径向压力作用下夹层圆板自由振动理论解

基于小挠度薄板理论,建立径向均布压力作用下夹层圆板的振动控制方程。采用分离变量法导出夹层圆板的固有频率及振型解析式,计算径向均布压力作用下周边固支夹层圆板固有频率和振型,讨论径向均布压力和夹心层比率对固有频率的影响。研究表明夹层圆板的固有频率随径向压力增大而减小,临界压力随阶次的增大而增大;作用径向压力的夹层圆板固有频率随夹心层比率增大,先缓慢增大,到峰值后减小,该趋势与无径向压力时相同。     

敷设覆盖层圆板水下爆炸响应理论计算方法研究

为研究敷设覆盖层圆板水下爆炸响应,提出一种理论计算方法。敷设覆盖层对圆板水下爆炸响应影响包括两方面:一为对冲击载荷的影响,二为在冲击载荷作用下对响应的影响。该理论计算方法运用波在多层介质传播理论得到湿表面压力,并积分得到冲量,运用等效均一化理论得到覆盖层与钢板整体结构的等效参数,根据圆板振动理论得到圆板真空振动方程,通过考虑水附加质量的影响修正圆板振动频率,最后根据初始条件得到圆板的响应。将理论方法的结果与有限元结果通过实例进行对比,证明该理论计算方法可以很好地预测圆板振动的位移响应。     

Analytical Solution to the Plane Bending Task of the Multilayer Beam with a Circular Axis under Normal Uniform Loading

Strength of Materials - Circular bars are widespread elements in building and mechanical engineering. They allow one to enhance the strength of the multilayer composite materials along with their...     

An Analytical Solution of Vector Diffraction for Focusing Optical Systems

Abstract

Vector diffraction theory for optical systems has been of interest for a long time. Ignatovsky and Wolf have formulated these problems in terms of diffraction integrals and Wolf has presented very interesting results. Usually, the quadrature of diffraction integrals is numerically intensive, therefore these problems have remained of interest and many authors have worked on the Ignatovsky-Wolf formulation or some variation thereof. This paper presents yet another method of solving diffraction integrals. Since a certain part of the kernel of these integrals is Riemann integrable in the interval [0, π], the Weierstrass theorem says that it can be approximated by a uniformly convergent series of orthogonal functions. Thus it is possible to expand these functions into a series of Gegenbauer polynomials of the first kind. Once these expansions are substituted in the diffraction integrals, the resulting integrals are readily evaluated, over the surface of unit sphere, in terms of the spherical Bessel functions and Gegenbauer polynomials. The results are particularly simple if the image plane is the focal plane. In this paper, we evaluate the diffraction integrals for several optical systems of arbitrary numerical aperture with or without obscuration, and for a parabolic reflector. The results presented here are in agreement with previously published results. The numerical computations are easy since all the functions are evaluated by adding a finite series. The calculations which for the basis of results presented in this paper were performed on a personal computer.     

The Verification of an Analytical Solution: An Important Engineering Lesson

Too often, as long as they “match the answer book,” results based on analytical methods are not subjected to much scrutiny. In contrast, computational results and those based on physical measurements are nearly always met with skepticism. Here we show an example from radiation heat transfer in which an exact analytical solution, when reduced to numbers in the generally-practiced manner, gives a patently wrong answer. Efforts to verify a new computational algorithm brought this long-standing error to light.     

地下双洞室在SV波入射下动力响应问题解析解

采用波函数展开法给出了地下双洞室在平面SV波入射下动力响应二维问题的一个解析解，数值结果表明：当两个洞室之间距离较近时，洞室之间的相互作用对地下双洞室的动应力集中具有显著的放大作用，两个洞室情况动应力集中系数可能达到单个洞室的5．2倍以上，动应力集中系数的峰值位于两个洞室相对的区域内。     

考虑桩体粘性的变阻抗桩受迫振动问题的解析解

建立了考虑桩体材料粘弹性、桩长有限、桩端为弹性支承时,考虑桩侧土作用、桩截面声阻抗发生突变状态下(有两个突变界面),桩顶受纵向激振时基桩受迫振动的定解问题,求得了稳态正弦及瞬态半正弦激振条件下的解析解,并对所得解进行了研究分析,结果显示,桩体材料粘性对变阻抗界面处的特征反射有着较大的影响。     

两黏性颗粒间切向阻力的渐近解析解

从分析两黏性颗粒的相对切向运动着手,化二阶变系数非齐次液桥流体压力微分方程为欧拉方程,解得具有相对运动的不等径颗粒间液桥流体压力和切向黏性阻力的渐近解析解,并与Goldman意义上的近似解和其他文献中的数值解进行对比。结果表明:利用这些解析解可直接定义黏性颗粒力学模型,也可分析不同参数条件下液桥流体压力与颗粒间切向阻力的变化规律。     

