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This paper conducted the free vibration analysis of a sandwich annular thin plate with whirl motion. The upper and lower faces of the annular plate are made of uniform solid metal, while its core is porous foamed metal reinforced by graphene nanoplatelets (GPLs). Both uniform and non-uniform distributions of GPLs and porosity along the direction of plate thickness which leads to a functionally graded (FG) core are taken into account. The effective material properties including Young's modulus, Poisson's ratio and mass density are calculated by employing the Halpin–Tsai model and the rule of mixture, respectively. Based on the Kirchhoff plate theory, the differential equations of motion are derived by applying the Lagrange's equation. Then, the assumed mode method is utilized to obtain free vibration behaviors of the sandwich annular plate. The finite element method is adopted to verify the present model and vibration analysis. The effects of porosity coefficient, porosity distribution, graphene nanoplatelet (GPL) distribution, graphene nanoplatelet (GPL) weight fraction, graphene nanoplatelet length-to-thickness ratio (GPL-LTR), graphene nanoplatelet length-to-width ratio (GPL-LWR), spinning speed, outer radius-to-thickness ratio and inner radius-to-thickness ratio of the plate, are examined in detail. [ABSTRACT FROM AUTHOR]

In the work, we firstly report the facile and large-scale synthesis of defective black TiO2−x(B) nanosheets via a dual-zone NaBH4 reduction method. The structure, physico-chemical, and optical properties of TiO2−x(B) nanosheets were systematically characterized by powder X-ray diffraction, Raman spectroscopy, UV-Vis absorption spectroscopy, and X-ray photoelectron spectroscopy, etc. The concentration of Ti3+ can be well tuned by NaBH4 reduction. With increasing the mass ratio of NaBH4 to TiO2(B), the generation of Ti3+ defects gives rise to the increased intensity of a broad band absorption in the visible wavelength range. It is demonstrated that the TiO2−x(B) photocatalyst synthesized with the mass ratio of NaBH4 to TiO2(B) of 3:1 exhibited an optimum photocatalytic activity and excellent photostability for hydrogen evolution under visible-light irradiation. By combining the advantages of 2D TiO2(B) nanosheets architecture with those of Ti3+ self-doping and simultaneous production of oxygen vacancy sites, the enhanced photocatalytic performance of the defective TiO2−x(B) nanosheets was achieved. [ABSTRACT FROM AUTHOR]