Digital determination of photoelastic birefringence using two wavelengths

A new approach for digital determination of photoelastic birefringence is proposed. The relationships between the intensity values and the fringe orders of two wavelengths are derived. This scheme allows for automatic determination of fringe orders of a full-field photoelastic fringe pattern without using zero-order fringes in the fringe pattern. The usefulness of this method was demonstrated on two experimental fringe patterns with different wavelengths.     

Lubricated cross-slot flow of a low density polyethylene melt

Flow-induced birefringence and particle tracking velocimetry are used to investigate the lubricated flow of a low density polyethylene melt in a cross-slot geometry. The numerical predictions of the extended Pom-Pom (XPP) model in its original and modified (mXPP) version as well as those of the Giesekus model are analyzed along selected streamlines in two-dimensional (2D) complex flows involving a mixture of shear and planar extensional deformations at two Weissenberg numbers of Wi=21 and 29. Oil film light reflections perturbing the particle tracking velocimetry data analysis together with multiple orders of retardation occurring within the laser beam close to the stagnation point prevent a conclusive discrimination between the mentioned models. Although the agreement with the experimental data is mostly qualitative, the Pom-Pom model does not overestimate the data along the cross-slot symmetry lines contrary to what was observed in other cross-slot experiments without lubrication. This is a clear indicator that end effects play a central role in unlubricated cross-slot geometries having a large aspect ratio.     

Neck development in metal/elastomer bilayers under dynamic stretchings

Dynamic stretching of bilayer plates comprised of an elastomer layer bonded to a metal layer is studied with emphasis on neck development under plane strain. Neck retardation and multiple necks in the metal layer are promoted by the elastomer layer under quasi-static conditions and also by inertia in the all-metal layer under dynamic stretching. The present study explores the interaction of these two effects under the assumption that ductility is unlimited. The study reveals the roles of the elastomer modulus, the metal strength and the rate of stretching in giving rise to necking retardation.     

From h to p efficiently: optimal implementation strategies for explicit time‐dependent problems using the spectral/hp element method

We investigate the relative performance of a second‐order Adams–Bashforth scheme and second‐order and fourth‐order Runge–Kutta schemes when time stepping a 2D linear advection problem discretised using a spectral/hp element technique for a range of different mesh sizes and polynomial orders. Numerical experiments explore the effects of short (two wavelengths) and long (32 wavelengths) time integration for sets of uniform and non‐uniform meshes. The choice of time‐integration scheme and discretisation together fixes a CFL limit that imposes a restriction on the maximum time step, which can be taken to ensure numerical stability. The number of steps, together with the order of the scheme, affects not only the runtime but also the accuracy of the solution. Through numerical experiments, we systematically highlight the relative effects of spatial resolution and choice of time integration on performance and provide general guidelines on how best to achieve the minimal execution time in order to obtain a prescribed solution accuracy. The significant role played by higher polynomial orders in reducing CPU time while preserving accuracy becomes more evident, especially for uniform meshes, compared with what has been typically considered when studying this type of problem.© 2014. The Authors. International Journal for Numerical Methods in Fluids published by John Wiley & Sons, Ltd.     

多重应力奇异性及其强度系数的数值分析方法

以具有两个应力奇异性次数的平面问题为例,提出了一种利用普通的数值分析结果确定奇异点附近多重应力奇异性的各阶次数以及相应的应力强度系数的数值分析方法,计算实例表明,本方法可以精确地求得各阶应力奇异性的次数,并且可以很方便地应用外插法确定出对应的应力强度系数。     

Photoelastic measurements by means of computer-assisted spectral-contents analysis

A new method of photoelastic measurement has been developed. The light emerging from a polariscope is spectrally separated and projected on a photodiode array. It is shown that the relative retardation can be retrieved from light intensity measured at several wavelengths. Key parameters affecting the precision of this approach are discussed and evaluated.Paper was presented at V International Congress on Experimental Mechanics held in Montreal, Quebec, Canada on June 10–15, 1984.     

