As bifunctional oxygen evolution/reduction electrocatalysts, transition-metal-based single-atom-doped nitrogen–carbon (NC) matrices are promising successors of the corresponding noble-metal-based catalysts, offering the advantages of ultrahigh atom utilization efficiency and surface active energy. However, the fabrication of such matrices (e.g., well-dispersed single-atom-doped M-N4/NCs) often requires numerous steps and tedious processes. Herein, ultrasonic plasma engineering allows direct carbonization in a precursor solution containing metal phthalocyanine and aniline. When combining with the dispersion effect of ultrasonic waves, we successfully fabricated uniform single-atom M-N4 (M = Fe, Co) carbon catalysts with a production rate as high as 10 mg min−1. The Co-N4/NC presented a bifunctional potential drop of ΔE = 0.79 V, outperforming the benchmark Pt/C-Ru/C catalyst (ΔE = 0.88 V) at the same catalyst loading. Theoretical calculations revealed that Co-N4 was the major active site with superior O2 adsorption–desorption mechanisms. In a practical Zn–air battery test, the air electrode coated with Co-N4/NC exhibited a specific capacity (762.8 mAh g−1) and power density (101.62 mW cm−2), exceeding those of Pt/C-Ru/C (700.8 mAh g−1 and 89.16 mW cm−2, respectively) at the same catalyst loading. Moreover, for Co-N4/NC, the potential difference increased from 1.16 to 1.47 V after 100 charge–discharge cycles. The proposed innovative and scalable strategy was concluded to be well suited for the fabrication of single-atom-doped carbons as promising bifunctional oxygen evolution/reduction electrocatalysts for metal–air batteries.

Natural vibration analysis of stiffened panels represents an important issue in different kinds of engineering applications. In this article, a procedure for the vibration analysis of stiffened panels with arbitrary edge constraints is presented. It is based on the assumed mode method, where natural frequencies and modes are determined by solving an eigenvalue problem of a multi-degree-of-freedom system matrix equation derived by using Lagrange's equations of motion. The Mindlin thick plate theory is applied for a plate, while the effect of stiffeners having the properties of Timoshenko beams is accounted for by adding their strain and kinetic energies to the corresponding plate energies. The accuracy of the proposed procedure is justified by several numerical examples which include the natural vibration analysis of stiffened panels with different framing sizes, their lengths and orientations, plate thicknesses and different combinations of boundary conditions. A comparison of results with those obtained by the finite element method is provided, and good agreement is achieved.

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