Frequency-dependent Elastic Modulus Research Articles

Effect of multi-layered IIR/EP on noise reduction of aluminium extrusions for high-speed trains

Damping treatment is effective for noise and vibration control. However, there is a lack of research on the relationship between the fabrication and mechanical property characterisation of damping materials and the vibroacoustic characteristic analysis after damping materials are applied to actual composite structures. We performed such a study. First, modified butyl rubber (IIR) with high damping performance was prepared, and its frequency-dependent elastic modulus and loss factor were identified. Second, the vibration and damping characteristics of the modified IIR used in multi-layered constrained-layer damping (MLCLD) were investigated via cantilever-beam experiments and simulations. Third, the noise reduction (both sound radiation and sound insulation) effects of the MLCLD on aluminium extrusions were examined using prediction models, which were validated according to acoustic laboratory tests. The results indicated that the structural vibroacoustic characteristics are affected by not only the number of layers but also the application objects, structural parameters, and material properties. The final lightweight optimisation design of the aluminium extrusion using the MLCLD reduced the radiated sound power level by 2.7 dB, improved the sound insulation level by 3.0 dB, and reduced the total mass by 14.4%.

Investigating propensity of roller spatter during application of water-based architectural paints: effect of thickeners and volume solids

During roll coating application of water-based architectural paints, fibers are formed between roller and substrate. These fibers progressively thin and break up into several tiny droplets leading to the wastage of paints. This defect is widely known as spattering. In the current study, the propensity to spatter in fully formulated mid pigment volume concentration water-based architectural paints based on varying the type of thickeners, namely a combination of cellulosic with clay, cellulosic, and hydrophobically modified poly acetal/ketal polyether (HMPAPE), at similar and varying volume solids is investigated. The spatter tendency of paint is qualitatively assessed using ASTM D4707. Also, a new approach to quantify the spread area of spattered droplets is developed by thresholding-based image segmentation using an image processing toolbox of Mathematica. This newly developed quantitative approach will greatly help the formulator to better differentiate between formulations. Rheological tests, namely viscosity curve, amplitude sweep, frequency sweep, and first normal stress difference test, are carried out to unravel the flow and viscoelastic properties of paints in depth. An in-house custom-built fiber drawing device on a contact angle drop shape analyzer instrument is fabricated to study the extensional properties of paints. At the same volume solids, the paint based on a combination of cellulosic with clay thickener spatters the most, while the paint based on HMPAPE thickener spatters the least. This is mainly attributed to the chemistry, molecular weight, and thickening mechanism of thickeners. Eventually, a reliable correlation is established between observed spatter and the frequency-dependent elastic modulus outside the linear viscoelastic range at the same and varying solids for paints based on the different types of thickener. This correlation will help chemists to quickly screen formulations to minimize the spattering during roll coat application, thus saving time, cost, and manpower.

Investigation of the Elastic Modulus of Polymer Sleepers Under a Quasistatic and Cyclic Loading

Abstract In ballasted track, the wheel load is transmitted to the subgrade via sleepers commonly made of impregnated wood, prestressed concrete, steel or recently developed polymer sleepers. Mentioned material types of sleepers are characterized by different elastic moduli being a key parameter in any numerical model. Hence, this paper aims to determine the elastic modulus of sleepers subjected to a laboratory four-point bending test. Traffic resembling load level of 60 kN adopted from a typical axle load distributed by the rails to the sleeper was applied in a quasistatic and cyclic loading. The samples included sleepers made of polymers complemented with wood and pre-stressed concrete. The results of this paper are based on the elastic modulus investigation. Main conclusions are focused on the sleeper’s elastic modulus under changing loading frequencies. Wood and prestressed concrete sleepers indicated mainly elastic behaviour resulting in a constant elastic modulus. However, polymer sleepers showed a loading frequency dependent elastic modulus as a result of their viscous elastic behaviour. Moreover, the conclusions of this paper involve E-modulus measurements of impregnated beech sleepers in order to describe their piece by piece elasticity variation due to their natural origin.

