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In this study, free vibration of the sandwich microbeam with porous core and FG carbon nanotubes reinforced composite face sheets which is rested on Winkler‐Pasternak substrate is investigated. It is assumed the beam is in thermal environment and is subjected to thermal load and the displacement components are described based on sinusoidal shear deformation beam theory. The small scale effects are taken into account according to the modified couple stress theory. The core and face sheets properties are diffused through the thickness. The motion equations are derived and solved using Hamilton's principle and Navier's method, respectively. Effect of different parameters such as porosity coefficient and distributions, different types of CNTs distribution, small scale and geometrical size of the beam is considered. The results show by enhancing the porosity, the frequency decreased. The findings of the current study can be used to design prominent role in modern engineering applications.

A novel quasi-3D hyperbolic shear deformation theory (QHSDT) with five unknowns is here employed, together with the Hamilton’s principle and the modified couple stress theory (MCST) to analyze the vibrational behavior of rectangular micro-scale sandwich plates resting on a visco-Pasternak foundation. The sandwich structure features a Nomex or Glass phenolic honeycomb core, and two composite face sheets reinforced with graphene nanoplatelets (GPLs). The effective properties of both face sheets are evaluated by means of the Halpin-Tsai and extended rule of mixture (ERM) micromechanical schemes. The governing equations of the problem are derived by applying the Hamilton’s principle, whose solutions are determined theoretically according to a classical Navier-type procedure. A parametric study checks for the effect of different material properties, length-scale parameters, foundation parameters and geometrical properties of the honeycomb cells, and the reinforcing GPLs, on the vibration response of the layered structure, which can be of great interest for many modern engineering applications and their optimization design.

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