained results are compared with the results of a model in which the mass diffusion effect is ignored. Furthermore the mass diffusion effects on the damping ratio are studied for the various micro-beam thicknesses, ambient temperature and length scales parameters. The results show that in the valid region based on Euler-Bernoulli beam theory and before the critical thickness there is no difference between the results of mass diffusion and thermo-elastic damping and also the results indicate that by increasing the length scale parameter damping ratio decreases.

Keywords: MEMS, Mass diffusion, Non-‎Fourier heat conduction, Non-Fickian mass diffusion, Modified couple stress theory

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