Modeling and experimental verification of an ultra-wide bandgap in 3D phononic crystal

This paper reports a comprehensive modeling and experimental characterization of a three-dimensional phononic crystal composed of a single material, endowed with an ultra-wide complete bandgap. The phononic band structure shows a gap-mid gap ratio of 132% that is by far the greatest full 3D bandgap in literature for any kind of phononic crystals. A prototype of the finite crystal structure has been manufactured in polyamide by means of additive manufacturing technology and tested to assess the transmission spectrum of the crystal. The transmission spectrum has been numerically calculated taking into account a frequency-dependent elastic modulus and a Rayleigh model for damping. The measured and numerical transmission spectra are in good agreement and present up to 75 dB of attenuation for a three-layer crystal.

Modeling the high-frequency complex modulus of silicone rubber using standing Lamb waves and an inverse finite element method.

To gain an understanding of the high-frequency elastic properties of silicone rubber, a finite element model of a cylindrical piezoelectric element, in contact with a silicone rubber disk, was constructed. The frequency-dependent elastic modulus of the silicone rubber was modeled by a fourparameter fractional derivative viscoelastic model in the 100 to 250 kHz frequency range. The calculations were carried out in the range of the first radial resonance frequency of the sensor. At the resonance, the hyperelastic effect of the silicone rubber was modeled by a hyperelastic compensating function. The calculated response was matched to the measured response by using the transitional peaks in the impedance spectrum that originates from the switching of standing Lamb wave modes in the silicone rubber. To validate the results, the impedance responses of three 5-mm-thick silicone rubber disks, with different radial lengths, were measured. The calculated and measured transitional frequencies have been compared in detail. The comparison showed very good agreement, with average relative differences of 0.7%, 0.6%, and 0.7% for the silicone rubber samples with radial lengths of 38.0, 21.4, and 11.0 mm, respectively. The average complex elastic moduli of the samples were (0.97 + 0.009i) GPa at 100 kHz and (0.97 + 0.005i) GPa at 250 kHz.

Parametric identification of elastic modulus of polymeric material in laminated glasses

This paper addresses an inverse approach to characterize the frequency-dependent elastic modulus of the polymer layer in laminated structures. Represented by fractional derivative models, the modulus is identified based on a finite element model of the laminated structure from the experimental frequency response functions. An efficient Markov Chain Monte Carlo method is implemented to learn the identification parameters from a Bayesian perspective. A surrogate model is applied to alleviate Bayesian computation through the use of artificial neutral network. The proposed approach is experimentally validated on a laminated glass.

Viscoelastic characterization of a new guar gum derivative containing anionic carboxymethyl and cationic 2-hydroxy-3-(trimethylammonio)propyl substituents

A new guar gum derivative (CMHTPG) containing anionic carboxymethyl and cationic 2-hydroxy-3-(trimethylammonio)propyl substituents was characterized with the help of a stress-controlled rheometer for its linear viscoelastic behavior in aqueous systems. The frequency-dependent elastic modulus ( G′) and viscous modulus ( G″) curves for 0.5, 1.0, 1.5 and 2.0 g/dl of aqueous CMHTPG solutions were found to cross at a given frequency. The crossover frequency value decreased with the increase of CMHTPG concentration. At 25 °C, the longest relaxation time was obtained to be 5.556 s for aqueous 2.0% CMHTPG solution while the shortest relaxation time to be 0.027 s for aqueous 0.5% CMHTPG solution, showing a strong concentration dependence on the viscoelastic properties. Moreover, the complex viscosity ( η*) of aqueous CMHTPG solution was found to increase with the increase of CMHTPG concentration, and to decrease with the increase of frequency. By investigating the viscoelastic properties of aqueous CMHTPG salt solutions containing various concentrations of NaCl, it was observed that the addition of NaCl could lead to a slight increase in the G′ , G″ or η* value. Temperature was confirmed to have an important influence on the viscoelastic properties of aqueous CMHTPG solution. For aqueous 1.0% CMHTPG solution, the activation energy reflecting the temperature sensitivity of the complex viscosity was determined at the frequency of 1.0 rad/s and found to be 16.94 kJ/mol.

