Effect of mass diffusion on the damping ratio in a functionally graded micro-beam

The present paper is aimed at studying the effects of mass diffusion on the quality factor of a functionally graded cantilever micro-beam in which the material properties of the micro-beam vary continuously along the beam thickness according to a power-law. 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 by using two dimensional non-Fourier heat conduction and non-Fickian mass diffusion models with one relaxation time based on continuum theory frame. The free vibration of the micro-beam resonators is analyzed by using Galerkin reduced order model formulation for the first mode of vibration. The mass diffusion effects on the quality factor are studied for the various micro-beam thicknesses and temperatures. Numerical computations are performed for specific materials and the results obtained are represented graphically. The effect of different power law exponent on the quality factor of the micro-beam is studied and Comparisons are made within the theory in the presence and absence of the mass diffusion effect.