微重力下圆管毛细流动解析近似解研究

应用同伦分析法研究微重力环境下圆管毛细流动解析近似解问题, 给出了级数解的表达公式. 不同于其他解析近似方法, 该方法从根本上克服了摄动理论对小参数的过分依赖, 其有效性与所研究的非线性问题是否含有小参数无关, 适用范围广. 同伦分析法提供了选取基函数的自由, 可以选取较好的基函数, 更有效地逼近问题的解, 通过引入辅助参数和辅助函数来调节和控制级数解的收敛区域和收敛速度, 同伦分析法为圆管毛细流动问题的解析近似求解开辟了一个全新的途径. 通过具体算例, 将同伦分析法与四阶龙格库塔方法数值解做了比较, 结果表明, 该方法具有很高的计算精度. 关键词： 圆管 微重力 毛细流动 同伦分析法     

周界固定带裂纹薄圆板的振动基频

在将裂纹板挠度表示为正交多项式的基础上，用分区技术的瑞利一里兹方法求解了含不同长度径向裂纹和弧向裂纹的周界固定圆板的振动基频。实验上用小球撞击法测定了裂纹圆板的辐射声场频谱，并得出了谱的基频。此外用有限元法对裂纹板作了理论计算。三项结果基本符合。探究了裂纹长度对圆板基频的影响规律。     

Large amplitude vibrations of clamped circular plates of linearly varying thickness

The large amplitude vibrations of clamped circular plates of linearly varying thickness are investigated, by applying the procedure proposed by Banerjee and Datta [1].     

An analytical and experimental study of the vibration response of a clamped ribbed plate

An analytical solution is presented in this paper for the vibration response of a ribbed plate clamped on all its boundary edges by employing a traveling wave solution. A clamped ribbed plate test rig is also assembled in this study for the experimental investigation of the ribbed plate response and to provide verification results to the analytical solution. The dynamic characteristics and mode shapes of the ribbed plate are measured and compared to those obtained from the analytical solution and from finite element analysis (FEA). General good agreements are found between the results. Discrepancies between the computational and experimental results at low and high frequencies are also discussed. Explanations are offered in the study to disclose the mechanism causing the discrepancies. The dependency of the dynamic response of the ribbed plate on the distance between the excitation force and the rib is also investigated experimentally. It confirms the findings disclosed in a previous analytical study [T.R. Lin, J. Pan, A closed form solution for the dynamic response of finite ribbed plates, Journal of the Acoustical Society of America 119 (2006) 917–925] that the vibration response of a clamped ribbed plate due to a point force excitation is controlled by the plate stiffness when the source is more than a quarter plate bending wavelength away from the rib and from the plate boundary. The response is largely affected by the rib stiffness when the source location is less than a quarter bending wavelength away from the rib.     

Optimization of a clamped plate silencer

A previous theoretical study [L. Huang, J. Acoust. Soc. Am. 119, 2628-2638 (2006)] shows that, in a duct, a simply supported plate covering a side-branch rigid cavity can function effectively as a wave reflector over a broad range of low to medium frequencies. In this study, analytical formulation is extended to the boundary condition of clamped plate, which is easier to implement in practice. The theoretical model is tested experimentally using balsawood, which has a very high stiffness to mass ratio. The spectral peaks and shapes of the measured TL are in agreement with those calculated theoretically, attempts are also made to account for the considerable sound absorption in the rig. Further numerical studies based on the validated model show that, for a uniform plate, the optimal stopband is narrower and the lower band limit is worse than that of the simply supported configuration. However, a wave reflector using nonuniform, clamped plates with thinner ends out-performs the simply supported configuration in every aspect. Analyses show that the improvement is attributed to the increased acoustic radiation efficiency over the bulk length of the nonuniform plate, which behaves more like a rigid plate.     

On computation of random response of a clamped plate

The free vibrations of elastically connected circular plate systems with elastically restrained edges and initial radial tensions are investigated analytically. By using the equations developed for the general n-plate system, the plate systems consisting of three and two identical plates with identical boundary conditions and a uniform radial tension are treated in detail. Both axisymmetric and non-axisymmetric vibrations are considered. Attention is directed to the influence of the radial tension and the elastic edge constraints on the first nine eigenvalues and the corresponding natural frequencies of the systems.     

Effect of shear strain on the deflection of a clamped magnetostrictive film-substrate system

The effect of in-plane shear strain of a clamped bimorph on the deflection produced by magnetization of the film is investigated. The deflection is found by minimizing the Gibbs free energy with respect to four parameters, strains and curvatures along x and y directions at the interface, by assuming that the curvature in the y direction varies as a function of aspect ratio w/l along x. A set of standard linear equations of four parameters are obtained and the deflection is expressed in terms of the four parameters by solving the equations using Cramer rules. The inconsistencies pointed out by previous authors are also reviewed. For actuators made of thick and short clamped film-substrate system, the in-plane shear deformation should not be omitted. The present calculation model can give a relatively simple and accurate prediction of deflection for thick and short specimens of aspect ratio w/l<10, which supports the results obtained by finite element modeling.     

