Measured and finite element simulated frequency response functions are used to characterize the low strain (∼10−7) complex moduli of an asphalt concrete specimen. The frequency response functions of the specimen are measured at different temperatures by using an instrumented hammer to apply a load and an accelerometer to measure the dynamic response. Theoretical frequency response functions are determined by modeling the specimen as a three-dimensional (3D) linear isotropic viscoelastic material in a finite element program. The complex moduli are characterized by optimizing the theoretical frequency response functions against the measured ones. The method is shown to provide a good fit between the frequency response functions, giving an estimation of the complex modulus between minimum 500 Hz and maximum 18|000 Hz depending on the temperature. Furthermore, the optimization method is shown to give a good estimation of the complex modulus master curve.

Characterizing the low strain complex modulus of asphalt concrete specimens through optimization of frequency response functions.

Evaluation of the dynamic properties of PVC foams under flexural vibrations

A new system to determine experimentally the complex Young's modulus of highly compliant elastomers at elevated hydrostatic pressures and as a function of temperature is presented. A sample cut in the shape of a bar is adhered to a piezoelectric ceramic shaker and mounted vertically inside a pressure vessel equipped with glass windows. Two independent measurement methods are then used: a resonant technique, to obtain low-frequency data, and a wave propagation technique, to obtain higher-frequency data. Both techniques are implemented utilizing laser Doppler vibrometers. One vibrometer detects sample resonances through a window located at the bottom of the pressure vessel, and a set of two separate vibrometers monitors the speed of longitudinal waves propagating in the sample, through windows located on the sides of the vessel. The apparatus is contained inside an environmental chamber for temperature control. Using this approach, Young's modulus data can be obtained at frequencies typically ranging from 100 Hz to 5 kHz, under hydrostatic pressures ranging from 0 to 2.07 MPa (300 psi), and at temperatures between -2 degrees C and 50 degrees C. Experimental results obtained on two commercial materials, Rubatex R451N and Goodrich Thorodin AQ21, are presented. The effects of lateral inertia, resulting in dispersive wave propagation, are discussed and their impacts on Young's modulus measurements are examined.

A dynamic Young's modulus measurement system for highly compliant polymers.

Complete elastic characterization of viscoelastic materials by dynamic measurements of the complex bulk and Young's moduli as a function of temperature and hydrostatic pressure

Methods for estimation of the complex modulus generally produce data from which discrete results can be obtained for a set of frequencies. As these results are normally afflicted by noise, they are not necessarily consistent with the principle of causality and requirements of thermodynamics. A method is established for noise-corrected estimation of the complex modulus, subject to the constraints of causality, positivity of dissipation rate and reality of relaxation function, given a finite set of angular frequencies and corresponding complex moduli obtained experimentally. Noise reduction is achieved by requiring that two self-adjoint matrices formed from the experimental data should be positive semidefinite. The method provides a rheological model that corresponds to a specific configuration of springs and dashpots. The poles of the complex modulus on the positive imaginary frequency axis are determined by a subset of parameters obtained as the common positive zeros of certain rational functions, while the remaining parameters are obtained from a least squares fit. If the set of experimental data is sufficiently large, the level of refinement of the rheological model is in accordance with the material behavior and the quality of the experimental data. The method was applied to an impact test with a Nylon bar specimen. In this case, data at the 29 lowest resonance frequencies resulted in a rheological model with 14 parameters. The method has added improvements to the identification of rheological models as follows: (1) Noise reduction is fully integrated. (2) A rheological model is provided with a number of elements in accordance with the complexity of the material behavior and the quality of the experimental data. (3) Parameters determining poles of the complex modulus are obtained without use of a least squares fit.

/pdf/noise-corrected-estimation-of-complex-modulus-in-accord-with-180yr95los.pdf

Noise-Corrected Estimation of Complex Modulus in Accord With Causality and Thermodynamics: Application to an Impact Test

CYP81A68 confers metabolic resistance to ALS and ACCase-inhibiting herbicides and its epigenetic regulation in Echinochloa crus-galli.

Analysis of the data from the resonant-bar technique for determining wave speed and internal friction is presented. Internal friction has been included in the longitudinal and torsional wave equations and the analytical solution has been obtained. In determining the acoustical constants of lossy materials, a broad frequency spectrum is used that includes many resonances and not just data at or near the individual resonances. Corrections due to the mass, length, stiffness, and damping of the transducers are also presented. The theoretical solutions are compared with the measured magnitude and phase response data for torsional, longitudinal, and flexural measurements and are shown to be in good agreement.

Determination of the dynamic elastic moduli and internal friction using thin resonant bars

Forced vibration mechanism and suppression method for thin-walled workpiece milling

The flexural wave equation including internal friction and the correction due to rotatory inertia and shear deflection for thin bars is solved. The system response of the forced‐free bar excited in flexural vibrations is obtained. Corrections for rotatory inertia and shear deflection have to be included for a best fit. The numerical factor representing the correction effect of shear deflection is smaller than previous results which means that shear deflection has a greater correction contribution than previously thought. At low‐frequency range, the Young’s modulus obtained from flexural modes is different from that from longitudinal modes. This may suggest that more correction effects need to be included for the flexural system. [Work supported by the Ph.D. Program and the Strategic Environtechnology Partnership (STEP) through the Advanced Technology Center at the University of Massachusetts Dartmouth.]

Determination of Young’s modulus and internal friction coefficient from flexural wave in thin bars

The use of resonant free–free bars to determine the elastic properties of materials has been presented previously [Garrett, ‘‘Resonant acoustic determination of elastic moduli,’’ J. Acoust. Soc. Am. 88, 210–221; Brown, ‘‘Characterization of viscoelastic materials using the resonant modes of a ‘free–free’ bar,’’ J. Acoust. Soc. Am. 94, 2294(A) (1993)]. The preferred excitation and detection method is based on electrodynamic transduction in which a coil of wire is attached to each bar end, which in turn is subjected to a strong magnetic field. The effect of the added transducer mass on the observed resonant frequency and quality factors of longitudinally driven bars used to determine Young’s modulus and damping will be reported. [Work supported by the University of Massachusetts Dartmouth.]

Qiushuang Guo

Papers

CYP81A68 confers metabolic resistance to ALS and ACCase-inhibiting herbicides and its epigenetic regulation in Echinochloa crus-galli.

Determination of the dynamic elastic moduli and internal friction using thin resonant bars

Forced vibration mechanism and suppression method for thin-walled workpiece milling

Determination of Young’s modulus and internal friction coefficient from flexural wave in thin bars

Effects of transducer mass on resonance frequency and quality factor of free–free bars