Thermal stresses in a viscoelastic three-phase composite cylinder

A thermoviscoelastic analysis of a three-phase composite cylinder is presented in this work. The solutions of the heat conduction and thermoelastic problem for three dissimilar media are derived based on the method of analytic continuation associated with the alternation technique. A rapidly convergent series solution for both the temperature and stress field, which is expressed in terms of an explicit general term of the corresponding homogeneous potential, is obtained in an elegant form. The hereditary integral in conjunction with the Kelvin–Maxwell model is applied to simulate the thermoviscoelastic properties while a thermorheologically simple material is considered. According to the correspondence principle, the Laplace transformed thermoviscoelastic solution is directly determined from the corresponding thermoelastic one. The real time solution can then be solved numerically by taking inverse Laplace transform. Finally, some typical examples of interfacial stresses are discussed.     

Topography and Dispersion Effects in Bottom Layer Dynamics

A hyperbolic model of a shallow water flow is considered with allowance for nonlinear and dispersion effects. The structure of traveling waves above a flat bottom is studied. Stability of small disturbances of a homogeneous flow and development of instability of a nonstationary flow above an inclined bottom are analyzed.     

Wing characteristics and flapping behavior of flying insects

This paper is concerned with the flapping characteristics and the structure dynamics of insect wings. The flapping behavior of some insects is studied using a threedimensional motion analysis system. The experimental system is composed of two high-speed video cameras, a motion grabber, and a personal computer. The three-dimensional representation of insect flapping can be gained by the system. The extrinsic skeleton vibration produced by insect flapping is examined with the optical displacement detector system. The structural properties of some insect wings are also studied by a three-dimensional, optical shape measurement system. Some functional principles underlying insect wing design are revealed by the measurements of surface roughness and flapping analysis.     

The effect of laminations on the vibrational modes of circular annular plates

The purpose of this article is to present an experimental study of the effect of laminations on the vibrations of circular annular plates. To obtain a basis for comparison with experimental data, the natural frequencies and mode shapes of a series of solid circular annular plates were calculated using the finite element method. An extensive range of experiments were performed on both a series of solid models and a series of laminated models under a range of normal clamping pressures. Based on the analytical and experimental results, it was found that the vibrational behavior of the laminated plates was dominated by that of the individual plate of which they were composed and that the effects of the laminations on vibrations were mode type dependent. The effects on the transverse vibrational modes were dependent on both the normal clamping pressure and the number of plates. The amplitude of the frequency response function for these modes reduced quickly, and the resonant frequency of such modes shifted higher as the clamping pressure or the number of plates increased. For the in-plane vibrational modes, the amplitude of the frequency response function reduced slightly as the number of plates increased; the resonant frequency of such modes could be considered to be a constant and independent of both the clamping pressure and the number of plates.     

Mixing quantification by visual imaging analysis

This paper reports on development of a method for quantifying two measures of mixing, the scale and intensity of segregation, through flow visualization, video recording, and software analysis. This non-intrusive method analyzes a planar cross section of a flowing system from an instantaneous data record, thereby eliminating the need for statistical analysis of a large number of point measurements at multiple locations throughout the system to characterize the mixing. The method is applied to a cold flow model of a high temperature, gas/solid reactor so that reactor design and operation can be optimized to promote reaction efficiency. This method may be useful for studying a variety of mixing systems in which multiphase components or tracers are visually distinguishable.List of symbols mixing coefficient (defined by Eq. (17)) - standard deviation - a mixing coefficient (defined by Eq. (16)) - C(k, m) sample grayscale covariance (defined by Eq. (3)) - d distance (defined by Eq. (8)) - D divisor (defined by Eq. (3)) - d ^* value of d for which R _I (d) approaches zero - D ₅₀ mass median diameter - I intensity of segregation (defined by Eq. (20)) - M sample size (defined by Eq. (16)) - n number of contiguous pixels - n ^* value of n for which SSE _Q /SSE _L is maximized - n _c number of columns of pixels - N_R number of rows of pixels - P number of pixels per linear distance - r radius of Cold Flow Model - R(k, m) sample correlation function (defined by Eq. (5)) - R _C (k) column correlation function (defined by Eq. (7)) - R _I (d) isotropic correlation function (defined by Eq. (9)) - R _R (m) row correlation function (defined by Eq. (6)) - SSE _Q residual sum of squared errors from the least squares fit of the quadratic model to Eq. (14) - SSE _L residual sum of squared errors from the least squares fit of the linear model to Eq. (14) - S _y ² sample grayscale variance (defined by Eq. (2)) - S _c column scale of segregation (defined by Eqs. (7) and (13)) - S _D Danckwerts' scale of segregation (defined by Eq. (10)) - S _R row scale of segregation (defined by Eqs. (6) and (13)) - S _s scale measure developed in this paper (defined by Eq. (13)) - V _n sample variance of contiguous pixels (defined by Eq. (11)) - V _n ^* normalized variance function (defined by Eq. (12)) - sample grayscale mean (defined by Eq. (1)) - Y _i,j grayscale value at pixel (i,j)     

