One-dimensional nonuniform temperature flow with heat transfer by convection

In ref. [1], V. E. Najenov studied the conditions that when the viscosity of the liquid is an exponential function of temperature, the pipe flow, having steady heat transfer, is one dimensional and with nonuniform temperature. For plane canal and circular pipe he still studied the velocity and the temperature fields.In this paper, the author presents two new methods for solving the same problem. The method as in ref. [1] may be regarded as the natural branch of the methods of this paper. One of our new methods only can solve the same problem as in ref. [1] and the complex degree of its computing process is nearly the same as that in ref. [1]. But the other can go beyond the studying scope of ref. [1], namely, for the case that the curvatures of circumference of the cross section of the pipe are not equivalent everywhere, the problem may also be solved.     

Nonlinear dynamic behaviors of viscoelastic shallow arches

The nonlinear dynamic behaviors of nonlinear viscoelastic shallow arches sub- jected to external excitation are investigated. Based on the d＇Alembert principle and the Euler-Bernoulli assumption, the governing equation of a shallow arch is obtained, where the Leaderman constitutive relation is applied. The Galerkin method and numerical in- tegration are used to study the nonlinear dynamic properties of the viscoelastic shallow arches. Moreover, the effects of the rise, the material parameter and excitation on the nonlinear dynamic behaviors of the shallow arch viscoelastic shallow arches may appear to have a are investigated. The results show that chaotic motion for certain conditions.     

On the effect of Reynolds number on von Kármán’s constant

Fully developed turbulence measurements in pipe flow were made in the Reynolds number ranging from 10×10³ to 350×10³ with a hot-wire anemometer and a Pitot tube. Comparisons were made with the experimental results of previous work. The mean velocity profile and the turbulent intensity in the experiments indicate that for the mean velocity profile, in the fully developed turbulent pipe flow, von Kármán's constant κ is a function of Reynolds number, i.e. κ increases slowly with the Reynolds number. The empirical relationships could not be considered to be accurate enough to describe the fully developed turbulence over the whole Reynolds number range in pipe flow. The project supported by the Deutscher Akademische Austauschdienst (DAAD)     

The probability stability of viscoelastic plates

The almost sure stability of homogeneous viscoelastic plates subjected to a random wide-band stationary in-plane load is investigated. The viscoelastic behavior of the plate is described in terms of the Boltzmann superposition principle, the relaxation kemels of which are represented by the sums of exponents. On the assumption that the in-plane load is random wide-band stationary process, sufficient conditions for almost sure stability of viscoelastic plates are obtained by the applications of Lyapunov's direct method. Project supported by the National Natural Science Foundation of China (No. 59635140) and the National Postdoctoral Foundation.     

Stability and chaotic motion in columns of nonlinear viscoelastic material

ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｐｒｏｂｌｅｍｏｆｔｈｅｄｙｎａｍｉｃａｌｓｔａｂｉｌｉｔｙｏｆｖｉｓｃｏｅｌａｓｔｉｃｓｔｒｕｃｔｕｒｅｓｉｓｍｏｒｅｃｏｍｐｌｉｃａｔｅｄｔｈａｎｔｈａｔｏｆｅｌａｓｔｉｃｓｔｒｕｃｔｕｒｅｓ,ｓｉｎｃｅｔｈｅｓｔｒｅｓｓ＿ｓｔｒａｉｎｒｅｌａｔｉｏｎｏｆｖｉｓｃｏｅｌａｓｔｉｃｍａｔｅｒｉａｌｓｏｆｔｅｎｌｅａｄｓｔｏａｎｉｎｔｅｇｒｏ＿ｄｉｆｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎｏｆｍｏｔｉｏｎ .Ｉｎｔｈｅｅａｒｌｙｒｅｓｅａｒｃｈｅｓｏｎｌｉｎｅａｒｖｉｓｃｏ…     

The existence of buckled states on a perforated thin plate

On the basis of the generalized yon Kàrmàn theory for perforated thin plates established in [1, 2], the existence of buckled states for perforated plates subjected to self-equilibrating inplane forces along each edge systematically is investigated. This work completely generalizes the results in [3, 4].     

Nonlinear dynamic stability of composite laminated plates

Catastrophe theory was applied to the investigation of nonlinear dynamic stability of composite laminated plates. The influence of large deflection, initial imperfection,support conditions and ply-angle of the fibers were considered. The catastrophic models and the critical conditions of dynamic buckling of composite laminated plates are obtained.     

