Elastic deformation of the rotating functionally graded annular disk with rigid casing

An accurate solution for a rotating functionally graded annular disk is presented. Material properties of the present annular disk are assumed to be graded in the radial direction according to a simple exponential-law distribution. The inner surface of the disk is pure metal whereas the outer surface of the disk is pure ceramic. The boundary condition of rigid casing is considered herein, that is the vanishing of the radial displacement at the outer surface. The boundary condition at the inner surface of the disk is taken to be vanishing either radial displacement or radial stress. Analytical solutions for the elastic deformation of the rotating functionally graded annular disks subjected to these boundary conditions are obtained. Numerical results for radial displacement, circumferential and radial stresses are presented. Comparisons between the different rotating homogeneous and functionally graded annular disks are made at the same angular velocity. The results show that distributions of stresses and displacement through the radial direction of the rotating annular disk vary with different parameters.     

Study on a new type of radial composite piezoelectric ultrasonic transducers in radial vibration

In this paper, a new type of radial composite ultrasonic transducers in radial vibration is presented and studied. The radial composite ultrasonic transducer consists of a solid piezoelectric ceramic thin disk and a hollow metal thin, circular ring in radial vibration; and they are connected together in the radial direction. The radial vibrations of a piezoelectric ceramic thin disk and a hollow, metal, thin, circular ring are analyzed, respectively. Their radial electromechanical equivalent circuits are obtained. Based on the electromechanical equivalent circuits and using the boundary conditions between the piezoelectric ceramic thin disk and the hollow, metal, thin ring, the electromechanical equivalent circuit of the radial composite ultrasonic transducer is derived and the resonance frequency equation is obtained. The theoretical results from the resonance frequency equation are in good agreement with the measured radial resonance frequencies, and they also are in a good agreement with the results from the numerical method.     

Beam propagation properties of radial laser arrays

A detailed study of phase-locked and non-phase-locked radial laser arrays is presented. The closed-form propagation expressions for the beamlets and the resulting beam are given, which enable us to study beam propagation properties of radial laser arrays for both phase-locked and non-phase-locked cases. Numerical calculation examples are given to illustrate the application of our analytical results and the differences between phase-locked and non-phase-locked radial arrays.     

考虑润滑和波纹度影响的球轴承径向刚度

建立了考虑波纹度影响的球轴承非线性振动模型,该模型可以用来仿真球轴承的径向刚度。该模型考虑了外圈的五个自由度,并且还同时考虑了流体弹性动力润滑(EHD)油膜的影响。仿真结果表明球轴承表面的波纹度使得球轴承的刚度发生周期性的改变,油膜虽然增大了刚度,但也只是增加了不到1%。最后还通过实验验证了润滑对轴承径向刚度的影响。     

Radial inflow between two flat disks

Summary A numerical solution to the radial inflow between two flat disks is presented. The pressure and the radial velocity distribution are shown to be functions of solely one non-dimensional parameter that combines the Reynolds number and the radial distance. The numerically predicted pressure correlates well with the experiment. By comparison to the results of the linearized theory, the radial velocity profile is seen to be lower at the mid-plane and larger near the disk surface.     

基于神经网络的固体火箭发动机比冲性能的预示研究

将神经网络方法引入了固体火箭发动机的比冲性能预测,该方法避开了系统具体规律分析以及相应数学模型建立所带来的困难,直接用神经网络模型来模拟真实的系统关系。采用了一种改进的Ⅱ型RBF神经网络,克服了传统的RBF神经网络径向基函数个数未知的缺陷,并将其预测结果与传统的BP神经网络的预测结果进行了比较。     

Thermal stress in rotating functionally graded hollow circular disks

The analysis of thermoelastic problem of a rotating functionally graded hollow circular disk is made. The hollow disk is assumed to have varying material properties along the radial direction. An analytical method is presented to investigate steady thermal stresses in a functionally graded circular annulus rotating with constant angular velocity about its central axis. The associated boundary value problem is reduced to a Fredholm integral equation. The thermal stresses and radial displacement are obtained by numerically solving the resulting equation. A comparison of the numerical results with the exact ones for material properties of special power-law profile confirms the effectiveness of the method. For generally varying material parameters, numerical results are presented graphically to show the effects of gradient parameter, temperature change, angular velocity and thickness of the disk on the distribution of thermal stresses and radial displacement.     

