Bending and vibration analysis of S-FGM microplates embedded in Pasternak elastic medium using the modified couple stress theory

• An S-FGM composed of two power-law functions to define volume fraction is proposed.
• A modified couple stress theory with first order shear deformation is developed.
• The model contains one material length scale parameter and can capture the size effect.
• The Pasternak׳s parameter has more effect on variation of structural responses.

A model for sigmoid functionally graded material (S-FGM) microplates based on the modified couple stress theory with first order shear deformation is developed. The advantages of the theory are the use of rotation–displacement as dependent variable and the use of only one constant to describe the material׳s micro-structural characteristics. The present model of microplate can be viewed as a simplified couple stress theory in engineering mechanics. The present models contain one material length scale parameter and can capture the size effect, and two-constituent material variation through the plate thickness. The equations of motion are derived from Hamilton׳s principle based on the modified couple stress theory, and the power law variation of the material through the thickness of the plate. Material properties of functionally graded plate are assumed to vary according to two power law distribution of the volume fraction of the constituents. The elastic medium is modeled as Pasternak elastic medium. Analytical solution of rectangular plates is derived, and the obtained results are compared well with reference solutions. Finally, the influences of power law index, material length scale parameter, thickness ratio, and elastic medium parameter on the deflection and the natural frequency of plates have been investigated.