Vibrations and stability of cylindrical panels with elliptical cross section

Summary The free vibrations of cylindrical panels with elliptical cross section subjected to an initial stress state are investigated. The buckling problem of the panel under the stress state considered is studied as special case of the free vibration problem.

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Übersicht Es wird die freie Schwingung offener Zylinderschalen mit elliptischem Querschnitt behandelt, die sich in einem Anfangspannungszustand befinden. Das Schalenbeulproblem wird als Spezialfall der freien Schwingung untersucht.

     

Periodic electrostatic focusing of abeam of elliptical cross section

An exact analytic solution has been given [1] for the shaping of a flat beam with a nonmonotonic potential variation at the boundary. It has been shown that construction of a periodic focusing system amounts to calculation of the equipotentials in a part with a potential distribution symmetric about the center and to coupling of two such elements via sufficiently thick screening grids whose charge density varies in a definite way. Here I derive a simple analytic solution for the shaping of a beam of elliptical cross section by approximating the potential at the boundary via a quadratic parabola [2].     

Supersonic flow over elongated blunt bodies with a cross section of elliptical shape

Up to now computational algorithms have been developed for, and systematic studies have been made of, supersonic flow over axisymmetric bodies both by a stream of ideal gas and by an air stream with equilibrium and nonequilibrium physicochemical transformations [1–6]. Conical flows around bodies having cross sections of different shapes and in a wide range of angles of attack have been studied in detail [7–11]. With the further development of numerical methods the next problem has become the analysis of supersonic flow over blunt bodies of large elongation having cross sections of sufficiently arbitrary shape. The effects of essentially three-dimensional flow (without planes of symmetry) over bodies whose cross sections represent ellipses with a constant or variable ratio of axes along the length of the body are discussed in the present paper.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6. pp. 155–159, November–December, 1976.     

On the stress-strain state of toroidal shells of elliptical cross section formed from nonlinear elastic orthotropic materials

Problems of the statics of toroidal shells with elliptical cross sections, which are formed from nonlinear elastic orthotropic materials, were examined. Investigations were carried out in accordance with a procedure based on the method of successive approximations, the variational-difference method, and the method of Lagrangian multipliers. Calculations were performed by varying the ellipticities of the cross section of the torus and the radii of the circular axis of the torus over a broad range. Numerical and analytical results are presented in tables and graphs. Attention was focused on the accuracy of the computational results obtained, and agreement between the internal and external forces in the cross section was adopted as an integral criterion. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 36, No. 1, pp. 103–109. January, 2000.     

On the rotating rod with variable cross section

Summary Stability of a heavy rotating rod with a variable cross section is studied by energy method. Bifurcation points for the system of equilibrium equations are analyzed. It is shown that for the case when the rotation speed exceeds the critical one, the trivial solution ceases to be the minimizer of the potential energy, so that rod loses stability, according to the energy criteria. Also, a new estimate of the maximal rod deflection in the post-critical state is obtained. Accepted for publication 11 November 1996     

对矩形截面杆弹性自由扭转的探讨

利用柱体扭转问题的经典弹性力学解析解,结合自编电算程序绘制了沿截面控制线上剪应力的分布图,同时利用ANSYS有限元分析软件模拟了等直矩形截面杆的自由扭转问题. 将各种材料力学教材中的截面剪应力分布图与准确计算结果进行了比较,并对截面剪应力分布规律进行了总结.     

Bending behavior of a rectangular plate with a bitrapezoidal cross section

A theory is developed for the transverse deflections when a rectangular plate having a bitrapezoidal cross section is subjected to a uniform longitudinal curvature. The theoretical solutions are compared with earlier results presented by Lamb and Fung and Wittrick. Experimental results are compared with the theory and good agreement is obtained over the range of curvatures tested.     

Secondary flow structures in developing viscoelastic fluid flow through curved ducts with square cross section

Meccanica - The present paper numerically investigates viscoelastic fluid flow in the developing flow regime through both straight and 90-degree curve ducts. The aim is to investigate the effects...     