Flow of branched polymer melts in a lubricated cross-slot channel: a combined computational and experimental study

Numerical simulations have been performed to evaluate the accuracy of the multimode Giesekus model in predicting the flow behavior of a rheologically well characterized low-density polyethylene melt in a lubricated cross-slot channel. Specifically, the fidelity of the numerical results is established by detailed comparison with flow-induced birefringence measurements in a new optical rheometer with lubricated side walls that allows the creation of ideal two-dimensional flow kinematics that lead to the elimination of end effects commonly encountered in flow birefringence measurements. Based on these comparisons, the ability of the multimode Giesekus model to capture the flow characteristics with reasonable accuracy in the experimentally available Wi range of 21 to 29 has been established. However, it should be noted that the model predictions are, at best, qualitative in the vicinity of the stagnation point. The discrepancy between numerically predicted and experimentally observed stresses in this region is mainly attributed to the inaccuracy of the experimental data that stem from the occurrence of multiple orders of retardation within the measurement volume. Overall, these studies have paved the way for the development of a hi-fidelity lubricated cross-slot channel rheometer.     

Relaxation and retardation functions of the Maxwell model with fractional derivatives

A four-parameter Maxwell model is formulated with fractional derivatives of different orders of the stress and strain using the Riemann-Liouville definition. This model is used to determine the relaxation and retardation functions. The relaxation function was found in the time domain with the help of a power law series; a direct solution was used in the Laplace domain. The solution can be presented as a product of a power law term and the Mittag-Leffler function. The retardation function is determined via Laplace transformation and is solely a power law type.The investigation of the relaxation function shows that it is strongly monotonic. This explains why the model with fractional derivatives is consistent with thermodynamic principles.This type of rheological constitutive equation shows fluid behavior only in the case of a fractional derivative of the stress and a first order derivative of the strain. In all other cases the viscosity does not reach a stationary value.In a comparison with other relaxation functions like the exponential function or the Kohlrausch-Williams-Watts function, the investigated model has no terminal relaxation time. The time parameter of the fractional Maxwell model is determined by the intersection point of the short- and long-rime asymptotes of the relaxation function.     

论迟滞与时滞

迟滞和时滞是自然科学、工程科学、乃至社会科学中常见的两种现象,但在我国学术界常被混淆. 从两种现象的定义和本质出发,阐述两者的共性、个性及其联系. 通过多个例子说明:迟滞现象反映两个相关参变过程周期变化时彼此间的相位滞后关系;而时滞现象则反映两个相关动态过程任意变化时彼此间的时间滞后关系.在某些特定的情况下, 它们可以等同; 但在一般情况下,它们是具有不同性质的两类现象, 尤其在描述记忆特性方面, 两者有本质的差异.      

Remarks on the Perturbation Methods in Solving the Second-Order Delay Differential Equations

The paper presents a study on the validity of perturbation methods, suchas the method of multiple scales, the Lindstedt–Poincaré method and soon, in seeking for the periodic motions of the delayed dynamic systemsthrough an example of a Duffing oscillator with delayed velocityfeedback. An important observation in the paper is that the method ofmultiple scales, which has been widely used in nonlinear dynamics, worksonly for the approximate solutions of the first two orders, and givesrise to a paradox for the third-order approximate solutions of delaydifferential equations. The same problem appears when theLindstedt–Poincaré method is implemented to find the third-orderapproximation of periodic solutions for delay differential equations,though it is effective in seeking for any order approximation ofperiodic solutions for nonlinear ordinary differential equations. Apossible explanation to the paradox is given by the results obtained byusing the method of harmonic balance. The paper also indicates thatthese perturbation methods, despite of some shortcomings, are stilleffective in analyzing the dynamics of a delayed dynamic system sincethe approximate solutions of the first two orders already enable one togain an insight into the primary dynamics of the system.     

