Parametric excitation in non-linear dynamics

Consider a one-mass system with two degrees of freedom, non-linearly coupled, with parametric excitation in one direction. Assuming the internal resonance 1:2 and parametric resonance 1:2 we derive conditions for stability of the trivial solution by using both the harmonic balance method and the normal form method of averaging. If the trivial solution becomes unstable, a stable periodic solution may emerge, there are also cases where the trivial solution is stable and co-exists with a stable periodic solution; if both the trivial solution and the periodic solution(s) are unstable, we find an attracting torus with large amplitudes by a Neimark-Sacker bifurcation. The results of the harmonic balance method and averaging are compared, as well as the results on the Neimark-Sacker bifurcation obtained by the numerical software package CONTENT and by averaging. In all cases we have good agreement.     

Step and steady shear responses of nearly monodisperse highly entangled 1,4-polybutadiene solutions

Nonlinear relaxation dynamics of highly entangled solutions of high molecular weight 1,4-polybutadiene (PB) in a PB oligomer are studied in steady shear and step shear flows. Polymer entanglement densities vary in the range 14hN/N_e(J)⣴, allowing systematic investigation of entanglement effects on nonlinear rheological response. In agreement with previous steady shear studies using well entangled polystyrene solutions, a flow regime is found where both the steady-state shear stress and first normal stress difference remain constant or increase quite slowly with shear rate, leading to a plateau in the steady-state orientation angle. The magnitude of the average orientation angle in the plateau range is in accordance with predictions of a recent theory by Islam and Archer (2001). In step shear, the nonlinear relaxation modulus G(t,%) is approximately factorable into time-dependent G(t) and strain-dependent h(%) functions only at long times, t>5_k, where 5_k,O(F_d0). This finding is consistent with earlier observations for entangled polystyrene solutions; however the complex crossing pattern in G(t,%)h^-1(%) that precede factorability in the latter materials is not observed. For all but the most entangled sample, apparent shear damping functions h (%,t)=(G(t,%))/(G(t)) immediately following imposition of shear are in nearly quantitative accord with the damping function h_DEIA predicted by Doi-Edwards theory.     

DYNAMICS OF ROTORS IMMERSED IN ECCENTRIC ANNULAR FLOW. PART 2: EXPERIMENTS

In order to validate the theoretical approach described in Part 1, an extensive experimental study has been performed at Instituto Tecnológico e Nuclear (I.T.N.), using a test rig presenting some improvements over previous experiments by the authors. In agreement with the theoretical model, concentric configurations always display flutter instability of the forward mode only, at velocities much higher than the critical unbalance-excited rotor velocity. Also predicted by theory, an instability of the backward mode may occur at much lower spinning velocities, for some eccentric configurations—which is a conclusion of practical significance. Therefore, rotor-annulus eccentricity is a very important parameter, when stability of the system is addressed. The quantitative agreement of both modal frequencies and damping values, with respect to the rotor spinning velocity, is quite satisfactory at lower velocities. However, it deteriorates somewhat at higher velocities, even for concentric configurations. Discrepancies are discussed, in connection with experimental difficulties (some unavoidable three-dimensional flow effects in the test rig) or other possibly pertinent phenomena (dynamic flow nonlinearities)—which were not accounted for in the theoretical model. However, these problems should not be overstressed, as theoretical instability boundaries are usually fairly close to the experimental results.     

Experimental study of the Kolmogorov refined similarity variable

Recently Thoroddsen and Van Atta (1992, Phys. Fluids A4, 2592) showed that Kolmogorov's refined similarity hypothesis (1962, J. Fluid Mech. 13, 77; 82) is supported by experimental data from a wind-tunnel study of a cylinder wake, at Re_λ of 550. We show here that the probability density of the Kolmogorov similarity variable approaches a Gaussian distribution. The data also suggest that it may obey an even more demanding conditional similarity, which leads to important conclusions regarding the scaling exponents.     

A review of pool and forced convective boiling of binary mixtures

Boiling of binary mixtures is characterized by a close linking between heat and mass transfer processes, with the evaporation rate usually being limited by the mass transfer process. This is significantly different from single-component systems where interfacial mass transfer rates are normally very high. Information on pool boiling of binary mixtures is widely available in the literature, whereas research on forced convective boiling of mixtures has become significant only over the last few years. This paper presents a brief review of experimental results obtained in pool and forced convective boiling of binary mixtures and upgrades the empirical or theoretical predictive tools for both situations.     

