Electrostatic Attraction and Repulsion Explained and Modelled Mathematically Using Classical Physics—A Detailed Mechanism Based on Particle Wave Functions

The phenomenon of electrical attraction and repulsion between charged particles is well known, and described mathematically by Coulomb’s Law, yet until now there has been no explanation for why this occurs. There has been no mechanistic explanation that reveals what causes the charged particles to accelerate, either towards or away from each other. This paper gives a detailed explanation of the phenomena of electrical attraction and repulsion based on my previous work that determined the exact wave-function solutions for both the Electron and the Positron. It is revealed that the effects are caused by wave interactions between the wave functions that result in Electromagnetic reflections of parts of the particle’s wave functions, causing a change in their momenta.

Free vibration analysis of functionally graded laminated sandwich cylindrical shells integrated with piezoelectric layer

An analytical method for the three-dimensional vibration analysis of a functionally graded cylindrical shell integrated by two thin functionally graded piezoelectric （FGP） layers is presented. The first-order shear deformation theory is used to model the electromechanical system. Nonlinear equations of motion are derived by considering the von Karman nonlinear strain-displacement relations using Hamilton＇s principle. The piezoelectric layers on the inner and outer surfaces of the core can be considered as a sensor and an actuator for controlling characteristic vibration of the system. The equations of motion are derived as partial differential equations and then discretized by the Navier method. Numerical simulation is performed to investigate the effect of different para- meters of material and geometry on characteristic vibration of the cylinder. The results of this study show that the natural frequency of the system decreases by increasing the non-homogeneous index of FGP layers and decreases by increasing the non-homogeneous index of the functionally graded core. Furthermore, it is concluded that by increasing the ratio of core thickness to cylinder length, the natural frequencies of the cylinder increase considerably.

Sound radiation of a functionally graded material cylindrical shell in water by mobility method

Based on the fundamental dynamic equations of functionally graded material (FGM) cylindrical shell, this paper investigates the sound radiation of vibrational FGM shell in water by mobility method. This model takes into account the exterior fluid loading due to the sound press radiated by the FGM shell. The FGM cylindrical shell was excited by a harmonic line radial force uniformly distributing along the generator. The FGM shell equations of motion, the Helmholtz equation in the exterior fluid medium and the continuity equation at fluid-shell interface are used in this vibroacoustic problem. The expressions of sound radiation efficiency and sound field of the FGM shell have been derived by mobility method. Radiation efficiency, modal mobility and the directivity pattern of the sound field are solved numerically. In particular, radiation efficiency and directivity pattern with various power law index are analyzed.

Nonlinear dynamic responses of sandwich functionally graded porous cylindrical shells embedded in elastic media under 1:1 internal resonance

In this article, the nonlinear dynamic responses of sandwich functionally graded(FG) porous cylindrical shell embedded in elastic media are investigated. The shell studied here consists of three layers, of which the outer and inner skins are made of solid metal, while the core is FG porous metal foam. Partial differential equations are derived by utilizing the improved Donnell's nonlinear shell theory and Hamilton's principle. Afterwards, the Galerkin method is used to transform the governing equations into nonlinear ordinary differential equations, and an approximate analytical solution is obtained by using the multiple scales method. The effects of various system parameters,specifically, the radial load, core thickness, foam type, foam coefficient, structure damping,and Winkler-Pasternak foundation parameters on nonlinear internal resonance of the sandwich FG porous thin shells are evaluated.

METHOD OF GREEN’S FUNCTION OF CORRUGATED SHELLS

By using the fundamental equations of axisymmetric shallow shells of revolution, the nonlinear bending of a shallow corrugated shell with taper under arbitrary load has been investigated. The nonlinear boundary value problem of the corrugated shell was reduced to the nonlinear integral equations by using the method of Green＇s function. To solve the integral equations, expansion method was used to obtain Green＇s function. Then the integral equations were reduced to the form with degenerate core by expanding Green＇s function as series of characteristic function. Therefore, the integral equations become nonlinear algebraic equations. Newton＇ s iterative method was utilized to solve the nonlinear algebraic equations. To guarantee the convergence of the iterative method, deflection at center was taken as control parameter. Corresponding loads were obtained by increasing deflection one by one. As a numerical example,elastic characteristic of shallow corrugated shells with spherical taper was studied.Calculation results show that characteristic of corrugated shells changes remarkably. The snapping instability which is analogous to shallow spherical shells occurs with increasing load if the taper is relatively large. The solution is close to the experimental results.

