Parametric amplification effects in acoustical test facilities

In acoustical test facilities, elastic structures like satellites are exposed to noise excitations in order to detect those parts with a significant risk of failure. Statistically representative test signals are generated from white noise by means of a spectrum shaper. Subsequently, these electrical signals are amplified and transformed into an acoustical reverberant pressure field in the sound chamber. The transformation is due to a parametric amplification effect in the control space of the horns which modulates the signals in the form of a parametrically excited system. In a sense, the Monte Carlo method of non-linear stochastic mechanics is implemented in the laboratory. The paper presents a finite element model of the compressible gas medium in the horn and in the sound chamber. It derives mean values, variances and power spectra of the stationary velocity fluctuations of the flowing gas medium.     

Numerical investigation of the aerodynamic and acoustical properties of a shrouded rotor

The problem of shrouded rotor rotation is numerically solved basing on the Navier–Stokes equations in a noninertial coordinate system. The configuration considered is a model helicopter tail rotor.The calculations are performed using edge-based reconstruction (EBR) schemes on unstructured tetrahedral grids with the variables determined at gridpoints. The numerical results on the aerodynamic forces and the acoustic radiation intensity and direction in the far field are presented and analyzed.     

On the effects of dilute polymers on driven cavity turbulent flows

Effects of dilute polymer solutions on a lid-driven cubical cavity turbulent flow are studied via particle image velocimetry (PIV). This canonical flow is a combination of a bounded shear flow, driven at constant velocity and vortices that change their spatial distribution as a function of the lid velocity. From the two-dimensional PIV data we estimate the time averaged spatial fields of key turbulent quantities. We evaluate a component of the vorticity–velocity correlation, namely 〈ω₃v〉, which shows much weaker correlation, along with the reduced correlation of the fluctuating velocity components, u and v. There are two contributions to the reduced turbulent kinetic energy production −〈u v〉S_uv, namely the reduced Reynolds stresses, −〈u v〉, and strongly modified pointwise correlation of the Reynolds stress and the mean rate-of-strain field, S_uv. The Reynolds stresses are shown to be affected because of the derivatives of the Reynolds stresses, ∂〈u v〉/∂y that are strongly reduced in the same regions as the vorticity–velocity correlation. The results, combined with the existing evidence, support the phenomenological model of polymer effects propagating from the polymer scale to the velocity derivatives and through the mixed-type correlations and Reynolds stress derivatives up to the turbulent velocity fields. The effects are shown to be qualitatively similar in different flows regardless of forcing type, homogeneity or presence of liquid–solid boundaries.     

The effect of dissolved polymers on the rheological properties of coating colours

Coating colours used for the coating of paper and board consist mainly of a mineral pigment, which is very often clay, a synthetic binder such as a styrenebutadiene latex, dispersion agents and water retention aids. The latter are often water soluble polymers. These polymers have a very strong influence on the rheological properties of the coating colours, both on the strain rate dependence of the apparent viscosity and on the viscoelasticity. The effects of two different grades of carboxymethylcellulose (CMC) and one grade of hydroxyethylcellulose (HEC), on the rheological properties at room temperature of a clay-based coating colour at pH 8, have been investigated. It is concluded that the high values of the dynamic modulus of the colours are due to interactions between the cellulose derivatives and the solid particles, i.e. mainly the clay particles. For HEC this interaction is associated with adsorption of the polymeric molecules on the clay particles. In the case of CMC, the adsorption is strongly retarded by the presence of the dispersant (a polyacrylate salt). It is suggested that the marked elasticity of the CMC-containing colour in addition to a possible polymer adsorption may be due to charge interactions and/or depletion flocculation. The effect of CMC and HEC on the water-retention properties of the colour is also discussed.     

