Vibration response of small-scaled FG-CNTRC sandwich plates with MR fluid core supported by Kerr elastic substance

The current work is a continuation of the previous work by proposing the refined zigzag theory (RZT) for the vibration response of the micro sandwich plate. The face sheets of this structure are magnetostrictive and reinforced with single-walled carbon nanotubes (SWCNT) in four different patterns (FG-AV, FG-O, FG-X, and UD) following the rule of mixtures (ROM). The core material contains magnetorheological (MR) fluid which can work as a damper under a magnetic field. The micro sandwich plate is supported by an elastic substance utilizing the Kerr model. Additionally, the modified couple stress theory (MCST) is employed to predict size effects, and the magnetostrictive material (MsM) properties are considered viscoelastic based on the Kelvin–Voigt model. The Hamilton principle is applied to derive the size-dependent equations of motion. Then, an analytical solution is presented to evaluate the efficacies of various parameters including the volume fractions and the functional arrangement of carbon nanotubes, the geometrical aspect ratio of the system, the magnetic field intensity, the type of MR fluid, the small-scale parameter, damping coefficients of the system, and the elastic medium. Consequently, 29% increase in the dimensionless frequency for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:msup> <mml:mi>h</mml:mi> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>c</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:msup> <mml:mo>/</mml:mo> <mml:msup> <mml:mi>h</mml:mi> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>t</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:msup> </mml:mrow> <mml:mo>=</mml:mo> <mml:mn>5</mml:mn> </mml:mrow> </mml:math> is indicated when the small scale changes from <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mn>1</mml:mn> <mml:mo> </mml:mo> <mml:mi>μ</mml:mi> <mml:mi>m</mml:mi> </mml:mrow> </mml:math> to <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mn>2</mml:mn> <mml:mo> </mml:mo> <mml:mi>μ</mml:mi> <mml:mi>m</mml:mi> </mml:mrow> </mml:math> . This research can be contributed to the design and optimization of systems that use micro sandwich plates, addressing practical and essential engineering considerations.