Relaxation processes and their spectra in liquating glasses

We theoretically analyze the possibility of using certain relaxation functions (relaxation kernels) for dissipative processes discovered in the internal friction spectra of two-phase unordered glassy systems at temperatures higher than the vitrification temperature. It has been found that the most acceptable functions for describing the continuous spectra of relaxation times are the Maxwell and Kohlrausch functions. We consider one of the possible methods for determining the parameters of the Kohlrausch function from the internal friction spectra of the relaxation process in the vitrification region of liquating glasses.     

Relaxation time spectra of star polymers

 The linear viscoelastic data for model star polymer melts with varying functionality and arm molecular weight were represented by means of a modified Baumgaertel-Schausberger-Winter (BSW) relaxation time spectrum, based on data analysis with the parsimonius model of Baumgaertel et al., reported in 1990. In the case of high arm functionality, the second slow terminal relaxation observed by Vlassopoulos et al. in 1997, was captured with a straightforward extension of the BSW model using broad cut-off functions. This study represents a potentially promising attempt to extend the applicability of this representation of viscoelastic data to more complex architectures, beyond simple linear chains which are characterized by self-similarity. The casting of linear viscoelastic data into spectra allows the exploration of star polymer behavior. It is a necessary step in preparation for large scale complex flow calculations in conjunction with constitutive models and for material databases. Received: 18 November 1998/Accepted: 12 August 1999     

Higher-order moments and spectra of velocity fluctuations in adverse-pressure-gradient turbulent boundary layer

The characteristics of turbulent boundary layer flows with adverse pressure gradients (APGs) differ significantly from those of canonical boundary layers. We have investigated the effects of an APG on the higher-order moments and spectra of velocity fluctuations. The local wavelet spectra reveal a large difference in energy-containing frequencies of streamwise and wall-normal components of turbulent velocities, which results in smaller Reynolds shear stress production. Moreover, an analysis of bispectra in the Fourier space has revealed that non-local interactions, consisting of streamwise fluctuating velocity with low frequency and wall-normal velocity with high frequency, occur in the APG flow. However, the small-scale motions are not affected by imposing an APG.     

Spiral piezoelectric transducer in torsional motion as low-frequency power harvester

A structure consisting of a spiral piezoelectric transducer and a concentrated mass is proposed as a low-frequency piezoelectric power harvester. A theoretical model is developed for the system from the theory of piezoelectricity. An analysis is performed to demonstrate the low-frequency nature of the system. Other basic characteristics of the power harvester including the output power, voltage, and efficiency are also calculated and examined.     

Relaxation time spectra from short frequency range small-angle dynamic rheometry

In this work, the influence of the experimental frequency range over the relaxation time spectrum is studied. The relaxation time spectra were calculated from dynamic moduli, a well-known ill-posed problem, using a regularization method. The method solves the ill-posed problem by simultaneous minimization of the regularized standard deviation and a restriction function. The solution was validated using a simulated spectrum. Truncated moduli data generated from simulated spectra were used to evaluate the method for smaller frequency range data. Finally, experimental data of a wormlike micellar system mixed in aqueous solution with a zwitterionic copolymer were used to validate the method. It was possible to obtain relaxation time spectra from short frequency range data if the relaxation time range is allowed to be higher than the inverse of the highest and lowest experimental frequencies. These spectra can be used qualitatively to describe complex systems when no time-temperature superposition experiments are feasible.     

Reduction of noise and bias in randomly sampled power spectra

We consider the origin of noise and distortion in power spectral estimates of randomly sampled data, specifically velocity data measured with a burst-mode laser Doppler anemometer. The analysis guides us to new ways of reducing noise and removing spectral bias, e.g., distortions caused by modifications of the ideal Poisson sample rate caused by dead time effects and correlations between velocity and sample rate. The noise and dead time effects for finite records are shown to tend to previous results for infinite time records and ensemble averages. For finite records, we show that the measured sampling function can be used to correct the spectra for noise and dead time effects by a deconvolution process. We also describe a novel version of a power spectral estimator based on a fast slotted autocovariance algorithm.     

Generating line spectra from experimental responses. Part I: Relaxation modulus and creep compliance

We describe a recursive computer algorithm which generates line spectra from relaxation modulus or creep compliance data without producing negative spectrum lines. We apply the algorithm here to data read from mathematical models for the relaxation modulus. Since these data were thus free of the usual experimental error, we could use a relatively simple form of the basic algorithm that is applicable also to smoothed data. The spectra faithfully reproduced the input functions and may serve for data storage as well as for predicting other experimental responses.     

Optical technique for direct measurement of power spectra in compressible turbulence

We present exploratory tests of a new optical method which measures directly two components of the 3-D power spectrum of the refractive-index fluctuation. The method was applied to a Mach 2 turbulent shear layer. Length scales of 0.1 mm to 1.0 mm were resolved within a shear-layer thickness ranging from 5 mm to 10 mm. At low-to-moderate wavenumbers, the spectral behavior is roughlyκ ⁻³, while at higher wavenumbers it isκ ^−3.7. These spectral slopes are in agreement with prevailing theoretical predictions for anisotropic (low-wavenumber) and isotropic (high-wavenumber) turbulence. ]This study was funded by a grant from Lawrence Livermore National Laboratory and by a grant from the California Space Institute. DP is indebted to HFR and Dr. Alfred C. Buckingham of LLNL for their support.     

