Nonlocal strain gradient plate model for nonlinear large-amplitude vibrations of functionally graded porous micro/nano-plates reinforced with GPLs

Because of rapid development of manufacturing technology, functionally graded porous materials have gained commercially attraction in promoted engineering applications. It is common to reinforce the porous materials with nanofillers to improve their mechanical properties efficiently. The prime objective of the present investigation is to explore the size dependency in nonlinear large-amplitude vibrational response of functionally graded porous micro/nano-plates reinforced with graphene platelets (GPLs). To accomplish this purpose, the newly proposed unconventional continuum theory namely as the nonlocal strain gradient theory incorporating size effects more comprehensively is adopted to the refined exponential shear deformation plate theory. Based upon the closed-cell Gaussian-Random field scheme in conjunction with the Halpin-Tsai micromechanical modelling, the mechanical properties of the porous material with uniform and three different functionally graded patterns of porosity dispersion reinforced with GPLs are extracted. Using Hamilton's principle, the nonclassical form of differential equations of motion are derived. Thereafter, an improved perturbation technique is put to use to construct analytical expression for the nonlocal strain gradient nonlinear frequency associated with the large-amplitude vibration of functionally graded porous micro/nano-plates reinforced with GPLs. It is indicated that by increasing the plate deflection, the significance of the both size effects on the nonlinear frequency of the porous micro/nano-plates decreases. Also, it is displayed that for vibrations with higher amplitude, the role of porosity dispersion pattern in the significance of size effects on the nonlinear frequency of functionally graded micro/nano-plates becomes more important.