Dynamic stability of a viscoelastic plate with concentrated masses

The paper addresses the geometrically nonlinear problem of dynamic stability of a viscoelastic plate with concentrated masses. The Bubnov-Galerkin method based on polynomial approximation is used to reduce the problem to a system of nonlinear Volterra-type integro-differential equations with singular relaxation kernels. This system is solved by numerical method based on quadrature formulas. The critical loads are found and their dependence on the arrangement and number of concentrated masses is studied for a wide range of mechanical and geometrical parameters of the plate. The choice of a relaxation kernel for dynamic problems for viscoelastic thin-walled plate-like structures is justified. Results produced by different theories are compared __________ Translated from Prikladnaya Mekhanika, Vol. 44, No. 2, pp. 109–118, February 2008.     

Dynamical Behavior of Viscoelastic Cylindrical Shells Under Axial Pressures

ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｏｒｙｏｆｖｉｓｃｏｅｌａｓｔｉｃｉｔｙａｎｄｉｔｓａｐｐｌｉｃａｔｉｏｎｓｈａｖｅｂｅｅｎｂｅｃｏｍｉｎｇａｖｅｒｙａｔｔｒａｃｔｉｖｅｒｅｓｅａｒｃｈｆｉｅｌｄｓｉｎｃｅｖｉｓｃｏｅｌａｓｔｉｃｓｔｒｕｃｔｕｒｅｓｗｅｒｅｗｉｄｅｌｙａｐｐｌｉｅｄｉｎｔｏｖａｒｉｏｕｓｅｎｇｉｎｅｅｒｉｎｇ .Ｂｕｔｔｏｔｈｅａｕｔｈｏｒｓ’ｋｎｏｗｌｅｄｇｅ,ｔｈｅｒｅａｒｅｒａｒｅｆｏｒｐａｐｅｒｓｃｏｎｃｅｒｎｉｎｇｗｉｔｈｄｙｎａｍｉｃａｌｂｅｈａｖｉｏｒｏｆｖｉｓｃｏｅ…     

Stretching surface in rotating viscoelastic fluid

The boundary layer flow over a stretching surface in a rotating viscoelastic fluid is considered. By applying a similarity transformation, the governing partial differ- ential equations are converted into a system of nonlinear ordinary differential equations before being solved numerically by the Keller-box method. The effects of the viscoelastic and rotation parameters on the skin friction coefficients and the velocity profiles are thor- oughly examined. The analysis reveals that the skin friction coefficients and the velocity in the x-direction increase as the viscoelastic parameter and the rotation parameter in- crease. Moreover, the velocity in the y-direction decreases as the viscoelastic parameter and the rotation parameter increase.     

几何缺陷浅拱的动力稳定性分析

研究了几何缺陷对粘弹性铰支浅拱动力稳定性能的影响。从达朗贝尔原理和欧拉-贝努利假定出发推导了粘弹性铰支浅拱在正弦分布突加荷载作用下的动力学控制方程,并采用Galerkin截断法得到了可用龙格-库塔法求解的无量纲化非线性微分方程组。同时引入能有效追踪结构动力后屈曲路径的广义位移控制法,对含几何缺陷浅拱的响应曲线进行几何、材料双重非线性有限元分析。用这两种方法分析了前三阶谐波缺陷对浅拱动力稳定性能的影响,其中动力临界荷载由B-R准则判定。主要结论有:材料粘弹性使浅拱动力临界荷载增大且结构响应曲线与弹性情况差别很大;二阶谐波缺陷影响显著,它使动力临界荷载明显下降且使得浅拱粘弹性动力临界荷载可能低于弹性动力临界荷载。     

A variational principle of perturbed motion on viscoelastic thin plates with applications

In this paper, in the light of the Boltzmann superposition principle in linear viscoelasticity, a mathematical model of perturbed motion on viscoelastic thin plates is established. The corresponding variational principle is obtained in a convolution bilinear form. For application the problems of free vibration, forced vibration and stability of a viscoelastic simply-supported rectangular thin plate are considered. The results show that numerical solutions agree well with analytical solutions. The project was supported by the National Natural Science Foundation of China (No. 19772027) and the Shanghai Municipal Development Foundation of Science and Technology (No. 98JC14032).     

ANM analysis of a wrinkled elastic thin membrane

In this work, we have investigated numerically the disappearance of wrinkles from a tended membrane by the Asymptotic Numerical Method (ANM) using the finite-element DKT18. The ANM is a path-following technique that has been used to solve bifurcation problems. We show numerically the influence of the terms corresponding to the membrane displacement gradient in the Föppl–von Kármán (FvK) theory on the bifurcation curves in the case of a stretched elastic membrane. We will also study numerically, by using the ANM algorithm, the influence of the thickness and of the aspect ratio on the re-stabilization of a rectangular elastic membrane during stretching. The results obtained by our model are compared with those obtained using the industrial code ABAQUS.     