Thermal buckling analysis of functionally graded cylindrical shells

Thermal buckling behavior of cylindrical shell made of functionally graded material（FGM） is studied. The material constituents are composed of ceramic and metal.The material properties across the shell thickness are assumed to be graded according to a simple power law distribution in terms of the volume fraction rule of mixtures. Based on the Donnell shell theory, a system of dimensionless partial differential equations of buckling in terms of displacement components is derived. The method of separation of variables is used to transform the governing equations to ordinary differential equations（ODEs）. A shooting method is used to search for the numerical solutions of the differential equations under two types of boundary conditions. Effects of the power law index, the dimensionless geometrical parameters, and the temperature ratio on the critical buckling temperature are discussed in detail.

Nonlinear analysis on dynamic buckling of eccentrically stiffened functionally graded material toroidal shell segment surrounded by elastic foundations in thermal environment and under time-dependent torsional loads

The nonlinear analysis with an analytical approach on dynamic torsional buckling of stiffened functionally graded thin toroidal shell segments is investigated. The shell is reinforced by inside stiffeners and surrounded by elastic foundations in a thermal environment and under a time-dependent torsional load. The governing equations are derived based on the Donnell shell theory with the yon Karman geometrical nonlinearity, the Stein and McElman assumption, the smeared stiffeners technique, and the Galerkin method. A deflection function with three terms is chosen. The thermal parameters of the uniform temperature rise and nonlinear temperature conduction law are found in an explicit form. A closed-form expression for determining the static critical torsional load is obtained. A critical dynamic torsional load is found by the fourth-order Runge-Kutta method and the Budiansky-Roth criterion. The effects of stiffeners, foundations, material, and dimensional parameters on dynamic responses of shells are considered.

Identifying the temperature effect on the vibrations of functionally graded cylindrical shells with porosities

The free thermal vibration of functionally graded material(FGM) cylindrical shells containing porosities is investigated. Both even distribution and uneven distribution are taken into account. In addition, three thermal load types, i.e., uniform temperature rise(UTR), nonlinear temperature rise(NLTR), and linear temperature rise(LTR), are researched to explore their effects on the vibration characteristics of porous FGM cylindrical shells. A modified power-law formulation is used to describe the material properties of FGM shells in the thickness direction. Love’s shell theory is used to formulate the straindisplacement equations, and the Rayleigh-Ritz method is utilized to calculate the natural frequencies of the system. The results show that the natural frequencies are affected by the porosity volume fraction, constituent volume fraction, and thermal load. Moreover,the natural frequencies obtained from the LTR have insignificant differences compared with those from the NLTR. Due to the calculation complexity of the NLTR, we propose that it is reasonable to replace it by its linear counterpart for the analysis of thin porous FGM cylindrical shells. The present results are verified in comparison with the published ones in the literature.

Three-dimensional magneto-thermo-elastic analysis of functionally graded cylindrical shell

The present paper presents the three-dimensional magneto-thermo-elastic analysis of the functionally graded cylindrical shell immersed in applied thermal and magnetic fields under non-uniform internal pressure. The inhomogeneity of the shell is assumed to vary along the radial direction according to a power law function, whereas Poisson＇s ratio is supposed to be constant through the thickness. The existing equations in terms of the displacement components, temperature, and magnetic parameters are derived, and then the effective differential quadrature method （DQM） is used to acquire the analytical solution. Based on the DQM, the governing heat differential equations and edge boundary conditions are transformed into algebraic equations, and discretized in the series form. The effects of the gradient index and rapid temperature on the displacement, stress components, temperature, and induced magnetic field are graphically illustrated. The fast convergence of the method is demonstrated and compared with the results obtained by the finite element method （FEM）.

Nonlinear stability of functionally graded material(FGM)sandwich cylindrical shells reinforced by FGM stiffeners in thermal environment

In this paper, Donnell＇s shell theory and smeared stiffeners technique are improved to analyze the postbuckling and buckling behaviors of circular cylindrical shells of stiffened thin functionally graded material （FGM） sandwich under an axial loading on elastic foundations, and the shells are considered in a thermal environment. The shells are stiffened by FGM rings and stringers. A general sigmoid law and a general power law are proposed. Thermal elements of the shells and reinforcement stiffeners are considered. Explicit expressions to find critical loads and postbuckling load-deflection curves are obtained by applying the Galerkin method and choosing the three-term approximate solution of deflection. Numerical results show various effects of temperature, elastic foundation, stiffeners, material and geometrical properties, and the ratio between face sheet thickness and total thickness on the nonlinear behavior of shells.

