Size-dependent vibration and frequency reversal mechanism in porous Ni-Al 2 O 3 microplates: a modified couple stress theory approach

Abstract This work presents a theoretical study on the size-dependent free vibration of porous nickel-alumina functionally graded (FGM) microplates. A refined continuum model is established by integrating the modified couple stress theory (MCST) with Kirchhoff plate theory. Unlike traditional models, this framework explicitly incorporates a power-law distribution of the material length scale parameter and corrects for the physical neutral surface shift. The vibration characteristics under four distinct porosity distribution patterns (Even, X, O, and V-types) are systematically evaluated. Significantly, a counter-intuitive ‘frequency reversal phenomenon’ is revealed in the Ni-Al 2 O 3 system. It is found that while the uniform (Even) porosity yields higher fundamental frequencies in ceramic-rich regimes, the optimal strategy shifts to uneven distributions (specifically O-type) in metal-rich regimes. This reversal mechanism is attributed to the competition between global mass reduction and local stiffness preservation, driven by the extreme density contrast of the nickel phase. These findings provide new physical insights into the mass-stiffness coupling effect in micro-scale composites, offering theoretical guidance for high-performance MEMS resonator design.