连续变密度圆形和环形薄膜的轴对称振动

本文采用打靶法数值分析了质量密度沿径向连续变化的圆形和环形薄膜的轴对称横向自由振动。针对密度以半径的二次函数变化的情形,计算了系统的一阶大有频率,并与文献（７）中分别用Ｄｉｆｆｅｒｅｎｔｉａｌ Ｑｕａｄｒａｔｕｒｅ Ｍｅｔｈｏｄ和Ｒａｙｌｅｉｇｈ’ｓ Ｑｕｏｔｉｅｎｔ Ｍｅｔｈｏｄ所得结果进行了比较,显示出本文结果的精确性和方法的优越性。然后,数值求解了密度沿半径以指数函数变化的非均匀圆形和环形膜     

Thermo-elastic/plastic semi-analytical solution of incompressible functionally graded spherical pressure vessel under thermo-mechanical loading

In this paper, numerical solutions to assess partially plastic and fully plastic deformation behavior of a functionally graded spherical pressure vessel are presented. The modulus of elasticity of the material is assumed to vary nonlinearly in the radial direction and axisymmetric displacements and stresses in the functionally graded spherical vessel subjected to thermal loading and uniform internal pressure are determined using plasticity theory. Tresca??s yield criterion and its associated flow rule are used to formulate different plastic regions for an ideal FG material. In this way, the material property varies by Young??s modulus that may be an arbitrary function of the radial coordinate. Therefore, the material is assumed to be functionally graded in the radial direction. Hence, the general analytical solutions of such equations are not available, the numerical method (semi-analytical) is applied and a new collection of equilibrium equations with small deflections is presented. Accordingly, the radial domain is divided into some virtual sub-domains in which the power-law distribution is used for the thermomechanical properties of the elemental components. By considering the necessary continuity conditions between adjacent sub-domains, jointly with the global boundary conditions, a set of linear differential equations is obtained. Solution of the linear differential equations yields the thermoelastic responses for each sub-domain as exponential functions of the radial coordinate. Subsequently, attributed to centrifugal force, results for the stress, strain, and displacement components along the radius in elastic and plastic area are presented.     

Multidimensional Flash Diffusivity Measurements of Orthotropic Materials

A generalization of the radial flash technique is presented whereby the thermal diffusivity of an orthotropic solid is measured in directions parallel and perpendicular to the flash source. The theoretical formulation is based on a Green's function approach which assumes a general orthotropic solid with three mutually orthogonal thermal diffusivities (or conductivities). Using this approach, a solution to this problem is presented which can be used to develop solutions for arbitrary pulse waveforms and incident geometries. Analytical and numerical results are presented for two-dimensional and three-dimensional cases of finite and semiinfinite solids. Characteristic equations which describe the ratio of the temperatures at two points along a principal axis are given. The equations show excellent agreement with numerical predictions as well as experimental results. A parameter estimation approach is given which improves on the accuracy of the radial flash technique in the determination of thermal diffusivity from experimental data.     

质量偏心旋转机械转子-机匣系统碰摩的失效研究

针对仅考虑质量偏心的Jeffcott转子-机匣系统碰摩的动力学方程，进行了旋转机械转子-机匣系统碰摩可靠性分析，研究了转轴刚度和阻尼，定子刚度和阻尼，偏心距和定子径向刚度对可靠度的影响，并给出了数值分析解。     

A radial basis function approach in the meshless local Petrov-Galerkin method for Euler-Bernoulli beam problems

A meshless local Petrov-Galerkin (MLPG) method that uses radial basis functions rather than generalized moving least squares (GMLS) interpolations to develop the trial functions in the study of Euler-Bernoulli beam problems is presented. The use of radial basis functions (RBF) in meshless methods is demonstrated for C¹ problems for the first time. This interpolation choice yields a computationally simpler method as fewer matrix inversions and multiplications are required than when GMLS interpolations are used. Test functions are chosen as simple weight functions as in the conventional MLPG method. Patch tests, mixed boundary value problems, and problems with complex loading conditions are considered. The radial basis MLPG method yields accurate results for deflections, slopes, moments, and shear forces, and the accuracy of these results is better than that obtained using the conventional MLPG method.Lockheed Martin Space Operations     

The stress intensity factors of internal radial cracks in rotating disks by the method of caustics

A technique based on the method of caustics is used to evaluate the stress intensity factors of internal radial cracks in rotating disks. The measurement strategy, experimental procedures and results are presented. The accuracy of the technique is demonstrated by comparing experimental results to theory.     

Bessel-like beams modulated by arbitrary radial functions

An approximate method for determining the radial and axial intensity of a Bessel-like beam is presented for the general case in which a radial Bessel distribution of any order is modulated by an arbitrary function. For Bessel-Gauss, generalized Bessel-Gauss, and Bessel-super-Gauss beams, this simple approximation yields results that are very close to the exact values, while they are exact for Bessel beams. A practical beam that can be generated with a combination of simple lenses is also analyzed and illustrated.     

