Free Vibration Characteristics of Composite Barrel and Hyperboloidal Coil Springs

The first six resonance frequencies of unidirectional composite noncylindrical helical springs (barrel and hyperboloidal types) made of carbon-epoxy (T300/N5208) material are determined theoretically based on the transfer matrix method. The rotary inertia, shear, and axial deformation effects are considered with the first-order shear deformation theory. The overall transfer matrix is obtained by integrating the 12 scalar ordinary differential equations with variable coefficients governing the free-vibration behavior of noncylindrical helical springs made of an anisotropic material. Numerical results are verified with the reported values for isotropic noncylindrical helices. A parametric study is performed to investigate the effects of the number of active coils (n = 5-10), the helix pitch angle ( f = 5° and 25°), the ratio of the minimum to maximum cylinder radii ( R min/ R max = 0.1 and 0.9), and the ratio of the maximum cylinder diameter to the wire diameter ( D max/ d = 5 and 15) on the free-vibration frequencies of constant-pitch composite barrel and hyperboloidal helical springs with circular sections and fixed-fixed ends.     

Dynamic Susceptibility of the Free Fermi Gas in 2D

A detailed discussion of the dynamic susceptibility of the two dimensional free Fermi gas at zero and finite temperature is presented. The behaviour and evolution of the coherent and incoherent components of the dynamic structure function with the temperature and momentum transfer are analyzed. Particular attention is paid to the way in which their relative contribution changes with respect to the ~T=0 case. The influence of thermal effects on the lowest order sum rules of the coherent and incoherent responses is also discussed. Finally, similar analysis are presented for the real part of the dynamic susceptibility.     

Dynamic analysis of composite coil springs of arbitrary shape

The dynamic behavior of composite coil springs of arbitrary shape is investigated. The Timoshenko beam theory is adopted in the derivation of the governing equation. The material of the rod is assumed to be homogeneous, linear elastic and anisotropic. The effects of the ratio maximum diameter of the cylinder/thickness (D_max/d), the number of active turns (n), the helix pitch angle (α) and the ratio of the minimum to maximum cylinder radii (R_min/R_max) on the dynamic behavior of the composite barrel and hyperboloidal springs are investigated. The free and forced vibrations of composite coil springs of arbitrary shape such as barrel and hyperboloidal springs are analyzed through various examples.     

局部褶皱对层状地基马蹄形孔洞散射的影响分析

水平岩层在构造作用下会产生局部褶皱,研究褶皱对层状地基马蹄形孔洞散射的影响,对地表结构地震安全性评价具有重要意义。基于子结构法建立了复杂场地散射问题的控制方程,将地震波散射问题的求解转化具有规则边界条件的层状地基(自由场)的动力刚度和波动响应的求解。通过Fourier变换和引入对偶变量,将波动方程转化为一阶常微分方程,采用精细积分算法对土层可实现高效合并,施加边界条件可得到内部节点的格林函数,进一步得到动力刚度。同时,采用精细积分算法代替原传递矩阵法的层间合并,可得到层状自由场的波动响应。这种改进传递矩阵法对土层厚度和层数没有任何限制。通过与文献中的结果对比,验证了方法的正确性,并分析了局部褶皱对层状地基中马蹄形孔洞散射场的影响。结果表明:局部褶皱对地表位移幅值的影响与入射波类型、入射波频率以及局部褶皱几何构造等因素均有关系;地表位移峰值受马蹄形孔洞和局部褶皱共同作用的影响,其影响特性与入射波类型无明显关系。     

分析结构自由振动的传递矩阵精确形式

本文以微分方程和矩阵分析理论为基础,导出了求解结构自由振动传递矩阵法的精确工,无论是在计算效率和精度上都是对传递矩阵法的一个很好推广。文中运用这种封闭的精确形式求解了分段变厚圆柱壳的自由振动。     

An iterative solution scheme for systems of boundary element equations

In this paper an iterative scheme of first order is developed for the purpose of solving linear systems of equations. In particular, systems that are derived from boundary integral equations are investigated. The iterative schemes to be considered are of the form Ex^(k+1) = Dx^(k) + d, where E and D are square matrices. It will be assumed that E is a lower matrix, i.e. the coefficients above the central diagonal are zero. It will be shown that by considering matrix D embedded in a vector space and reducing its size with respect to a chosen metric, that convergence rates can be substantially improved. Equation ordering and parameter matrices are used to reduce the magnitude of D. A number of examples are tested to illustrate the importance of the choice of metric, equation ordering and the parameter matrix. Computation times are determined for both the iterative procedure and Gauss elimination indicating the usefulness of iteration which can be orders of magnitude faster.     

基于灵敏度分析的EMT传感器优化设计

本文从线圈个数、线圈距离、线圈直径、线圈形状四个方面分析传感器的优化问题.计算了各种传感器模型下的灵敏度矩阵,分析了各灵敏度矩阵的特征值谱,总结了各参数对EMT传感器的影响规律,最终给出了EMT传感器的优化结果.     

