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Atomic diffusion in annealed Cu/SiO 2 /Si (100) system prepared by magnetron sputtering * Cao Bo(曹 博) a)b) , Jia Yan-Hui(贾艳辉) a) , Li Gong-Ping(李公平) a) † , and Chen Xi-Meng(陈熙萌) a)

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A new method-mixed boundary grid method (FBGM) is proposed to analyze the free vibration of cantilever plates with variable thickness. The fundamental differential equations of the plate are established for the bending problem. By transforming these equations into integral equations in a small area and using the trapezoidal rule of the approximate numerical integration, the solution of these equations is obtained and chosen as Green function to obtain the characteristic equation of the free vibration. The accuracy of the numerical results for the natural frequency parameter calculated by the proposed method is investigated.