Vibration Behavior of a Sandwich Porous Elliptical Micro-Shell with a Magneto-Rheological Core Based on the Modified Couple Stress Theory (Advances in Applied Mathematics and Mechanics, 2023)
Recently, the use of porous materials has grown widely in many structures,such as beams, plates, and shells. The characteristics of porous materials change in thethickness direction by different functions. This study has investigated the free vibration analysis of a sandwich porous elliptical micro-shell with a magneto-rheologicalfluid (MRF) core for the first time. Initially, we examined the displacement of the middle layer’s macro- and micro-components, using Love’s shell theory. Next, we usedthe modified couple stress theory (MCST) to obtain the strain and symmetrical curvature tensors for the three layers. The Hamilton’s principle was implemented to derivethe equations of motion. We also used the Galerkin’s method to solve the equationsof motion, resulting in a system of equations in the form of a linear eigenvalue problem. By solving the governing equations, we obtained the various natural frequenciesand loss factors of the elliptical micro-shell, and compared them with the results inearlier studies. Lastly, we investigated the effects of thickness, porosity distributionpattern, aspect ratio, length scale parameter, and magnetic field intensity on the natural frequency and loss factor of the micro-shell. The data accuracy was validated bycomparing them with those of reputable previous articles.