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李雅普诺夫函数；剩余能量函数；耗散陀螺系统稳定性 1

混合体；积分方程；矩量法；加法定理；迭代 1

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Bending and vibration of a discontinuous beam with a curvic coupling under different axial forces

Heng LIU, Jie HONG, Dayi ZHANG

《机械工程前沿（英文）》 2020年第15卷第3期页码 417-429 doi: 10.1007/s11465-019-0584-4

摘要： The transverse stiffness and vibration characteristics of discontinuous beams can significantly differ from those of continuous beams given that an abrupt change in stiffness may occur at the interface of the former. In this study, the equations for the deflection curve and vibration frequencies of a simply supported discontinuous beam under axial loads are derived analytically on the basis of boundary, continuity, and deformation compatibility conditions by using equivalent spring models. The equation for the deflection curve is solved using undetermined coefficient methods. The normal function of the transverse vibration equation is obtained by separating variables. The differential equations for the beam that consider moments of inertia, shearing effects, and gyroscopic moments are investigated using the transfer matrix method. The deflection and vibration frequencies of the discontinuous beam are studied under different axial loads and connection spring stiffness. Results show that deflection decreases and vibration frequencies increase exponentially with increasing connection spring stiffness. Moreover, both variables remain steady when connection spring stiffness reaches a considerable value. Lastly, an experimental study is conducted to investigate the vibration characteristics of a discontinuous beam with a curvic coupling, and the results exhibit a good match with the proposed model.

关键词： discontinuous beam bending stiffness transverse vibration axial loads gyroscopic moments

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Improved prediction of pile bending moment and deflection due to adjacent braced excavation

《结构与土木工程前沿（英文）》 doi: 10.1007/s11709-023-0961-2

摘要： Deep excavations in dense urban areas have caused damage to nearby existing structures in numerous past construction cases. Proper assessment is crucial in the initial design stages. This study develops equations to predict the existing pile bending moment and deflection produced by adjacent braced excavations. Influential parameters (i.e., the excavation geometry, diaphragm wall thickness, pile geometry, strength and small-strain stiffness of the soil, and soft clay thickness) were considered and employed in the developed equations. It is practically unfeasible to obtain measurement data; hence, artificial data for the bending moment and deflection of existing piles were produced from well-calibrated numerical analyses of hypothetical cases, using the three-dimensional finite element method. The developed equations were established through a multiple linear regression analysis of the artificial data, using the transformation technique. In addition, the three-dimensional nature of the excavation work was characterized by considering the excavation corner effect, using the plane strain ratio parameter. The estimation results of the developed equations can provide satisfactory pile bending moment and deflection data and are more accurate than those found in previous studies.

关键词： pile responses excavation prediction deflection bending moments

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耗散陀螺系统的李雅普诺夫函数构造：剩余能量函数方法 Personal View

Cem CİVELEK, Özge CİHANBEĞENDİ

《信息与电子工程前沿（英文）》 2020年第21卷第4期页码 629-634 doi: 10.1631/FITEE.1900014

摘要：在自由度为4、张量有逆变（右上标）和协变（右下标）形式的耗散陀螺系统中，使用二阶线性微分方程建立拉格朗日耗散模型，即{L, D}模型。通过系统的{L, D}模型确定广义元素。满足勒让德变换先决条件时，可得哈密顿量。剩余能量函数（REF）由哈密顿量及损耗或耗散能量（为负）之和组成，将其作为李雅普诺夫函数，可通过李雅普诺夫第二方法作稳定性分析，并从数学上推导出稳定性条件。

关键词：李雅普诺夫函数；剩余能量函数；耗散陀螺系统稳定性

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任意金属—介电混合体面体面电场积分方程（SVS-EFIE）的增强解 Research Article

王涵,庞铭杰,林海

《信息与电子工程前沿（英文）》 2022年第23卷第7期页码 1098-1109 doi: 10.1631/FITEE.2100387

摘要：利用矩量法求解面体面电场积分方程（SVS-EFIE），公式复杂，实现困难，算法复杂度高。本文提出求解任意金属—介电混合体电磁散射问题的通用矩阵方程（GME），并给出该方程的增强解。矩量法只考虑包含3个区域的金属—介电混合体，且SVS-EFIE的两步过程导致两个积分符号，难以实现且算法复杂度高。为解决该问题，本文首次提出能够用于分析均匀介质体和超过3个区域金属—介电混合体的GME方法。提出基于耦合度和子区域间距相关的GME加速求解策略，并自适应设置耦合度标准以平衡精度和效率。将变形后的加法定理用于强耦合情况，将迭代法用于弱耦合情况。并行性可以方便地应用于该增强解。数值结果表明，与直接解相比，该方法平均只需11.6%的内存和11.8%的中央处理器时间。

关键词：混合体；积分方程；矩量法；加法定理；迭代

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Uncertainty propagation analysis by an extended sparse grid technique

X. Y. JIA, C. JIANG, C. M. FU, B. Y. NI, C. S. WANG, M. H. PING

《机械工程前沿（英文）》 2019年第14卷第1期页码 33-46 doi: 10.1007/s11465-018-0514-x

摘要： In this paper, an uncertainty propagation analysis method is developed based on an extended sparse grid technique and maximum entropy principle, aiming at improving the solving accuracy of the high-order moments and hence the fitting accuracy of the probability density function (PDF) of the system response. The proposed method incorporates the extended Gauss integration into the uncertainty propagation analysis. Moreover, assisted by the Rosenblatt transformation, the various types of extended integration points are transformed into the extended Gauss-Hermite integration points, which makes the method suitable for any type of continuous distribution. Subsequently, within the sparse grid numerical integration framework, the statistical moments of the system response are obtained based on the transformed points. Furthermore, based on the maximum entropy principle, the obtained first four-order statistical moments are used to fit the PDF of the system response. Finally, three numerical examples are investigated to demonstrate the effectiveness of the proposed method, which includes two mathematical problems with explicit expressions and an engineering application with a black-box model.

关键词： uncertainty propagation analysis extended sparse grid maximum entropy principle extended Gauss integration Rosenblatt transformation high-order moments analysis