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Bending Solutions of FGM Reddy-Bickford Beams in Terms of Those of the Homogenous Euler-bernoulli Beams

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Acta Mechanica Solida Sinica 2019年第4期32卷 499-516页

作者： You-Ming Xia Shi-Rong Li Ze-Qing Wan School of Civil Science and Engineering Yangzhou UniversityYangzhou 225127 China

In this paper, correspondence relations between the solutions of the static bending of functionally graded material (FGM) Reddy-Bickford beams (RBBs) and those of the corresponding homogenous Euler-bernoulli beams are presented. The effective material properties of the FGM beams are assumed to vary continuously in the thickness direction. Governing equations for the titled problem are formulated via the principle of virtual displacements based on the third-order shear deformation beam theory, in which the higher-order shear force and bending moment are included. General solutions of the displacements and the stress resultants of the FGM RBBs are derived analytically in terms of the deflection of the reference homogenous Euler- bernoulli beam with the same geometry, loadings and end conditions, which realize a classical and homogenized expression of the bending response of the shear deformable non-homogeneous FGM beams. Particular solutions for the FGM RBBs under specified end constraints and load conditions are given to validate the theory and methodology. The key merit of this work is to be capable of obtaining the high-accuracy solutions of thick FGM beams in terms of the classical beam theory solutions without dealing with the solution of the complicated coupling differential equations with boundary conditions of the problem.

关键词： Functionally graded material beams Reddy-Bickford beam theory Euler- bernoulli beam theory Bending solution Shear deformation

The Exact Inference of Beta Process and Beta bernoulli Process From Finite Observations

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Computer Modeling in Engineering & Sciences 2019年第10期121卷 49-82页

作者： Yang Cheng Dehua Li Wenbin Jiang School of Artificial Intelligence and Automation Huazhong University of Science and TechnologyWuhan430074China School of Computer Science and Technology Huazhong University of Science and TechnologyWuhan430074China.

Beta Process is a typical nonparametric Bayesian model.and the Beta bernoulli Process provides a Bayesian nonparametric prior for models involving collections of binary valued features.Some previous studies considered the Beta Process inference problem by giving the Stick-Breaking sampling method.This paper focuses on analyzing the form of precise probability distribution based on a Stick-Breaking approach,that is,the joint probability distribution is derived from any finite number of observable samples:It not only determines the probability distribution function of the Beta Process with finite observation(represented as a group of number between[0,1]),but also gives the distribution function of the Beta bernoulli Process with the same finite dimension(represented as a matrix with element value of 0 or,1)by using this distribution as a prior.

关键词： Beta process joint distribution beta bernoulli process exact inference

Generalized Series of bernoulli Type

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Advances in Pure Mathematics 2023年第9期13卷 537-542页

作者： Thomas Beatty Nicholas Bianco Nicole Legge Department of Mathematics Florida Gulf Coast University Fort Myers FL USA

The problem of evaluating an infinite series whose successive terms are reciprocal squares of the natural numbers was posed without a solution being offered in the middle of the seventeenth century. In the modern era, it is part of the theory of the Riemann zeta-function, specifically ζ (2). Jakob bernoulli attempted to solve it by considering other more tractable series which were superficially similar and which he hoped could be algebraically manipulated to yield a solution to the difficult series. This approach was eventually unsuccessful, however, bernoulli did produce an early monograph on summation of series. It remained for bernoulli’s student and countryman Leonhard Euler to ultimately determine the sum to be . We characterize a class of series based on generalizing bernoulli’s original work by adding two additional parameters to the summations. We also develop a recursion formula that allows summation of any member of the class.

关键词： bernoulli Series Convergence Sum Recursion Formula Zeta-Function Sine Maclaurin Series Infinite Product

Identities for degenerate bernoulli polynomials and Korobov polynomials of the first kind

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Science China Mathematics 2019年第5期62卷 999-1028页

作者： Taekyun Kim Dae San Kim Department of Mathematics Kwangwoon University Department of Mathematics Sogang University

In this paper, we derive five basic identities for Sheffer polynomials by using generalized Pascal functional and Wronskian matrices. Then we apply twelve basic identities for Sheffer polynomials, seven from previous results, to degenerate bernoulli polynomials and Korobov polynomials of the first kind and get some new identities. In addition, letting λ→ 0 in such identities gives us those for bernoulli polynomials and bernoulli polynomials of the second kind.