Single pulsed field magnetization for a Gd–Ba–Cu–O high-temperature superconductor large bulk with a diameter of 140 mm

For practical machine application of high-temperature superconductor (HTS) bulk magnet, a pulsed field magnetization (PFM) using small-sized magnetization coils is quite essential. HTS bulk with a diameter of 60 mm has been magnetized successfully and has made the tested axial-type motor to be stable operation by using a couple of vortex-type armature coils. In the present study we report the pulsed magnetization of HTS bulk with a diameter of 140 mm. The crystallization of such large bulk tends to be inhomogeneous around the periphery. For the sample of GdBa₂Cu₃O_y−δ with 140 mm in diameter and 20 mm thickness, new split-type magnetizing coils of 100 and 140 mm in diameter were employed. When the PFM was performed with the coils of 100 mm in diameter, magnetic fluxes penetrate near the center rather than periphery. On the other hand, when we used the coils of 140 mm in diameter, magnetic flux penetrates the whole body, and magnetic flux tends to be immobile in the area. Thus, the PFM with the coils of 100 mm in diameter is effective to magnetization for near the center of HTS bulk. They are also effective to obtain a conical shape trapped flux density distribution. The PFM with the coils of 140 mm in diameter is effective to enhance the total magnetic flux.     

圆锥壳的渐进分布传递函数解

本文给出一种求解圆锥薄壳线弹性变形的渐进传递函数方法。壳体的三个位移函数首先沿环向展开为Fourier级数,由此得到解耦的偏微分方程,它包括一个空间变量和一个时间变量。对时间变量进行Laplace变换后进一步将其简化为含复参数s的常微分方程,它的系数是坐标的函数。引入小参数ε＝L／r0sinα,用摄动方法得到一组常微分方程,它可以用渐进分布传递函数方法求解。将各子锥段的解进行综合,构造出了由多段锥壳构成的组合壳体的传递函数解。文中给出了数值算例并与有限元的结果进行了比较。     

Evaporation heat and mass transfer in natural convection pipe flow

Abstract

A numerical analysis has been performed to examine film evaporation on natural convection heat and mass transfer in a vertical pipe. Coupled governing equations for liquid film and induced gas flow were simultaneously solved by the implicit finite difference method. Results for interfacial heat and mass transfer coefficients are specifically presented for ethanol film and water film vaporization. The predicted results indicate that the heat transfer from gas‐liquid interface to the gas flow is predominated by the transport of latent heat in association with film evaporation. The results are also contrasted with those of zero film thickness and show that the assumption of extremely thin film thickness made by Chang et al. [5] and Yan and Lin [19] is only valid for a system with a low liquid Reynolds number Re _l1. But as the liquid Reynolds number is high, the assumption becomes inappropriate.     

Unsteady nonsimilar compressible laminar two-dimensional and axisymmetric boundary-layer flows

Summary Unsteady nonsimilar laminar compressibletwo-dimensional and axisymmetric boundarylayer flows have been studied when external velocity varies arbitrarily with time and the flow is nonhomentropic. The governing nonlinear partial differential equations with three independent variables have been solved using an implicit finite difference scheme with quasilinearization technique from the origin to the point of zero skin-friction. The results have been obtained for (i) an accelerating stream and (ii) a fluctuating stream. The skin friction responds to the fluctuations in the free stream more compared to the heat transfer. It is observed that Mach number and hot wall cause the point of zero skin friction to occur earlier whereas cold wall delays it.With 16 Figures     

An optimal method for the solution of the constrained eigenvalue/response problem for large structures comprising rigidly-connected substructures

Dynamic substructuring or modal synthesis is established as a powerful means by which the computational effort required to perform dynamic analyses of large structures comprising many degrees of freedom can be reduced. For the case where the substructures are rigidly connected a method of synthesis is proposed which gives very substantial improvements in efficiency over existing methods both in terms of the number of floating-point operations which must take place and the on-board computer memory required. The proposed method makes use of a stable co-ordinate transformation which reduces the mass matrix for the constrained composite-system to the identity matrix and makes the stiffness matrix banded. The bandwidth is exactly equal to twice the total number of constraints plus 1. This is usually very small in comparison with the total number of degrees of freedom in the constrained composite-system. The proposed method is ideal for combining a number of substructures into a single new substructure in an efficient way without necessarily disposing of any degrees of freedom. Approximate formulae are presented which give the ratios of the number of operations required for established methods compared with the number needed for the proposed method. These formulae determine when it is appropriate to use the method proposed here.     

