Fast parametrically excited van der Pol oscillator with time delay state feedback

We investigate the effect of a fast vertical parametric excitation on self-excited vibrations in a delayed van der Pol oscillator. We use the method of direct partition of motion to derive the main autonomous equation governing the slow dynamic in the vicinity of the trivial equilibrium. Then, we apply the multiple scales method on this slow dynamic to derive a second-order slow flow system describing the modulation of slow dynamic. In particular we analyze the slow flow to obtain the effect of a fast excitation on the regions in parameter space where self-excited vibrations can be eliminated. We have shown that in the case where the time delay and the feedback gains are imposed, fast vertical parametric excitation can be an alternative to suppress undesirable self-excited vibrations in a delayed van der Pol oscillator.     

2:1 and 1:1 frequency-locking in fast excited van der Pol–Mathieu–Duffing oscillator

The frequency-locking area of 2:1 and 1:1 resonances in a fast harmonically excited van der Pol–Mathieu–Duffing oscillator is studied. An averaging technique over the fast excitation is used to derive an equation governing the slow dynamic of the oscillator. A perturbation technique is then performed on the slow dynamic near the 2:1 and 1:1 resonances, respectively, to obtain reduced autonomous slow flow equations governing the modulation of amplitude and phase of the corresponding slow dynamics. These equations are used to determine the steady state responses, bifurcations and frequency-response curves. Analysis of quasi-periodic vibrations is carried out by performing multiple scales expansion for each of the dependent variables of the slow flows. Results show that in the vicinity of both considered resonances, fast harmonic excitation can change the nonlinear characteristic spring behavior from softening to hardening and causes the entrainment regions to shift. It was also shown that entrained vibrations with moderate amplitude can be obtained in a small region near the 1:1 resonance. Numerical simulations are performed to confirm the analytical results.     

Modélisation de fissures elliptiques internes par hybridation de fonctions de poidsEmbedded elliptical cracks modeling with hybridization of weight functions

A method improving the evaluation of the stress intensity factor by hybridization of two weight functions is presented and applied to embedded elliptical cracks under various loadings. The hybridization consists in using one or the other function in the zone of the crack where it is the most efficient. The delimitation of the two zones is achieved after optimizing the axes ratio and the curvature radius of the crack. During this optimization we seek to reduce the effects of the singularities present in the weight functions as well as to take better into account the influence of the ellipse curvature. To cite this article: B. El Khalil Hachi et al., C. R. Mecanique 334 (2006).     

Effets d'une modulation en phase de température à la frontière sur l'instabilité convective d'une couche liquide viscoélastiqueEffects of a temperature modulation in phase at the frontier on the convective instability of a viscoelastic layer

In this Note we study the effects of the temperature modulation, applied at the horizontal boundaries, on the onset of convection of a horizontal liquid Maxwellian layer. It is assumed that the temperature imposed features a steady component and a time dependent component. To analyse the effect of the temperature modulation, the study is restricted to a linear stability analysis. Thus the Floquet theory and a technique of converting a boundary value problem to an initial value problem are used to solve the system of equations corresponding to the onset of convection. Results obtained may be used to characterize the influence of modulation effects and that of the viscoelastic nature of liquid on the critical Rayleigh number. To cite this article: B. Oukada et al., C. R. Mecanique 334 (2006).     

Estimation of aerodynamic noise generated by forced compressible round jetsEstimation du bruit d'origine aérodynamique rayonné par des jets ronds forcés compressibles

An acoustic numerical code based on Ligthill's analogy is combined with large-eddy simulations techniques in order to evaluate the noise emitted by subsonic $(M=0.7)$ and supersonic $(M=1.4)$ round jets. We show first that, for centerline Mach number $M=0.9$ and Reynolds number $\mathit{Re}=3.6\times {10}^3$, acoustic intensities compare satisfactorily with experimental data of the literature in terms of levels and directivity. Afterwards, high Reynolds number $(\mathit{Re}=3.6\times {10}^4)$ free and forced jets at Mach 0.7 and 1.4 are studied. Numerical results show that the jet noise intensity depends on the nature of the upstream mixing layer. Indeed, the subsonic jet is 4 dB quieter than the free jet when acting on this shear layer by superposing inlet varicose and flapping perturbations at preferred and first subharmonic frequency, respectively. The maximal acoustic level of the supersonic jet is, on the other hand, 3 dB lower than the free one with a flapping upstream perturbation at the second subharmonic. The results reported in this paper confirm previous works presented in the literature demonstrating that jet noise may be modified according to the inlet conditions. To cite this article: M. Maidi, C. R. Mecanique 334 (2006).     