关键词： generalized Pascal functional matrix Wronskian matrix degenerate bernoulli polynomial Krobov polynomial of the first kind

Fault Detection for Complex Systems with Channel Fadings, Randomly Occurring Multiple Delays and Infinitely Distributed Delays

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Journal of Systems Science & Complexity 2018年第2期31卷 419-435页

作者： WANG Yanqin REN Weijian LU Yang School of Mechanical and Electrical Engineering Daqing Normal University Daqing 163712 China College of Electrical and Information Engineering Northeast Petroleum University Daqing 163318 China

这份报纸涉及差错察觉(FD ) 为有隧道 fadings，随机发生的多重通讯延期，和无穷地分布式的延期的分离时间的随机的系统的一个班的问题。所有三现象有随机发生和互相独立，但是服从 bernoulli 分发的随机的变量的三个序列的特征被采用... 详细信息

这份报纸涉及差错察觉(FD ) 为有隧道 fadings，随机发生的多重通讯延期，和无穷地分布式的延期的分离时间的随机的系统的一个班的问题。所有三现象有随机发生和互相独立，但是服从 bernoulli 分发的随机的变量的三个序列的特征被采用描述他们。这份报纸的目的是设计一个 FD 过滤器以便 FD 动力学在吝啬的平方并且，同时是指数地稳定的在剩余信号和差错信号之间的错误被使尽可能小。集中的分析被利用为设计 FD 过滤器导出足够的条件，它保证指数的稳定性和规定 H 表演。FD 过滤器参数被解决一个凸的优化问题获得。一个解说性的例子被提供表明 FD 设计计划的有效性。

关键词：复杂系统分布式随机延期隧道无穷多重 bernoulli

bernoulli Loops in Smoke Rings

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Natural Science 2019年第10期11卷 285-287页

作者： Kern E. Kenyon 4632 North Lane Del Mar CA USA

bernoulli’s law is applied to the closed streamlines of a smoke ring, and the centrifugal force of the curved flow is balanced by a pressure gradient. Two equations in two unknowns, pressure and velocity, are combined into one equation in one unknown, velocity. Solving the governing equation algebraically produces a radial shear in the velocity such that the speed decreases outward inversely as the radius increases, which is the main result. Measurements are needed to verify the predicted structure of the velocity field.

关键词： Smoke Rings bernoulli Loops

Several Expressions of Dirichlet L-function at Positive Integers

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Acta Mathematica Sinica,English Series 2019年第9期35卷 1549-1562页

作者： Yuan HE School of Mathematics and Information Science Neijiang Normal University

In this paper, by making use of Abel’s theorem on power series, the reflection formula and the function equation for Hurwitz zeta function, we establish several expressions of Dirichlet Lfunction at positive integers by means of some finite sums of different types. Some special cases as well as immediate consequences of the results presented here are also considered.

关键词： Dirichlet L-function trigonometric sums gauss sums bernoulli polynomials combinatorial identities

ANALYSIS OF LEAKAGE CHARACTERISTICS OF LABYRINTH SEALS

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Chinese Journal of Aeronautics 1990年第4期5卷 233-238页

作者： Zhu, Yizhang He, Feng Beijing Inst of Chemical Technology Beijing China

This paper presents the leakage characteristics of labyrinth seals, which were introduced by theoretical analysis and experiment results. The study of the dissipative process converting the kinetic energy to the thermal energy within the labyrinth chamber is emphasized. Experiments were carried out using a model of Straight-Through Labyrinth. By changing the Reynolds number, pressure ratio, and the ratios of clearance and depth to the length of the chambers, the flow coefficient, carry-over factor and ideal labyrinth function can be determined. Additionally, by applying the continuity equation, energy equation. bernoulli’s equation and the equation of state to the vortex chambers, a closed set of equations is obtained. Solving the equations simultaneously and numerically, the velocity, pressure and temperature in each vortex- chamber can be determined completely. Finally, the leakage of the labyrinth is acquired.

关键词： chambers length vortex continuity leakage emphasized carry converting bernoulli clearance

Dynamic Analysis of Kineto-Elastic Beam System with Second-order Effect

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Journal of Donghua University(English Edition) 2009年第3期26卷 313-318页

作者：陆念力罗冰夏拥军 School of Mechatronics Engineering Harbin Institute of Technology

Dynamic equations of motional flexible beam elements were derived considering second-order effect. Non-linear finite element method and three-node Euler-bernoulli beam elements were used. Because accuracy is higher in non-linear structural analysis,three-node beam elements are used to deduce shape functions and stiffness matrices in dynamic equations of flexible elements. Static condensation method was used to obtain the finial dynamic equations of three-node beam elements. According to geometrical relations of nodal displacements in concomitant and global coordinate system,dynamic equations of elements can be transformed to global coordinate system by concomitant coordinate method in order to build the global dynamic equations. Analyzed amplitude condition of flexible arm support of a port crane,the results show that second-order effect should be considered in kinetic-elastic analysis for heavy load machinery of big flexibility.

关键词：动力学分析二阶效应弹性梁 bernoulli 动力学方程非线性有限元方法非线性结构分析节点位移