Complex-mode Galerkin approach in transverse vibration of an axially accelerating viscoelastic string

Under the consideration of harmonic fluctuations of initial tension and axially velocity, a nonlinear governing equation for transverse vibration of an axially accelerating string is set up by using the equation of motion for a 3-dimensional deformable body with initial stresses. The Kelvin model is used to describe viscoelastic behaviors of the material. The basis function of the complex-mode Galerkin method for axially accelerating nonlinear strings is constructed by using the modal function of linear moving strings with constant axially transport velocity. By the constructed basis functions, the application of the complex-mode Galerkin method in nonlinear vibration analysis of an axially accelerating viscoelastic string is investigated. Numerical results show that the convergence velocity of the complex-mode Galerkin method is higher than that of the real-mode Galerkin method for a variable coefficient gyroscopic system.     

轴向变速运动正交各向异性板的动态稳定性

研究面内载荷作用下轴向变速运动正交各向异性薄板的横向振动及其稳定性。利用Galerkin法与平均法,在激励频率为2倍固有频率或为两阶固有频率之和附近时得到自治的常微分方程组;在参数激励频率和激励振幅平面上,分析由共振引发的失稳区域。数值算例验证了面内载荷、轴向速度、加速度参数对失稳区域的影响。     

Stability analysis of viscoelastic curved pipes conveying fluid

Based on the Hamilton' s principle for elastic systems of changing mass, a differential equation of motion for viscoelastic curved pipes conveying fluid was derived using variational method, and the complex characteristic equation for the viscoelastic circular pipe conveying fluid was obtained by normalized power series method. The effects of dimensionless delay time on the variation relationship between dimensionless complex frequency of the clamped-clamped viscoelastic circular pipe conveying fluid with the Kelvin-Voigt model and dimensionless flow velocity were analyzed. For greater dimensionless delay time, the behavior of the viscoelastic pipe is that the first, second and third mode does not couple, while the pipe behaves divergent instability in the first and second order mode, then single-mode flutter takes place in the first order mode.     

具损伤压电智能层合中厚板的非线性动力稳定性分析

基于各向异性损伤理论和压电理论，采用能量法和Lagrange方程，建立了具损伤压电智能层合中厚板在参数激励下的非线性运动控制方程，应用增量谐波平衡法，求解了具损伤压电智能层合中厚板的非线性动力稳定性问题。算例中，分析了损伤参数和压电效应对压电智能层合板非线性动力稳定性的影响，揭示了力电耦合效应的内在特征，并与有关文献的结果进行了比较。     

Global stability analysis of a ratio-dependent predator-prey system

A ratio dependent predator-prey system with Holling type Ⅲ functional response is considered. A sufficient condition of the global asymptotic stability for the positive equilibrium and existence of the limit cycle are given by studying locally asymp- totic stability of the positive equilibrium. The condition under which positive equilibrium is not a hyperbolic equilibrium is investigated using Hopf bifurcation.     

Theory of nonlinear dynamic stability for composite laminated plates

In this paper,the general equations of dynamic stability for composite laminatedplates are derived by Hamilton principle.These general equations can be used to considerthose different factors that affect the dynamic stability of laminated plates.The factors aretransverse shear deformation,initial imperfections,longitudinal and rotational inertia,andply-angle of the fiber,etc.The solutions of the fundamental equations show that someimportant characteristics of the dynamic instability can only be got by the considerationand analysis of those factors     

A Time Domain Method for Quasi-Static Analysis of Viscoelastic Thin Plates

ＩｎｔｒｏｄｕｃｔｉｏｎＩｎｔｈｅｃａｓｅｏｆｇｅｏｍｅｔｒｉｃｎｏｎｌｉｎｅａｒｉｔｙ ,ｔｈｅｍａｔｈｅｍａｔｉｃａｌｍｏｄｅｌｏｆｖｉｓｃｏｅｌａｓｔｉｃｓｔｒｕｃｔｕｒｅｓｇｅｎｅｒａｌｌｙｉｓｔｈｅｓｙｓｔｅｍｏｆｎｏｎｌｉｎｅａｒｉｎｔｅｇｒｏ＿ｐａｒｔｉａｌ＿ｄｉｆｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎｓ.Ｉｔｉｓｖｅｒｙｄｉｆｆｉｃｕｌｔｔｏｆｉｎｄｔｈｅｅｘａｃｔｓｏｌｕｔｉｏｎｔｏｓｕｃｈｐｒｏｂｌｅｍｓ.Ｏｎｌｙｎｕｍｅｒｉｃａｌｓｏｌｕｔｉｏｎｓｃｏｕｌｄｂｅｏｂｔａｉｎｅｄｂｙ…