Propagation of Transient Acoustic Waves in Layered Porous Media: Fractional Equations for the Scattering Operators

Acoustic waves scattering from a rigid air-saturated porous medium is studied in the time domain. The medium is one dimensional and its physical parameters are depth dependent, i.e., the medium is layered. The loss and dispersion properties of the medium are due to the fluid-structure interaction induced by wave propagation. They are modeled by generalized susceptibility functions which express the memory effects in the propagation process. The wave equation is then a fractional telegraphists equation. The two relevant quantities are the scattering operators—transmission and reflection operators—which give the scattered fields from the incident wave. They are obtained from Volterra equations which are fractional equations for the scattering operators.     

Effect of Al<Subscript>2</Subscript>O<Subscript>3</Subscript> phases on the enhancement of thermal conductivity and viscosity of nanofluids in engine oil

Thermal conductivity of α-Al₂O₃ was measured using hot wire method. α-Al₂O₃ (20 nm in size) was synthesized by microwave method for which, the results were compared with commercially available γ-Al₂O₃. Thermal conductivity of nanofluids was investigated considering, it is dependency on Al₂O₃ phase. It was observed that by adding 3 wt% of nano γ-Al₂O₃ and α-Al₂O₃ to the engine oil, thermal conductivity increases by 37 and 31%, respectively. The corresponding viscosity increase for the same amount of nano γ-Al₂O₃ and α-Al₂O₃ were 36 and 38%, respectively. It was concluded that the differences in thermal conductivity originate from higher specific surface area of γ-Al₂O₃ compared to the α-Al₂O₃ which is the result of porosity difference, obtained during the synthesis process.     

Predicting Homoclinic Bifurcations in Planar Autonomous Systems

An analytical method to predict the homoclinic bifurcation in a planar autonomous self-excited weakly nonlinear oscillator is presented. The method is mainly based on the collision between the periodic orbit undergoing the homoclinic bifurcation and the saddle fixed point. To illustrate the analytical predictive criteria, two typical examples are investigated. The results obtained in this work are then compared to Melnikov's technique and to a previous criterion based on the vanishing of the frequency. Numerical simulations are also provided.     

Normal and cross-flow Reynolds stresses: differences between confined and semi-confined flows

Understanding turbulent wall-bounded flows remains an elusive goal. Most turbulent phenomena are non-linear, complex and have broad range of scales that are difficult to completely resolve. Progress is made only in minute steps and enlightening models are rare. Herein, we undertake the effort to bundle several experimental and numerical databases to overcome some of these difficulties and to learn more about the kinematics of turbulent wall-bounded flows. The general scope of the present work is to quantify the characteristics of wall-normal and spanwise Reynolds stresses, which might be different for confined (e.g., pipe) and semi-confined (e.g., boundary layer) flows. In particular, the peak position of wall-normal stress and a shoulder in spanwise stress never described in detail before are investigated using select experimental and direct numerical simulation databases available in the open literature. It is found that the positions of the á v￠² ñ ⁺ \left\langle {v'{^2} } \right\rangle^{ + } -peak in confined and semi-confined flow differ significantly above δ ⁺ ≈ 600. A similar behavior is found for the position of the á u￠v￠ ñ ⁺ \left\langle {u'v'} \right\rangle^{ + } -peak. The upper end of the logarithmic region seems to be closely related to the position of the á v￠² ñ ⁺ \left\langle {v'{^2} } \right\rangle^{ + } -peak. The á w￠² ñ ⁺ \left\langle {w'{^2} } \right\rangle^{ + } -shoulder is found to be twice as far from the wall than the á v￠² ñ ⁺ \left\langle {v'{^2} } \right\rangle^{ + } -peak. It covers a significantly large portion of the typical zero-pressure-gradient turbulent boundary layer.     

Inhibition Effect of Hydantoin Compounds on the Corrosion of Iron in Nitric and Sulfuric Acid Solutions

Summary.  The inhibition of corrosion of iron in 2 M nitric acid and 2 M sulfuric acid solutions by substituted phenylhydantoin, thiohydantoin, and dithiohydantoin compounds was measured using thermometric, weight loss, and polarization methods. The three methods gave consistent results. The polarization curves indicated that the hydantoin compounds act as mixed-type inhibitors. The adsorption of the inhibitors were found to obey the Temkin adsorption isotherm. The higher inhibition efficiency of the additives in nitric with respect to sulfuric acid solution may be attributed to the reduced formation of soluble quaternary nitrogen salts in nitric acid medium, favouring adsorption of the parent additive on the metal surface. The obtained results indicate that the corrosion rate of iron in both acids increases with increasing temperature, both in absence and presence of the tested inhibitors. Kinetic-thermodynamic model functions and Temkin isotherm data are compared and discussed. The synergistic effect of halide anions on the inhibition efficiency of the hydantoin compounds was also investigated. Received June 5, 2000. Accepted (revised) September 13, 2000