Fourier transform mechanical spectroscopy of the sol-gel transition in zirconium alkoxide ceramic gels

The gelation of a ceramic precursor, zirconium alkoxide, has been studied using dynamic oscillatory measurements. The gelation time is controlled by varying the concentrations of zirconium propoxide, hydrolysis with water, and acetylacetone concentration which acts as a chelating ligand. Gelation times were varied from minutes to months. The gelation time varied with zirconium concentration to the –10 power, hydrolysis to the –7 power, and ligand concentration of the –17 power. The sol-gel transition was monitored using the criteria of Winter in which GG ⁿ and tan () = tan . It is shown that the use of multiple superimposed sinusoidal waves to simultaneously measure the moduli at several frequencies is faster than using individual frequency sweep experiments. The selection of rate and strain criteria for brittle network gels is discussed in detail.     

A phenomenological theory for elastic superconductors

The purpose of the present study is to develop a phenomenological theory for elastic superconductors that is based on a rigorous thermodynamical internal variable theory in which the concept of complex internal variable is introduced to include the phase effect of quantum mechanics. Two phenomena of superconductivity, i.e., perfect conductivity and perfect diamagnetism, can be explained in the formulation. In the equilibrium state, this theory can be reduced to the well-known Ginzburg-Landau (GL) theory. Upon linearizing the field equations, boundary conditions and constitutive equations, the governing equations of the rigid-body state and the perturbed state are obtained. These equations then serve to analyze the effect of the hydrostatic deformation on the penetration depth, the GL coherence length and the critical field.     

Orienting properties of discotic nematic liquid crystals in Jeffrey-Hamel flows

The orienting properties of incompressible discotic nematic liquid crystals for creeping flows between converging and diverging planar walls (Jeffrey-Hamel) are analyzed using the Leslie-Ericksen theory. The dependence of director orientation on the reactive parameter and the flow kinematics is presented. Closed form stationary solutions for the director orientation are found when elastic effects are neglected. Stationary numerical solutions for the velocity and director fields using the full Leslie-Ericksen theory are presented. The director field in converging flow is characterized by azimuthal (radial) centerline orientation, by being asymmetric with respect to the azimuthal (radial) direction, and by having an allowed orientation range that spans two half-quadrants (full quadrants). In the limiting case of perfectly flat disk ( –) the flow-induced director orientation in converging flow is the azimuthal direction, while in diverging flow the director rotates by a full n radians. By reducing the vertex angle between the walls to vanishingly small values, converging flow solutions properly reduce to those of flow between parallel plates, but diverging flows are expected to lead to a new instability.     

Die langsame Strömung einer einfachen viskoelastischen Flüssigkeit durch einen endlich breiten Spalt

Zusammenfassung Es wird die zweidimensionale schleichende Strömung einer einfachen viskoelastischen Flüssigkeit durch einen endlich breiten Spalt mit Hilfe einer Störungsrechnung untersucht. Dabei wird vorausgesetzt, daß die Relaxationslänge klein gegen die Spaltbreite ist.Für einige Werte der Strömungsparameter werden Ergebnisse für die Geschwindigkeitsverteilung im Spalt, den Stromlinienverlauf und die Reibungsspannungen graphisch dargestellt und diskutiert. Obwohl wegen der Beschränkung der Lösungsmethode die bei Experimenten beobachteten Zirkulationsströmungen nicht beschrieben werden können, zeigen die Ergebnisse, daß die Tendenz der Abweichung vom newtonschen Verhalten in die gleiche Richtung geht.

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Summary The two-dimensional creeping flow of a simple viscoelastic fluid through a finite gap located in an infinitely wide plate is analysed by using a perturbation method.Solutions for the streamline pattern, the velocity distribution in the gap and the stress components are derived and discussed. Because of the restrictions of the perturbation method no circular flow, as observed in some experiments, is predicted, but the results indicate at least some tendencies into this direction.

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Mit 8 Abbildungen     

Quasistatic thermal crack extension in the interfaces of bounded self-stressed multiphase compounds

The quasistatic growth of straight interface cracks in thermally loaded brittle multiphase solids consisting of two circular segments of brittle materials with different thermoelastic properties which are glued together at the interface with a special glass seal has been investigated. The resulting mixed boundary-value problems of the stationary plane thermoelasticity have been solved by applying the finite element method. Moreover, fracture mechanical data like crack surface displacements and strain energy release rates governing the propagation behavior of a quasistatic extending thermal interface crack have been calculated. The data obtained have been compared with the results of special cooling experiments in multiphase composite structures in which curved thermal cracks in one of the circular segments occur.