Plasmonic cloaking and scattering cancelation for electromagnetic and acoustic waves

One popular approach to cloaking objects from electromagnetic waves at moderately long wavelengths is the scattering cancelation technique. This mechanism is based on the use of a single homogeneous thin layer to cover an object of interest in order to provide scattering suppression in a given frequency band. This approach has also been recently extended to acoustic waves. This paper provides an investigation of the physical nature of scattering cancelation by a uniform thin layer for both electromagnetic and acoustic waves in inviscid fluids. Two distinct scattering cancelation regions are obtained within the available parameter space: a non-resonant plasmonic cloaking region and an anti-resonant cloaking region, which are identified and compared in both the electromagnetic and acoustic domains. Although both types of operations allow for the suppression of the dominant scattering orders, the resulting internal fields and physical functionality of the cloaks present distinct differences between the two domains. We discuss analogies and differences between these functionalities and their implications in electromagnetic and acoustic cloaking problems, with an insight into their practical implementation.     

Synchronization of nonidentical chaotic fractional-order systems with different orders of fractional derivatives

This paper addresses the problem of synchronization of chaotic fractional-order systems with different orders of fractional derivatives. Based on the stability theory of fractional-order linear systems and the idea of tracking control, suitable controllers are correspondingly proposed for two cases: the first is synchronization between two identical chaotic fractional-order systems with different fractional orders, and the other is synchronization between two nonidentical fractional-order chaotic systems with different fractional orders. Three numerical examples illustrate that fast synchronization can be achieved even between a chaotic fractional-order system and a hyperchaotic fractional-order system.     

Towards the achromatic quarterwave plate

A set of two retardation plates is analyzed in order to find the condition for the quarterwave-plate response. A nearly achromatic quarterwave plate is created when a set of two retarders has a matched ratio of the phase retardation equal to 2.     

On three-dimensional acoustic-gravity waves in model non-isothermal atmospheres

The propagation of acoustic-gravity waves is studied in a family of model non-isothermal atmospheres, including temperature profiles with any initial and asymptotic temperature and adjustable maximum temperature gradient. The equation for the vertical velocity of linear acoustic-gravity waves is solved exactly in terms of hypergeometric functions, the wave field being described to all orders in the scattering parameter kL, at all frequencies and distances, including wavelengths comparable to the scale of temperature change and atmospheric layers with a large temperature gradient. It is found that since the temperature is bounded, in the asymptotic regime waves grow in amplitude exponentially and phase increases linearly with altitude. The growth in amplitude is larger than exponential and the phase increases faster than linearly for atmospheres whose temperature increases with altitude, the effect being more marked for high frequency waves in regions of large temperature gradients. The accumulation of these effects leads to a wave field which is equivalent to the isothermal case at asymptotic temperature modified by a constant amplitude factor and phase shift which account for the history of propagation of the wave through the temperature gradients.     

Absolute phase measurement in extrinsic Fabry-Perot optical fiber sensors using multiple path-match conditions

This paper describes the use of the first and second optical return paths in a moderate-to-high finesse Fabry-Perot sensor to measure the absolute phase in extrinsic Fabry-Perot interferometry (EFPI) sensors. A path-matched differential interferometry (PMDI) using a highfinesse EFPI sensors, a low-finesse Fabry-Perot readout interferometer and a broadband light source consisting of amplified spontaneous emission (ASE) from an erbium-doped fiber amplifier (EDFA) is used to illustrate the idea. The first and second multiple paths in the Fabry-Perot readout sensor are used to provide two distinct path-match conditions from the same scanning Fabry-Perot readout interferometer. The difference in fringe numbers between the centers of two orders of interference fringe packets formed by the distinct path-match conditions makes possible a simple method of measuring the cavity length of EFPI sensors, which in turn can be used to measure absolute phase and the corresponding strain. Sensor cavity length measurement using the multiple return paths in the high-finesse Fabry-Perot sensor is correlated to that measurement using the modulation transfer function found using an optical spectrum analyzer; the multiple return path technique is then used to make strain measurements on a cantilever beam. Comparisons with resistance strain gage measurements are favorable. Characterization tests indicate that the proposed technique has a cavity length measurement resolution on the order of 1.1 μm, which translates to a strain resolution of 28 με for a 4-cm gage length sensor.     