Higher-order rod approximations for the propagation of longitudinal stress waves in elastic bars

The elementary one-dimensional wave theory is often used to describe the propagation of longitudinal stress waves along a slender bar. However, for relatively large diameter bars and high-frequency waves, geometrical wave dispersion due to lateral inertia occurs, rendering this single-mode theory inaccurate. In this paper, an approximate four-mode rod equation for a circular bar that takes wave dispersion into account is presented. Little difference is observed between the dispersion curves of the four-mode equation and the Pochhammer–Chree equation that gives the exact propagation coefficient for an infinite circular bar. The advantage of the former is that its solution can be computed directly whereas the latter requires an iterative procedure. Also presented are different orders of rod approximation equations derived from the Pochhammer equation, each of which can also be solved directly. Applications of the more accurate rod equations include correcting for wave dispersion in a split Hopkinson pressure bar (SHPB) test, and more accurately determining the frequency-dependent elastic modulus of a viscoelastic bar from an experimentally measured propagation coefficient.

Measurement of young's modulus via modal analysis experiments: a system identification approach

The stress-strain relationship of linear visco-elastic materials is characterized by a complex-valued, frequency dependent elastic modulus E(jω) (Young's modulus). Using system identification techniques it is shown in this paper how E(jω) can be measured accurately in a broad frequency band from forced f1exural (transverse) and longitudinal vibration experiments on a beam under free-free boundary conditions. The advantages of the proposed method are (i) it takes into account the disturbing noise and the non linear distortions, (ii) E(jω) is delivered with an uncertainty bound, (iii) the low sensitivity to non-idealities of the experimental set up, and (iv) the ability to measure lowly damped materials. The approach is illustrated on plexiglass and copper.

Identification of Young's modulus from broadband modal analysis experiments

The stress–strain relationship of linear viscoelastic materials is characterised by a complex-valued, frequency-dependent elastic modulus E( jω) (Young's modulus). Using system identification techniques it is shown in this paper how E( jω) can be measured accurately in a broad frequency band from forced flexural (transverse) and longitudinal vibration experiments on a beam under free–free boundary conditions. The advantages of the proposed method are (i) it takes into account the disturbing noise and the non-linear distortions, (ii) E( jω) is delivered with an uncertainty bound, (iii) the low sensitivity to non-idealities of the experimental set-up, and (iv) the ability to measure lowly damped materials. The approach is illustrated on brass, copper, plexiglass and PVC beams.

Viscoelasticity of dilute solutions of semiflexible polymers

We show using Brownian dynamics simulations and theory how the shear relaxation modulus G(t) of dilute solutions of relatively stiff semiflexible polymers differs qualitatively from that of rigid rods. For chains shorter than their persistence length, G(t) exhibits three time regimes: At very early times, when the longitudinal deformation is affine, G(t) approximately t(-3/4). Over a broad intermediate regime, during which the chain length relaxes, G(t) approximately t(-5/4). At long times, G(t) mimics that of rigid rods. A model of the polymer as an effectively extensible rod with a frequency dependent elastic modulus B(omega) approximately ((i)omega)(3/4) quantitatively describes G(t) throughout the first two regimes.

The liquid–glass transition in LiCl/H2O: Impulsive stimulated light scattering experiments and mode-coupling analysis

Impulsive stimulated light scattering (ISS) experiments have been conducted on aqueous LiCl solutions to characterize the structural relaxation dynamics at temperatures above, near and below the glass transition temperature Tg. The data provide acoustic velocities, attenuation and thermal diffusion rates over wide ranges of temperature and wave vector. At temperatures in the glass transition region, the dynamics of thermal expansion and subsequent contraction (not due to thermal diffusion) are observed as well. The acoustic information from ISS as well as from earlier Brillouin scattering results is used to determine the frequency-dependent elastic modulus in the MHz–GHz range. Analysis in terms of an empirical (stretched exponential) relaxation function is carried out and shown to be inadequate. The main analysis is inspired by predictions of mode-coupling theory concerning susceptibility spectra. Simple scaling for the α-peak and identical power law dependencies on frequency for both electrical and mechanical moduli, as predicted by theory, were confirmed.