Natural frequencies of rotating functionally graded cylindrical shells

Love＇s first approximation theory is used to analyze the natural frequencies of rotating functionally graded cylindrical shells. To verify the validity of the present method, the natural frequencies of the simply supported non-rotating isotropic cylindrical shell and the functionally graded cylindrical shell are compared with available published results. Good agreement is obtained. The effects of the power law index, the wave numbers along the x- and O-directions, and the thickness-to-radius ratio on the natural frequencies of the simply supported rotating functionally graded cylindrical shell are investigated by several numerical examples. It is found that the fundamental frequencies of the backward waves increase with the increasing rotating speed, the fundamental frequencies of the forward waves decrease with the increasing rotating speed, and the forward and backward waves frequencies increase with the increasing thickness-to-radius ratio.

Quasi-Green’s function method for free vibration of simply-supported trapezoidal shallow spherical shell

The idea of quasi-Green＇s function method is clarified by considering a free vibration problem of the simply-supported trapezoidal shallow spherical shell. A quasi- Green＇s function is established by using the fundamental solution and boundary equation of the problem. This function satisfies the homogeneous boundary condition of the prob- lem. The mode shape differential equations of the free vibration problem of a simply- supported trapezoidal shallow spherical shell are reduced to two simultaneous Fredholm integral equations of the second kind by the Green formula. There are multiple choices for the normalized boundary equation. Based on a chosen normalized boundary equa- tion, a new normalized boundary equation can be established such that the irregularity of the kernel of integral equations is overcome. Finally, natural frequency is obtained by the condition that there exists a nontrivial solution to the numerically discrete algebraic equations derived from the integral equations. Numerical results show high accuracy of the quasi-Green＇s function method.

Buckling analysis of functionally graded material(FGM) sandwich truncated conical shells reinforced by FGM stiffeners filled inside by elastic foundations

An analytical solution for buckling of an eccentrically stiffened sandwich truncated conical shell is investigated. The shell consists of two functionally graded material （FGM） coating layers and a core layer which are metal or ceramic subjected to an axial compressive load and an external uniform pressure. Shells are reinforced by stringers and rings, in which the material properties of shells and stiffeners are graded in the thickness direction following a general sigmoid law distribution. Two models of coated shell-stiffener arrangements are investigated. The change of the spacing between stringers in the meridional direction is taken into account. A couple set of three-variable- coefficient partial differential equations in terms of displacement components are solved by the Galerkin method. A closed-form expression for determining the buckling load is obtained. The numerical examples are presented and compared with previous works.

弹性支撑功能梯度微圆柱壳模态频率的研究

在建立弹性支撑功能梯度薄壁微圆柱壳模型的基础上,基于修正的偶应力理论和一阶剪切变形理论,推导了微圆柱壳的模态频率方程,讨论了弹性支撑、尺寸效应、温度梯度、材料组分指数、孔隙以及几何尺寸等参数对微圆柱壳模态频率的影响。结果表明:微尺度下,弹性刚度系数在0~105N/m^(3)范围内对微圆柱壳的模态频率基本无影响,剪切刚度系数在0~5×10^(4)N/m范围内对模态频率的影响较大,且增大剪切刚度系数有益于提高微圆柱壳的模态频率;由修正的偶应力理论得到的模态频率大于由经典连续体理论得到的模态频率;在弹性支撑和尺寸效应有无考虑的4种组合下,模态频率随温度梯度和微圆柱壳长度的增大而减小,随陶瓷体积分数指数的增大而增大,随孔隙体积分数和微圆柱壳厚度的变化规律不同;温度梯度对考虑尺寸效应或弹性基础的微圆柱壳模态频率影响较大,而孔隙调节具弹性支撑微圆柱壳的模态频率尤其显著。

Nonlinear thermo-mechanical stability of eccentrically stiffened functionally graded material sandwich doubly curved shallow shells with general sigmoid law and power law according to third-order shear deformation theory

In this paper, the nonlinear analysis of stability of functionally graded ma- terial （FGM） sandwich doubly curved shallow shells is studied under thermo-mechanical loads with material properties obeying the general sigmoid law and power law of four ma- terial models. Shells are reinforced by the FGM stiffeners and rest on elastic foundations. Theoretical formulations are derived by the third-order shear deformation theory （TSDT） with the von Karman-type nonlinearity taking into account the initial geometrical im- perfection and smeared stiffener technique. The explicit expressions for determining the critical buckling load and the post-buckling mechanical and thermal load-deflection curves are obtained by the Galerkin method. Two iterative algorithms are presented. The effects of the stiffeners, the thermal element, the distribution law of material, the initial imper- fection, the foundation, and the geometrical parameters on buckling and post-buckling of shells are investigated.