Liquid flow in foams

A model equation for describing liquid motion in a foam of polyhedral structure is proposed. A dimensionless parameter characterizing the structure of the foam, namely, the ratio of the volume energy densities of the capillary and gravitational forces, is introduced. When the gravitational forces predominate over the capillary forces, the out-flow process may be regarded as a kinematic wave that can be described by the Burgers equation. In the opposite case, the capillary absorption can be described by a quasilinear parabolic equation.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 103–108, March–April, 1988.The authors are grateful to A. V. Berlyand for discussing the problems associated with the solution of Eq. (3. 4).     

Experimental determination of bending strain power spectra from vibration measurements

Experimental results are presented of the power spectral density of the random bending strain on the surface of a beam obtained using a scanning laser vibrometer. The strain spectra were obtained by processing vibration data measured at discrete locations along the beam's length. The beam was driven by a stationary broad-band random force. The experimental setup is described along with the data analysis procedure. The results presented here indicate that the method is practical and can lead to reliable estimates.     

Arc current fluctuation power spectra in the system of a solid metal electrode and carbonate melt

Arc current fluctuations between a solid metal electrode and a liquid melt of alkaline carbonates at atmospheric pressure are measured. Arc current fluctuation power spectra are determined from the measurement data. It is shown that the fluctuation power is inversely proportional to the frequency (1/f-fluctuations). The fluctuations have a normal Gaussian distribution. The observed 1/f fluctuations exhibit scale invariance. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 1, pp. 11–15, January–February, 2007.     

Relaxation and propagation of pulses in fluids

Mathematical bases for the diagnostics of relaxing fluids in probing by sound pulses based on recording these pulse shapes are developed. Analysis of the change in the pulse shape makes it possible to establish the type of relaxation and to determine its parameters: the relaxation time, the dispersion jump in the velocity, and others. To calculate the pulse shape, the creep kernels for the three main types of relaxation in fluids are found: Kneser relaxation, resonance relaxation, and relaxation associated with diffusive transfer. The shape of the pulse (initially square) near the front is calculated for these types of relaxation.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 153–160, September–October, 1986.The authors are sincerely grateful to V. A. Borovikov for his valuable comments in the discussion of the present paper.     

泡沫铝泡孔动态变形特性研究

在SHPB实验中采用应变冻结法将试件冻结于设定的压缩应变,然后观察内部泡孔的变形情况并讨论其变形机理。分别对同一相对密度(40%)、不同基体材料的两种泡沫铝以及两种相对密度(19%和8%)、相同基体材料的泡沫铝进行实验,讨论了基体材料的本构关系、泡沫的相对密度对变形模式的影响。利用ANSYS/LS DYNA软件对泡沫铝在动态压缩时泡孔的变形进行数值模拟计算,进一步说明泡沫铝泡孔变形的模式与基体材料本构关系及相对密度的关系。     

Relaxation behavior and modeling

Load relaxation tests deliver several orders of magnitude of inelastic strain rate data while elastic strains are converted into inelastic strains [see Lemaitre and Chaboche, 1994. (Mechanics of Solid Materials, Oxford University Press, Cambridge p. 264)]. Hart used this test for providing information on the inelastic deformation behavior for modeling purposes. Characteristic relaxation curves were obtained with ductile metals and alloys at room and high temperature showing a scaling relation derived from Hart's theory. Subsequent testing with servo-controlled testing machines and strain measurement on the gage length showed that an increase of prior strain rate also increased the average relaxation rate. For relaxation tests starting in the flow stress region, the relaxation curves can be independent of the stress and strain at the start of the relaxation tests. For the modeling of these newly found relaxation behaviors and other phenomena the viscoplasticity theory based on overstress (VBO) has been introduced. It is shown that VBO admits a long-term (asymptotic) solution that can be used with sufficient accuracy for the flow stress region of the stress–strain diagram. The long-term solution predicts the observed relaxation behaviors and that the relaxation curves coincide when shifted along the stress axis. This behavior is observed for the recently obtained data and is confirmed by two sets of the Hart-type data when they are plotted according to the new method.     

Formation of shock waves in gas-liquid foams

The purpose of the present investigation is to analyze the phenomenon of shock wave formation in gas-liquid foams and to explain the qualitative differences which are found when comparing results from shock tube experiments performed with foams and bubbly liquids. It is well known that oscillatory pressure waves in bubbly liquids may reach an amplitude twice as large as that of the original pressure impulse. However, experiments showed that pressure disturbances in foams always attenuate without significant change in the wave pressure profile. In the present study this behavior is explained by analyzing shock wave formation using the Burgers equation which is derived from the conservation laws for a bubbly liquid. It is shown that the parameter of non linearity in the Burgers equation describing wave propagation in bubbly liquids is about 40 times higher than in foams. At the same time coefficient of bulk viscosity of a foam is about 10³ times greater than that of a bubbly liquid. This explains why in shock tube experiments with foams shock waves are not detected while they are easily observed when bubbly liquids are used under similar conditions.