Longitudinal free vibration of inhomogeneous elastic straight strut with a variable cross section

The scope of the present article, motivated by the case of the composite wooden propeller of an airplane, is to deal tentatively with the longitudinal free vibrationproblem of an elastic straight bar with a more general mathematical treatment.In this analysis, we have assigned to the modulus of elasticity, the bar cross section as well as the mass per unit length of the bar an exponential function variation, and then found a general solution, wherein three parameters were considered as the main factors to affect the longitudinal free vibration of the inhomogeneous elastic straight bar with a variable cross section.     

Flow and breakup characteristics of elliptical liquid jets

This paper presents the results of an experimental study on liquid jets discharging from elliptical orifices into still ambient air. The experiments were conducted with a set of elliptical orifices of approximately same area of cross section but varying orifice aspect ratio using water and water–glycerol mixture as experimental fluids. The flow behavior of liquid jets was analyzed using their photographs captured by an imaging system. The measurements obtained for the elliptical liquid jets were compared with the circular liquid jets discharging from a circular orifice of the same area of cross section. Elliptical geometry of the orifice results in a flow process by which the emanating liquid jet periodically switches its major and minor axes as it flows downstream of the orifice. In this paper, we attempt to characterize the axis-switching process through its wavelength and amplitude. For a given elliptical orifice, the axis-switching process is dominantly seen in a particular range of flow conditions. The effects of the orifice aspect ratio and liquid viscosity on the axis-switching process are revealed through this study. The experimental results on jet breakup show that axis-switching process has a destabilizing effect on elliptical liquid jets within a particular range of flow conditions and it results in shorter breakup lengths compared to the circular jet. The extent to which axis-switching destabilizes the jet is dictated by the viscosity of liquid. An increase in orifice aspect ratio destabilizes elliptical liquid jets with low viscosity like water; however, this behavior seems to get obscured in water–glycerol mixture elliptical jets due to high viscosity.     

变截面欧拉梁自由振动分析的重采样微分求积法

采用重采样微分求积法求解了变截面欧拉梁的自由振动问题。推导了变截面梁的控制方程离散格式,采用重采样矩阵方法对边界条件进行处理,给出了变截面梁自由振动算法。采用本文方法对不同类型截面形式和不同边界条件的变截面梁进行自由振动分析,并和其他解法进行比较。计算结果表明,本文方法可以适用于不同变截面类型和不同边界条件,计算精度与解析解吻合良好,具有良好的收敛性能。在同等精度条件下网格点数少于现有计算方法。重采样转换矩阵边界处理方法相比于传统边界处理方法具有更快的收敛性能。     

The influence of twist on the motion of straight elliptical jets

This paper is concerned with a fairly detailed analysis of the motion of a straight elliptical jet of an incompressible, inviscid fluid in which the jet is allowed to twist along its axis. Our study, which includes the effects of gravity and surface tension, utilizes the nonlinear differential equations of the one-dimensional theory of a directed fluid jet. A number of theorems are proved pertaining to the motion of a twisted elliptical jet and some special solutions are obtained which illustrate the influence of twist.     

On the behavior of a three-dimensional fractional viscoelastic constitutive model

In this paper a three-dimensional isotropic fractional viscoelastic model is examined. It is shown that if different time scales for the volumetric and deviatoric components are assumed, the Poisson ratio is time varying function; in particular viscoelastic Poisson ratio may be obtained both increasing and decreasing with time. Moreover, it is shown that, from a theoretical point of view, one-dimensional fractional constitutive laws for normal stress and strain components are not correct to fit uniaxial experimental test, unless the time scale of deviatoric and volumetric are equal. Finally, the model is proved to satisfy correspondence principles also for the viscoelastic Poisson’s ratio and some issues about thermodynamic consistency of the model are addressed.     

Magnetohydrodynamic pipe flow in ducts with partial circular ring cross section and annular cross section

In this paper we use the Green function method to solve the problem of steady one dimensional flow of an incompressible viscous, electrically conducting fluid through a pipe with partial circular ring cross section and one with annular cross section, in the presence of an applied transverse uniform magnetic field. We obtain analytic solutions and carry out some numerical calculations of the velocity distribution and induced magnetic field.