Rheological properties of binary associating polymers

Dynamics of associating polymer solutions above the reversible gelation point are studied. Each macromolecule consists of a soluble backbone (B) and a small fraction of specific strongly interacting groups (A or C stickers) attached to B. A mixture of B–A and B–C associating polymers with 1:1 stoichiometric ratio is considered. As a result of AC association, the polymers reversibly gelate above the overlap concentration. It is shown that (1) the network strands are linear complexes (double chains) of B–A and B–C; (2) “diffusion” of the network junction points is characterized by an apparent activation energy, which can be significantly higher than the energy of one AC bond; (3) most importantly, the randomness of sticker distribution along the chain can significantly slow down the network relaxation leading to a markedly non-Maxwellian viscoelastic behavior. The theory elucidates the most essential features of rheological behavior of polysaccharide associating systems (with A = adamantyl moiety, C = β-cyclodextrin, B = either chitosan or hyaluronan) including similar behavior of G ^′ and G ^″ in a wide frequency range, strong temperature dependence of the characteristic frequency ω _x , and an extremely strong effect of added free stickers (fC) on the dynamics. This paper was presented at Annual European Rheology Conference (AERC) held in Hersonisos, Crete, Greece, April 27–29, 2006.     

Strain-coupling effects in branched polymers

The applicability of a strain-coupling integral constitutive equation to the analysis of the nonlinear viscoelasticity of branched polymers is evaluated. A simpler and more efficient method is proposed for evaluating the material functions of the strain-coupling constitutive equation.     

The effect of molecular weight distribution on the elongational properties of linear polymers

The elongational properties of a series of six polypropylene and two polystyrene samples have been studied at constant rate of strain. A Wagner-type constitutive equation has been used to fit the experimental data, and the shape of the damping function has been correlated with the polydispersity index of the samples. As the memory function or relaxation function of linear viscoelasticity may be derived from the molecular-weight distribution using either molecular or phenomenological models, it is therefore possible to calculate the stress growth function of a linear polymer in elongation from its molecular-weight distribution.     

Optical and mechanical properties of birefringent polymers

The stress-strain behavior and corresponding birefringence of several polymers have been investigated within a limited range of temperatures (from ?65 to 70°F) and strain rates (from 0.0027 to 0.1613 sec^?1). One of these materials, a polyethylene resin, has been studied in more detail to ascertain the existence of a simple relationship between stress history, temperature, strain rate and birefringence. When the results were compared with the photoviscoelastic relations developed by E. H. Dill for a simple rheological material, it was concluded that the polyethylene tested does not completely satisfy this model. Polyethylene as well as the other materials investigated—nylon, a polyester, cellulose acetate butyrate, cellulose nitrate—exhibits a linear relation between birefringence and strain, independent of rate within the limits of the present experimental range.     

A review of the rheo-optical properties of linear high polymers

Some principles ans laws, expressing the mechanical and optical behavior of linear viscoelastic materials, are reviewed. The mechanical properties of the polymers in the transition region may be represented by a condensed general method containing Ferry's modulus or compliance-reduction scheme, the time-temperature superposition principle and the Gauss error integral representation. The optical behavior of high polymers is expressed by the stress- and strain-optical coefficients in creep or relaxation, which relate birefringence to stresses or strains. It was recently shown experimentally that, instead of a pair of independent linear differential operator relations, which characterize the mechanical properties of the viscoelastic materials, only one operator relation is needed and the initial value of another at the glassy or rubbery state. Then, a single test is sufficient for the complete determination of the mechanical and optical viscoelastic behavior, provided the value of another elastic constant at the glassy or rubbery state is also determined and the variation of birefringence with time is simultaneously measured with the mechanical-characteristic quantities of the material.     

Non-local elastic effects in electroactive polymers

In this work we study the onset of inhomogeneous deformations in thin electroactive polymers (EAPs) under voltage control. In order to account for the regularizing effects due to both the constitutive nature of the film and to its mechanical interaction with the compliant electrodes, we introduce a non-local energy term depending on the second gradient of deformation. We prove that very small non-local effects are sufficient to find realistic inhomogeneous deformations at the onset of the bifurcation, which are characterized by periodic thickness undulations with finite wavelength. Finally we prove that strong regularizing effects can suppress the onset of inhomogeneous deformations.     