气泡－水相界面上传质过程的自相似分析解

应用自相似方法求解气泡－水相界上的传质问题，并获得了计算相界面上传质量的表达式。     

碳纳米管增强镁基复合材料强化机制的解析法研究

采用剪切滞后模型理论分析了碳纳米管增强镁基复合材料受载时作用在复合材料上各组分的应力;考虑复合材料各种强化机制,建立碳纳米管增强镁基复合材料的屈服强度模型,研究了各组分性能参数对复合材料屈服强度的影响。结果表明,CNTs的长度对CNTs/Mg复合材料屈服强度的影响有限;碳纳米管层数越多或分散越稀疏越不利于提高复合材料的屈服强度;在一定范围内屈服强度随着温度差的增加而增加;CNTs的体积分数对复合材料屈服强度的影响存在最佳值。这表明该模型预测的复合材料屈服强度与实验结果较吻合。     

Analytical Solution of Another Ellipsometric Inverse Problem

Abstract

An analytical solution is given that allows one to obtain the depth of an arbitrary layer from the measured ellipsometric parameters ψ and Δ of an arbitrary plane-parallel isotropic layered structure if all the refractive indexes and the depths of the rest layers are known. An analysis of the relative errors is given.     

An Integration Depending on Parameter Ф for Analytical Solution of the Compression of Thin Workpiece

An integration depending on the parameter Ф hasbeen applied to the function Фdx so that an explicitformula of specific pressure calculation and an analyticalsolution are obtained.It has been found that the analyticalsolution is basically the same as the prevailing numericalone which is from the formula There-fore,it is justified theoretically that for the slip line field inthe compression of a thin workpiece a parametric integra-tion is perfectly possible for satisfactory analyticalsolution.     

Evaporation-Induced Flow Inside Circular Wells: Analytical Results and Simulations

The relationship between hydrodynamical flow inside a liquid sample in open circular well and the mode of evaporation is examined. For four different modes of evaporation, we found analytical expressions for the height averaged radial velocity as well as velocity field inside the circular well for the particular case of flat air–liquid interface.     

Analytical Modeling to Predict the Strain Energy of Circular GLARE Fiber-Metal Laminates Under Lateral Indentation

This article deals with the strain energy calculation of thin circular clamped Glass Reinforced （GLARE） fiber-metal laminates subjected to static indentation by a lateral hemispherical indentor. Using one-, two- and three-parameter Ritz approximations, analytical equations of the strain energy as a function of the central plate deflection are derived. Previously published analytical formulas, concerning the load-indentation response of circular GLARE plates, are used in order to determine the Ritz parameters and the first failure load and deflection due to tensile fracture of glass-epoxy layers. In this study, the membrane and bending strain energy components of aluminum and prepreg layers are determined. Also, the elastic and plastic strain energy absorbed during the indentation loading are calculated. The derived formulas are applied successfully for GLARE 2-2/1-0.3, GLARE 3-3/2-0.4 and GLARE 31 （special lay-up） circular plates subjected to lateral indentation. The strain energy results converge satisfactorily in all examined cases. The predicted strain energy-indentation response is compared with published experimental data and a good agreement is found. No other solution of this problem is known to the authors.     

Analytical Solution for an Orthotropic Elastic Plate Containing Cracks

The problem of estimating the bending stress distribution in the neighborhood of a crack located on a single line in an orthotropic elastic plate of constant thickness subjected to bending moment or twisting moment is examined. Using classical plate theory and integral transform techniques, the general formulae for the bending moment and twisting moment in an elastic plate containing cracks located on a single line are derived. The solution is obtained in a closed form for the case in which there is a single crack in an infinite plate and the results are compared with those obtained from the literature.     

Analytical Solution of Buckling of Beams with Two Delaminations

A stability problem of composite beams with multiple delamination was tackled. A closed-form solution was found and buckling loads of composite beams with two delaminations were determined in order to obtain their compressive load-carrying capacity. Crack-opening mode was assumed for each detached delaminated region. Seven different regions having different transverse deformations resulted from assumed positions of delaminations. Developing the derived continuity condition equations reduced the number of algebraic equations required to solve the problem analytically. The results of the work were validated by comparing them to those reported in the literature. The effects of length, location, and distribution of multiple delaminations were considered in the comparison, and the results showed very good agreement. Buckling load decreases as delamination size increases. Buckling load for a beam with two delaminations is lower than that for the same beam with a single delamination.     

A Two-Dimensional Analytical Solution for the Transient Short-Hot-Wire Method

Unlike the conventional transient hot-wire method for measuring thermal conductivity, the transient short-hot-wire method uses only one short thermal-conductivity cell. Until now, this method has depended on numerical solutions of the two-dimensional unsteady heat conduction equation to account for end effects. In order to provide an alternative and to confirm the validity of the numerical solutions, a two-dimensional analytical solution for unsteady-state heat conduction is derived using Laplace and finite Fourier transforms. An isothermal boundary condition is assumed for the end of the cell, where the hot wire connects to the supporting leads. The radial temperature gradient in the wire is neglected. A high-resolution finite-volume numerical solution is found to be in excellent agreement with the present analytical solution.