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2 2024

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

Wei Y. Y., Al-Furjan M. S. H., Shan L., Shen X., Kolahchi R., Rabani bidgoli M., Farrokhian A.

Archives of Civil and Mechanical Engineering

2024

Vol. 24, no. 1

art. no. e38, 2024

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.

Bending of a five-layered composite beam with consideration of two analytical models

Magnucki Krzysztof

Archive of Mechanical Engineering

2024

LXXI, nr 1

27--46

The subject of the work is a five-layered composite beam with clamped ends subjected to a uniformly distributed load along its length. Two analytical models of this beam are developed with consideration of the shear effect. The first model is formulated on the basis of the classical zig-zag theory. Whereas, the second model is developed using an individual nonlinear shear deformation theory with consideration of the classical shear stress formula (called Zhuravsky shear stress). The system of two differential equations of equilibrium for each beam model is obtained based on the principle of stationary total potential energy. These systems of equations are exactly analytically solved. The shear effect function and the maximum deflection are determined for each of these two beam models. Detailed calculations are carried out for exemplary beams of selected dimensionless sizes and material constants. The main goal of the research is to develop two analytical models of this beam, determine the shear effect function, the shear coefficient, and the maximum deflection in the elastic range for each model, as well as to perform a comparative analysis.