Length-scale effects on damage development in tensile loading of glass-sphere filled epoxy

Particle-reinforced polymers are widely used in load-carrying applications. The effect of particle size on damage development in the polymer is still relatively unexplored. In this study, the effect of glass-sphere size on the damage development in tensile loaded epoxy has been investigated. The diameter of the glass spheres ranged from approximately 0.5–50 μm. The first type of damage observed was debonding at the sphere poles, which subsequently grew along the interface between the glass spheres and epoxy matrix. These cracks were observed to kink out into the matrix in the radial direction perpendicular to the applied load. The debonding stresses increased with decreasing sphere diameter, whereas the length to diameter ratio of the resulting matrix cracks increased with increasing sphere diameter. These effects could not be explained by elastic stress analysis and linear-elastic fracture mechanics. Possible explanations are that a thin interphase shell may form in the epoxy close to the glass spheres, and that there is a length-scale effect in the yield process which depends on the strain gradients. Cohesive fracture processes can contribute to the influence of sphere size on matrix-crack length. Better knowledge on these underlying size-dependent mechanisms that control damage development in polymers and polymer composites is useful in development of stronger materials. From a methodology point of view, the glass-sphere composite test can be used as an alternative technique (although still in a qualitative way) to hardness vs. indentation depth to quantify length-scale effects in inelastic deformation of polymers.     

Influence of interphase and filler distribution on the elastic properties of nanoparticle filled polymers

The present work presents a preliminary study on the effect of the filler distribution on the elastic modulus of a nanoparticle filled polymer. To this end, two different theoretical approaches are implemented and compared. Both of them account for an interphase layer embedding the nanoparticle, with mechanical properties different from those of the matrix. Conversely, only one of them accounts for the variation of the interparticle distance. The comparison between these models allows to draw some conclusions on the effect of the filler distribution.     

Pressure of an arbitrary acoustical wave on a plane

A study is made of the perturbed flow of a gas, brought about by a weak shock wave, falling on a fixed surface at an arbitrary angle. A solution determining the field of the velocities behind the front of the wave in an initially boundary-value problem with movable boundaries for a three-dimensional wave equation is obtained in the form of a double integral, containing an arbitrarily given function determining the parameters of the gas in the incident wave. The region of integration is a region included within an ellipse, whose relative eccentricity is equal to the sine of the angle of inclination of the front of the incident wave. A formula is obtained for the distribution of the pressure at the plane.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 114–116, January–February, 1975.     

A thermodynamic approach to model the caloric properties of semicrystalline polymers

It is well known that the crystallisation and melting behaviour of semicrystalline polymers depends in a pronounced manner on the temperature history. If the polymer is in the liquid state above the melting point, and the temperature is reduced to a level below the glass transition, the final degree of crystallinity, the amount of the rigid amorphous phase and the configurational state of the mobile amorphous phase strongly depend on the cooling rate. If the temperature is increased afterwards, the extents of cold crystallisation and melting are functions of the heating rate. Since crystalline and amorphous phases exhibit different densities, the specific volume depends also on the temperature history. In this article, a thermodynamically based phenomenological approach is developed which allows for the constitutive representation of these phenomena in the time domain. The degree of crystallinity and the configuration of the amorphous phase are represented by two internal state variables whose evolution equations are formulated under consideration of the second law of thermodynamics. The model for the specific Gibbs free energy takes the chemical potentials of the different phases and the mixture entropy into account. For simplification, it is assumed that the amount of the rigid amorphous phase is proportional to the degree of crystallinity. An essential outcome of the model is an equation in closed form for the equilibrium degree of crystallinity in dependence on pressure and temperature. Numerical simulations demonstrate that the process dependences of crystallisation and melting under consideration of the glass transition are represented.