Thermoelastic analysis of a functionally graded rotating disk

A semi-analytical thermoelasticity solution for hollow and solid rotating axisymmetric disks made of functionally graded materials is presented. The radial domain is divided into some virtual sub-domains in which the power-law distribution is used for the thermomechanical properties of the constituent components. Imposing the necessary continuity conditions between adjacent sub-domains, together with the global boundary conditions, a set of linear algebraic equations are obtained. Solution of the linear algebraic equations yields the thermoelastic responses for each sub-domain as exponential functions of the radial coordinate. Some results for the stress, strain and displacement components along the radius are presented due to centrifugal force and thermal loading. Results obtained within this solution are compared with those of a finite element analysis in the literature. Based on the results, it is shown that the property gradation correlates with thermomechanical responses of FG disks.     

一种高效磁流变阀及其特性测试

介绍了一种同时具有圆环形和圆盘形阻尼间隙的磁流变阀的原理、结构及其模型,建立了测试磁流变阀的磁流变液压执行器系统及基于dSPACE实时仿真系统的虚拟测试系统.研究结果不仅显示实际测试结果与理论模型的一致性,而且表明当电流增加到0.80A时同时具有圆环形和圆盘形阻尼间隙的磁流变阀能产生最大压降,并且在一定压力作用下对磁流变液具有最佳阻断能力.     

Frequency spectra of extensional vibration in isotropic shortcolumns and thick circular disks

A simple analytical method based on the equivalent elastic theory is presented for predicting the natural frequencies of a short column or a thick circular disk of axially symmetrical coupled vibration in which the longitudinal, the radial and the thickness extensional vibrations are considered. A critical value of thickness/diameter ratio is given that defines a boundary between a short column and a thick disk. Theoretical analyses show that the longitudinal and radial vibrations in infinite length rods, the radial and thickness extensional vibrations in thin plate are the special vibrating modes of a short column or a thick disk. The calculated frequencies for an isotropic column or a disk are in good agreement with the measured results     

The sector problem in plane elastostatics

Using a biorthogonality relation, it is shown how solutions for the generalized plane stress problem for a sector whose radial edges are ‘stress-free’ or ‘built-in’ can be obtained for physically meaningful boundary functions prescribed on the curved edge. Numerical results are presented for the reproduction of the edge stresses when a self-equilibrating load is prescribed on the curved edge of the sector having its radial edges stress-free.     

波传播法求解低频激励下水中加端板圆柱壳的振动

采用波传播法研究了低频下水中壳体的振动与响应。水中壳体由有限长加流体载荷的圆柱壳和两端的圆形端板组成,其中外部流体载荷用无限长模型进行近似处理。为了模拟推动系统的激励及船体上某一点激励,分别考虑了不同位置的轴向载荷和径向载荷,讨论了单个周向模态下的位移在总位移中的比重。主要研究了4种载荷,即作用在端板中心的轴对称载荷、作用在端板与圆柱连接处的轴向载荷、作用在连接处的径向载荷和作用在壳体中间的径向载荷,比较得出了轴对称和非轴对称、同一点不同方向载荷、同一方向不同位置载荷的响应位移的不同。此外,还研究了两端端板对不同载荷下水中壳体响应的影响,得出了端板主要抑制了壳体的较高阶模态下径向位移的结论。解析法结果与有限元法结果进行了比较,验证了该方法的正确性。     

Effects of local thermal non-equilibrium on the pore pressure and thermal stresses around a spherical cavity in a porous medium

In this paper, we use a local thermal non-equilibrium (LTNE) thermo-poroelasticity theory to investigate temperatures, pore pressure and thermal stresses around a spherical cavity in an infinite fluid saturated porous medium. In the LTNE theory, the solid and fluid phases undergo different temperature variations which induce additional pore pressure and thermal stresses. The asymptotic short time solutions of temperature, pore pressure and thermal stresses are obtained using the Laplace transform technique. Numerical results for two porous materials (clay and sandstone) are presented to examine the effects of LTNE on the temperature, pore pressure and thermal stresses around the spherical cavity. The results show that for the clay, the LTNE radial stress has a significantly larger peak value (magnitude) than that of the classical radial stress. The influence of LTNE on the pore pressure and tangential stress, however, are marginal. For the sandstone, both the radial stress (magnitude) and pore pressure are significantly increased by the LTNE effect.