Large eddy simulations of a circular orifice jet with and without a cross-sectional exit plate

The effect of a cross-sectional exit plane on the downstream mixing characteristics of a circular turbulent jet is in- vestigated using large eddy simulation （LES）. The turbulent jet is issued from an orifice-type nozzle at an exit Reynolds number of 5 ×104. Both instantaneous and statistical velocity fields of the jet are provided. Results show that the rates of the mean velocity decay and jet spread are both higher in the case with the exit plate than without it. The existence of the plate is found to increase the downstream entrainment rate by about 10% on average over the axial range of 8-30de （exit diameter）. Also, the presence of the plate enables the formation of vortex rings to occur further downstream by 0.5-1 .Ode. A physical insight into the near-field jet is provided to explain the importance of the boundary conditions in the evolution of a turbulent jet. In addition, a method of using the decay of the centreline velocity and the half-width of the jet to calculate the entrainment rate is proposed.     

Reconstructing the adhesion stiffness distribution in a laminated elastic plate: Exact and approximate inverse scattering solutions

This paper formulates and solves a time harmonic inverse scattering problem to reconstruct the effective stiffness distribution of an adhesive bond in a layered elastic plate. The motivation is based on the assumption that localized adhesion flaws that diminish bond stiffness also tend to diminish bond strength. The formulation is based on the invariant imbedding method, applies to isotropic and anisotropic elastic layers, and is essentially that of identifying embedded acoustic sources in elastic layered structures. This paper presents two solutions for the inverse problem: the Born approximation and the exact solution. The example calculations compare the two solutions and show that when imperfections are too large in either magnitude or extent the accuracy of the Born approximation breaks down. The impact of noise and uncertainties in the background properties in the inversion is also investigated. A regularization strategy is introduced in the exact solution that controls solution sensitivity in regions with low signal to noise ratio.     

Singularity-free approximate analytical solution of capillary rise dynamics

正Capillary rise is one of the most well-known and vivid illustrations of capillarity(shown in Figure 1).Knowledge of capillarity laws is important in oil recovery,civil engineering,dyeing of textile fabrics,ink printing,and a variety of other fields.It is capillarity that brings water to the upper layer of soils,drives sap in plants,or lays the basis for the operation of pens[1-10].Washburn[1]developed an equation to describe the rate     

高阶色散效应常系数Ginzburg-Landau方程自相似脉冲演化的解析分析

采用自相似分析方法,基于常系数高阶色散的Ginzburg-Landau方程,通过分离变量法得出了高阶色散效应自相似脉冲演化的解析解,给出了自相似脉冲的振幅、相位、啁啾以及脉冲宽度的一般表达式.研究表明,在增益光纤的二阶正常色散区域,同时考虑高阶色散和增益色散双重效应影响下演化的自相似孤子脉冲仍然保持线性啁啾;振幅解析解的三阶色散效应显著.这与数值计算的结果非常一致. 关键词： 三阶色散 Ginzburg-Landau方程 自相似脉冲 二阶正常色散     

A note on forced vibrations of a clamped rectangular plate

Simple polynomial approximations and Galerkin's method are used to determine the response of a thin, elastic, rectangular plate clamped along the boundary and subjected to sinusoidal excitation. It also is shown that a one-term polynomial solution yields good accuracy in the case of a rectangular plate with simply supported edges.     

Nonequilibrium kinetics: Exact and approximate solutions

The relaxation of an internal state distribution in the presence of an excess of an inert gas is considered. The explicit time dependence of the nonequilibrium contributions to the transition rate coefficients is approximated using the Kapral-Hudson-Ross method. The resulting solution contains cross-correlation terms which do not appear when a single reaction is considered. It is shown that the first term of a perturbation expansion of an exact formal solution gives the Kapral-Hudson-Ross solution for short times, and the Chapman-Enskog solution at long times if there is a wide separation in time scales. The Kapral-Hudson-Ross, Chapman-Enskog, and exact solutions are compared for a two-state, hard-sphere model system.Based on a dissertation by S. Hudson, Massachusetts Institute of Technology, 1972.National Science Foundation predoctoral fellow, 1967–1971.     

Exact solutions of in-plane natural vibration of a circular plate with outer edge restrained elastically

We solve exactly the equations of in-plane natural vibration for a circular plate whose outer edge is restrained elastically. The mode shapes are represented by trigonometric functions with a number of nodal diameters in the circumferential direction and mode functions in the radial direction. We present the exact frequency equations and mode functions and tabulate the frequency parameters satisfying the frequency equations. The corresponding mode functions and two-dimensional mode shapes are illustrated when both radial and tangential stiffness are zero (free edge), infinity (clamped edge), or medium. Comparisons with previous reported results confirm the accuracy of the present work.     

Adaptive non-linear control of a clamped rectangular plate with PZT patches

The dynamic behavior and control of a clamped rectangular plate with bonded piezoelectric ceramic patches are investigated in this paper. The dynamic behavior is studied experimentally, showing that the plate exhibits dense modes, varying residual stress and non-linearity. An adaptive non-linear control scheme is then presented, which introduces a non-linear function into the normal adaptive feedforward control to non-linearize a reference signal. Vibration reductions using both the normal adaptive feedforward control and the adaptive non-linear control are compared in the cases of sinusoidal excitations at the first nine modal frequencies of the plate and a swept-frequency harmonic excitation below 100 Hz, indicating that the adaptive non-linear control can suppress not only the fundamental frequency vibration that the normal adaptive feedforward control can only attenuate, but also its higher harmonic components. Significant vibration reduction achieved by the adaptive non-linear control demonstrates its validity and reliability.