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Numerical Study of the Vibrations of Beams with Variable Stiffness under Impulsive or Harmonic Loading

World Journal of Engineering and Technology 2024年第2期12卷 401-425页

作者： Moussa Sali Fabien Kenmogne Jean Bertin Nkibeu Abdou Njifenjou Laboratory of Materials Mechanics and Civil Engineering National Higher Polytechnic School of Maroua University of Maroua Maroua Cameroon Department of Civil Engineering Advanced Teachers Training College of the Technical Education University of Douala Douala Cameroon Laboratory Engineering Civil and Mechanics National Advanced School of Engineering University of Yaound&#233 1 Yaound&#233 Cameroon Laboratory of Energy Materials Modeling and Method (E3M) National Advanced School of Engineering University of Douala Douala Cameroon Laboratory of Mathematical Engineering and Information Systems National Advanced School of Engineering University of Yaound&#233 1 Yaound&#233 Cameroon

The behavior of beams with variable stiffness subjected to the action of variable loadings (impulse or harmonic) is analyzed in this paper using the successive approximation method. This successive approximation method is a technique for numerical integration of partial differential equations involving both the space and time, with well-known initial conditions on time and boundary conditions on the space. This technique, although having been applied to beams with constant stiffness, is new for the case of beams with variable stiffness, and it aims to use a quadratic parabola (in time) to approximate the solutions of the differential equations of dynamics. The spatial part is studied using the successive approximation method of the partial differential equations obtained, in order to transform them into a system of time-dependent ordinary differential equations. Thus, the integration algorithm using this technique is established and applied to examples of beams with variable stiffness, under variable loading, and with the different cases of supports chosen in the literature. We have thus calculated the cases of beams with constant or variable rigidity with articulated or embedded supports, subjected to the action of an instantaneous impulse and harmonic loads distributed over its entire length. In order to justify the robustness of the successive approximation method considered in this work, an example of an articulated beam with constant stiffness subjected to a distributed harmonic load was calculated analytically, and the results obtained compared to those found numerically for various steps (spatial h and temporal τ ¯ ) of calculus, and the difference between the values obtained by the two methods was small. For example for ( h=1/8 , τ ¯ =1/ 64 ), the difference between these values is 17%.

关键词： Successive Approximations Method direct integration Differential Equations Beams of Variable Stiffness Quadratic Parabola Impulse and Harmonic Loads

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Electrochemical performance of thermally-grown SiO2 as diffusion barrier layer for integrated lithium-ion batteries

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Frontiers in Energy 2018年第2期12卷 225-232页

作者： X.D.HUANG X.F.GAN Q.A.HUANG J.Z.YANG Key Laboratory of MEMS of the Ministry of Education School of Electronic Science and EngineeringSoutheast UniversityNanjing 210096China School of Chemistry and Chemical Engineering Nanjing University of Science and TechnologyNanjing 210094China

direct integration of lithium-ion battery （LIB） with electronic devices on the same Si substrate can significantly miniaturize autonomous micro systems. For achieving direct integration, a barrier layer is essential to be inserted between LIB and the substrate for blocking Li^＋ diffusion. In this paper, the feasibility of thermal SiOa film as the barrier layer is investigated by electrochemical characterization and X-ray photoelectron spectroscopy （XPS）. Due to the negligible side reactions of thermal SiO2 with electrolyte, the solid electrolyte interphase （SEI） layer formed on the surface of the barrier layer is thin and the SEI content mainly consists of hydrocarbon together with slight polyethylene oxide （PEO）, LixPOyFz, and Li2CO3. Although 8-nm thermal SiO2 effectively prevents the substrate from alloying with Li^＋, the whole film changes to Li silicate after electrochemical cycling due to the irreversible chemical reactions of SiO2 with electrolyte. This degrades the performance of the barrier layer against the electrolyte penetration, thus leading to the existence of Li^＋（in the form of F-Si-Li） and solvent decompositions （with the products of hydrocarbon and PEO） near the barrier layer/substrate interface. Moreover, it is found that the reaction kinetics of thermal SiO2 with electrolyte decrease significantly with increasing the SiO2 thickness and no reactions are found in the bulk of the 30-nm SiO2 film. Therefore, thermal SiO2 with an appropriate thickness is a promising barrier layer for direct integration.

关键词： autonomous micro system direct integration barrier layer thermal SiO2 film X-ray photoelectron spectroscopy (XPS)

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SPATIAL－TEMPORAL　DISCRETE　COORDINATION　OF　FEM　AND　direct　INTEGRAL　METHOD　FOR　TRANSIENT　DYNAMIC　PROBLEMS

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Applied Mathematics and Mechanics(English Edition) 1994年第12期15卷 1169-1175页

作者：王怀忠 Shanghai Institute of Applied Mathematics and Mechanics Shanghai University Shanghai

In this paper, the coordination of spatial-temporal discrets of FEM and direct integral method is *** analyzing the numespatial-temporal discrete,the principle of balancing the principle of balancing the energy error induced by spatialdiscrete and the energy error induced by temporal discrete is presented, and the prioriprocess and adaptive method for the coordination of spatial discerand temporal discrete is obtained.

关键词： FEM direct integration spatial-temporal discrete coordination

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