Experiments on the dynamics of droplet collisions in a vacuum

Highly controlled experiments of binary droplet collisions in a vacuum environment are performed in order to study the collision dynamics devoid of aerodynamic effects that could otherwise obstruct the experimental observations by causing distortion or even disintegration of the coalesced mass. Pre-collision droplets are generated from capillary stream break-up at wavelengths much larger than those generated with the typical Rayleigh droplet formation in order to reduce the interactions among the collision products. Experimental results show that the range of droplet Weber number necessary to describe the boundaries between permanent coalescence and coalescence followed by separation is several orders of magnitude higher than has been reported in experiments conducted at standard atmospheric pressures with lower viscosity liquids (i.e. hydrocarbon fuels and water). Additionally, the time periods of both the oblate and prolate portions of the coalesced droplet oscillation have been measured and it is reported for the first time that the time period for the prolate portion of the oscillation grows exponentially with the Weber number. Finally, new pictorial results are presented for droplet collisions between non-spherical droplets. Received: 30 June 1998/Accepted: 15 October 1999     

Material aspects of dynamic neck retardation

Neck retardation in stretching of ductile materials is promoted by strain hardening, strain-rate hardening and inertia. Retardation is usually beneficial because necking is often the precursor to ductile failure. The interaction of material behavior and inertia in necking retardation is complicated, in part, because necking is highly nonlinear but also because the mathematical character of the response changes in a fundamental way from rate-independent necking to rate-dependent necking, whether due to material constitutive behavior or to inertia. For rate-dependent behavior, neck development requires the introduction of an imperfection, and the rate of neck growth in the early stages is closely tied to the imperfection amplitude. When inertia is important, multiple necks form. In contrast, for rate-independent materials deformed quasi-statically, single necks are preferred and they can emerge in an imperfection-free specimen as a bifurcation at a critical strain. In this paper, the interaction of material properties and inertia in determining neck retardation is unraveled using a variety of analysis methods for thin sheets and plates undergoing plane strain extension. Dimensionless parameters are identified, as are the regimes in which they play an important role.     

Two-wavelength method for full-field automated photoelasticity

A new method for the whole-field determination of the isoclinic angle α and the isochromatic parameter ϕ is presented. The problems appearing during the calculation of these two parameters are solved with the use of two different wavelengths. Indeed, when a monochromatic light is used as an incident light, α is not measurable at the points where ϕ is equal to 2kπ. In this method, each monochromatic light can compensate for the influence of ϕ to obtain the isoclinic angle for the entire model. Also, most of the methods calculate the fractional fringe order that is unwrapped afterward to obtain the isochromatic parameter. This unwrapping process needs an initialization, which cannot be automatic with only one isochromatic fringe pattern. The use of two wavelengths permits a complete automatic unwrapping of the isochromatic parameter, even for the initialization of the process.     

A double-beam method of spectral selection with flames

Summary A non-dispersive, optic-electrical filter instrument is described, which combines high spectral resolving power (∼0.1 ?) with large luminosity, at wavelengths which are of interest in spectrochemistry. The method is based on the balance of two light-beams emitted by a source S, which are periodically chopped in opposite phase. By placing a flame A containing vapour of some element into one light-beam, this balance is made critical for wavelengths that are specifically absorbed by this vapour. The applicability of a self-radiating flame as absorber could be realized by making use of an a.c. measuring device and by choosing a suitable position of the light-chopper. The described test experiments, which were made with a provisional instrument, prove the applicability of this method, especially in flame photometry.