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چکیده
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In this article, an analytical solution is provided for the free damped vibration analysis of a sandwich plate resting on a visco-Pasternak foundation. The plate consists of a magnetorheological elastomer (MRE) core reinforced with carbon nanotubes (CNTs) and laminated polymer-based face sheets enriched with graphene nanoplatelets (GPLs) and glass fibers. The governing equations and associated boundary conditions are derived utilizing Hamilton’s principle and are solved analytically using Navier’s method for a simply supported plate. The influences of various parameters on the natural frequencies and corresponding loss factors are examined such as aspect ratio of the plate, thickness-to-length of the plate, magnetic field intensity, thickness of the MRE core, mass fraction of the CNTs in the MRE core, mass fractions of the GPLs and fibers in the face sheets, and Winkler, Pasternak, and damping coefficients of the foundation. It is shown that subjoining CNTs to the MRE core leads to a small increase in the natural frequencies and loss factors of the plate. Consequently, due to the high cost of the CNTs, adding them to the MRE core to improve the vibrational characteristics of the sandwich plates with MRE core is not an optimum design.
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