Seismic gyrotropy as a result of rock-microstructure dissymmetry

Seismic investigations show that rocks exhibit not only anisotropic properties but also gyrotropic ones. Recently, the phenomenological theory has been developed to describe the phenomenon ‘seismic gyrotropy'. The paper gives a possible explanation of the gyrotropic properties of rocks on a microlevel. A gyrotropic model of grainy rock with dissymetry in its microstructure is presented. The model is built on a principle ‘azimuthal turn plus translation'. The mathematical and physical formulations of the problem are discussed. An algorithm is constructed to find the displacements, their first and second derivatives with respect to spatial coordinates as well as stresses inside a grain, an element of the model. Mathematical modelling of elastic-wave propagation in the model considered enabled to demonstrate that the model possesses gyrotropic properties, i.e., it rotates on a polarization vector. Gyration constants are determined.     

An experimental study on effects of solid concentration and ζ-potential on pseudoplastic flow of suspensions

The pseudoplastic flow of suspensions, alumina or styrene-acrylamide copolymer particles in water or an aqueous solution of glycerin has been studied by the step-shear-rate method. The relation between the shear rate,D, and the shear stress,, in the step-shear-rate measurements, where the state of dispersion was considered to be constant, was expressed as = AD ^1/2 +CD. The effective solid volume fraction,ø _F, andA were dependent on the shear rate and expressed byø _F =aD ^b andA = D . Combining the above relations, the steady flow curve was expressed by = D ^{1/2 +} + ₀ (1 – a D ^b/0.74)^–1.85 D, where ₀ is the viscosity of the medium.With an increase in solid volume fraction and a decreases in the absolute value of the-potential, the flow behavior of the suspensions changed from Newtonian ( = = b = 0), slightly pseudoplastic ( = b = 0), pseudoplastic ( = 0) to a Bingham-like behavior.The change in viscosity of the medium had an effect on the change in the effective volume fraction.     

The elastic field caused by a general ellipsoidal inclusion and the application to martensite formation 2

The elastic field throughout an ellipsoidal inclusion in an indefinitely-extended anisotropic material is investigated when an eigenstrain (a stress-free transformation strain) is periodically distributed throughout the inclusion. This is an extention of the results obtained by J.D. Eshelby (1961) for uniform eigenstrains and by R.J. Asaro and D.M. Barnett (1975) for polynomial eigenstrains. The solution is applied to the evaluation of elastic strain energies of a disc-shaped martensite with alternating twins and of a spherical precipitate with a banded structure. The significant amount of the elastic strain energies explains the necessity of the supercooling of austenite steel for the martensitic transformation to occur.     

Some rheological properties of dilute suspensions of polyoxymethylene crystals in p-xylene

Summary Dilute suspensions of polyoxymethylene crystals inp-xylene have been shown to behave as Bingham Plastic Fluids. The crystals are very thin hexagonal platelets and low concentrations are sufficient to provide a continuous high-voidage matrix which requires the application of a finite stress before deformation occurs. The behaviour of the system has been characterised with respect to changes in shear rate, temperature and concentration of suspended polymer.

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Zusammenfassung Es wurde gezeigt, daß sich verdünnte Lösungen von Polyoxymethylen-Kristallen in p-Xylol wie eine Bingham-Flüssigkeit verhalten. Die Kristalle sind sehr dünne hexagonale Plättchen. Niedrige Konzentrationen sind für eine beständige Matrix, die das Aufbringen einer endlichen Spannung erfordert, bevor eine Deformation auftritt, ausreichend. Das Verhalten dieses Systems wurde unter Berücksichtigung von Änderungen der Schergeschwindigkeit, der Temperatur und der Konzentration des suspendierten Polymers charakterisiert.

     

Transient flows of a second grade fluid

Exact analytical solutions for a class of unsteady unidirectional flows of an incompressible second-order fluid are constructed. The flows are generated impulsively from rest by motion of a plate or two plates or by sudden application of a pressure gradient. Expressions for velocity, flux and skin friction are obtained for both large and small times. It is found that large and small times solutions are dependent on the coefficient of viscoelasticity. The solutions corresponding to Newtonian fluids can be easily obtained from those for fluids of second order by letting the viscoelastic parameter to be zero.