橡子壳提取物成分分析及对小麦淀粉特性的影响

为开发低消化率面制食品,研究栓皮栎橡子壳提取物对小麦淀粉特性的影响,以栓皮栎橡子壳为试材,采用超声辅助乙醇提取,高分辨离子淌度-液质联用分析,对比试验和模拟消化试验,研究栓皮栎橡子壳乙醇提取物的制备,功能成分及其对小麦淀粉的糊化特性、凝胶特性及消化特性的影响。结果表明:栓皮栎橡子壳的乙醇提取物得率为2.40%,其总酚含量102.87 mg GAE/g、总黄酮含量41.72 mg RE/g,共鉴定出34种成分,主要为多酚、黄酮、萜、有机酸等活性成分。栓皮栎橡子壳乙醇提取物能明显降低小麦淀粉的糊化黏度及热稳定性,降低小麦淀粉凝胶的弹性、硬度、咀嚼性、胶黏性,使小麦淀粉凝胶表面变得更粗糙,组织结构更疏松,抑制了小麦淀粉凝胶的老化。当添加栓皮栎橡子壳乙醇提取物15%时,消化20 min,可降低消化率38.16%。结论:栓皮栎橡子壳乙醇提取物含有丰富的功能性成分,可改变小麦淀粉糊化特性和凝胶组织结构,降低小麦淀粉的消化率,可与小麦淀粉联合制备低消化率的面制食品。

双壳体核电厂空间减震结构的竖向动力试验研究

为降低核电厂内安全壳的竖向加速度,提出了一种双壳体空间减震结构,基于该结构的力学特性建立了简化三质点三自由度动力模型,进一步给出了结构响应传递函数并进行了参数分析,明确了结构质量比、阻尼比和频率比对结构竖向地震响应的影响规律,完成了双壳体空间减震结构的缩尺振动台动力试验。结果表明:双壳体空间减震结构可减小内安全壳的竖向加速度,减震率为12.23%~27.84%。双壳体空间减震结构的振动台试验响应结果与理论计算值吻合较好,验证了所提出的双壳体空间减震结构简化模型的准确性以及双壳体空间减震系统的有效性。

基于自适应Kriging的耐压球壳可靠性计算方法研究

为研究耐压球壳的可靠性计算问题,提出基于自适应Kriging的耐压球壳可靠性计算方法。该方法主要包括在开展试验设计的基础上,基于有限元方法获得样本点对应的承载能力,使用自适应Kriging方法结合ERF学习函数构建结构失效方程,并在此基础上开展可靠性计算。耐压球壳计算结果表明,10个验证样本点计算结果偏差均小于0.5‰,该方法具有较高精度和计算效率。基于计算结果提出在开展自适应方法建立Kriging模型过程中,学习函数的收敛指标应随着计算方法的精度进行适当地调整的结论。研究结果可为无失效方程结构的可靠性计算提供参考。

相变材料微胶囊的研究进展

为进一步提高能源利用率,满足当今社会对可持续能源的迫切需求,首先,列举了相变材料微胶囊的芯材和壁材的分类及其选择原则;其次,分析总结了相变材料微胶囊不同制备技术的国内外最新研究进展,重点对比归纳了物理法、化学法以及物理化学法等制备技术的原理、特点及其适用范围;然后,综述了相变材料微胶囊在纺织、医疗、建筑、能源等领域的应用进展并分析总结国内外最新相关研究;最后,针对相变材料微胶囊在生产制备和实际应用中的关键问题,提出其潜在解决方案和优先发展方向,以推进相变材料微胶囊不断向绿色化、多功能化方向深入发展。

曲线链式回转弹仓动力学模型不确定参数辨识

为了准确模拟曲线链式回转弹仓输送弹药过程中的非线性动力学特性,根据系统的拓扑结构和控制原理建立包含不确定参数的动力学模型。利用优化设计思想,基于系统测试数据建立不确定参数辨识模型。提出一种函数型时间序列相似度作为辨识准则,采用基于径向基函数的高维模型表示和径向基函数分别构建从机械系统和控制系统不确定参数到辨识准则的代理模型。将麻雀搜索算法嵌入岛屿模型进行多种群结构化,形成岛屿麻雀搜索算法,进行寻优求解。以工况1测试数据为基准,对机械系统和控制系统的不确定参数进行辨识。研究结果表明,辨识后的动力学模型对两种工况的输出结果与测试数据相似度较高,验证了建模的准确性和辨识的有效性,为动作可靠性分析和故障诊断研究提供了可靠的样本数据来源。