Micro-mass sensor-based vibration response of smart bidirectional functionally graded auxetic microbeams

Microsensor-based vibration of 2D smart functionally graded sandwich microbeam with attached microparticles is investigated using the strain gradient hypothesis. The application of micro-materials as active sensing particles in micro-sensors has increased the sensitivity performance of micro-sensors that can be able to detect particles, for example, bacteria with very nano-dimensions and low concentrations. The sandwich beam contains a negative Poisson’s ratio auxetic honeycombs covered by a piezoelectric smart layer at the top and a bidirectional functionally graded material (FGM) layer at the bottom layers. Partial differential equations of the simply supported sandwich beams are first attained using the energy method utilizing refined zigzag theory. The coupled final equations are solved analytically utilizing Galerkin’s technique to present the frequency. The impact of the position and mass of the microparticles, applied voltage, material distribution in the bottom layer, size scale parameter, the honeycomb auxetic core geometrical properties, and the layer thickness on the frequency are discussed. The obtained findings showed that by enhancing the mass of the nanoparticle, the frequency is reduced. In addition, the location of the nanoparticle on the beam is important so that when it is close to the beam center, the frequency decreases. Further, by enhancing the thickness of the face sheet, the microbeam frequency decreases but increasing the core layer thickness plays an inverse role. Besides, it is found that when the material in-homogeneity index P x or P z in the 2D-FGM layer is enhanced, the frequency decreases.