基于精细传递矩阵法的变厚度圆柱壳自由振动分析

结合精细积分和传递矩阵方法,对变厚度圆柱壳的自由振动进行计算分析。该方法基于圆柱壳的基本微分方程,推导得到关于位移内力向量的一阶齐次偏微分方程,采用精细积分求得场传递矩阵,将其进行组装得到总传递方程,根据边界条件求解总传递方程中系数矩阵的行列式,计算得到变厚度圆柱壳的固有频率。将计算结果与有限元结果进行对比,验证方法的准确性及有效性。同时探究了边界条件、厚度变化形式、厚度变化系数及长径比对自由振动的影响规律。     

计及二阶效应的梁杆系统动力响应分析方法研究

基于动力刚度法和有限元理论提出了一种考虑二阶效应计算梁杆动力响应的新方法。通过求解轴向力作用下Bernoulli-Euler 梁横向和轴向挠度自由振动微分方程,利用位移边界条件反解出待定系数,得到了动态精确形函数;使用经典有限元方法推导了考虑截面自身旋转惯量的质量阵和考虑二阶效应的刚度阵,该质量阵和刚度阵各元素均为轴力和圆频率的超越函数;建立了杆系结构瞬态动力学分析的动力平衡方程,给出了稳定和高效的求解方案。对几个典型的算例进行了计算分析,并与通用软件ANSYS 的计算结果进行了比较。计算结果表明:该分析梁杆系统动力响应的新方法具有较高的计算精度和效率,特别是能够准确地计入轴力对于梁杆动力响应的影响。     

主动约束层阻尼圆柱壳动力学分析的新传递矩阵法

基于作者最近导出的被动约束层阻尼(PCLD)圆柱壳的一阶整合矩阵微分方程,结合压电材料本构关系和比例微分负增益反馈控制策略(PD),建立了一种求解主动约束层阻尼(ACLD)圆柱壳动力学问题的新传递矩阵方法。提出的ACLD圆柱壳的一阶矩阵微分方程,采用了简化的机电耦合模型。通过对ACLD圆柱壳自由振动及其在地震激励作用下的动力学响应分析,表明ACLD圆柱壳的阻尼特性和减振效果相对于PCLD圆柱壳具有明显优势,并且发现采用周向分块敷设ACLD,且施加与结构变形中的占优模态相匹配的控制电压分布方式对地震激励的抑制效果更好。     

On the dynamic susceptibility of the bulging domain wall model of polycrystalline magnetic oxides

The static initial magnetic susceptibility due to domain wall motion in a polycrystalline magnetic oxide has been explained by Globuset al. [3] using a model of a bulging domain wall inside grains of uniform diameter,D. The present work deals with the dynamic response of this model by solving the equation of motion of such a wall. The resultant solution reproduces Globus' relation for the static case and further shows that the dispersion frequency is D ^–1 for small grainsizes and D ^–2 for large grain sizes.     

Unsteady three-dimensional combined heat and mass free convective flow over a stretching surface with time-dependent chemical reaction

Summary This paper investigates the combined effects of the free convective heat and mass transfer on the unsteady three-dimensional laminar boundary layer flow over a stretching surface. The stretching rates of the surface are assumed to vary as a reciprocal of a linear function of time. Generation or consumption of the diffusing species due to a homogeneous chemical reaction is considered. The chemical reaction rate is assumed to vary with time according to a power law. With appropriate similarity transformation, the boundary layer equations governing the flow are reduced to ordinary differential equations, which are numerically solved by applying a fifth-order Runge-Kutta-Fehlberg scheme with the shooting technique. The effects of the Prandtl number Pr, Schmidt number Sc, the unsteadiness parameter λ, the chemical reaction parameter γ₀ and the reaction order n are examined on the velocity, temperature and concentration distributions. Numerical data for the skin-friction coefficients, Nusselt and Sherwood numbers have been tabulated for various values of the parameters. A comparison is made between the present work and previous results.     

Determining equation of electric or magnetic deformation in isotropic materials

For isotropic materials, we construct and analyze the general expression and differential characteristics of the measure of “large” free [internal (inherent)] distortion depending on a single scalar parameter of state (e.g., thermal) and a single vector parameter (e.g., electric or magnetic). In particular, it is shown that if the initial value of the vector parameter is equal to zero, this distortion is equal to the deformation independent of the sign of the corresponding final value. __________ Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 41, No. 6, pp. 37–41, November–December, 2005.     

Effects of substrate protection and intraparticle diffusion on the stability of immobilized glucose isomerase

Abstract

The objective of this study is to investigate the adsorption of a chlorinated pesticide; lindane, with the presence of humic acid, has been found in a number of surface water supplies. This study includes developing equilibrium data and performing the adsorption column on lindane in the presence of different concentrations of humic acid with different pH conditions. A multicomponent model is used for data synthesis and for simulation and prediction of dynamic performance of carbon beds for removing lindane from the water containing humic acid. The film transfer coefficients (K_f ) and surface diffusivities (D_s ) used for predictive modeling are determined by micro‐column method.     

安装防振锤的分裂导线自由振动的有限元计算

提出了大跨越分裂导线的一种新型三维有限元模型,它可以直接处理安装防振锤的子导线。针对导线运动的小应变和小转角特点,结合间隔棒对导线的约束关系,推导建立了单元质量和刚度矩阵。应用获得的公式体系对实际大跨越分裂导线进行了自由振动计算,与实测结果比较,表明本文的方法和结果可靠、有效。