Frequency Dependence Of Modulus Research Articles

The interpretation of dynamic measurements on non-linear viscoelastic materials

A method is proposed for characterizing the dynamic mechanical behaviour of non-linear viscoelastic materials in terms of two frequency dependent moduli and two functions of the strain amplitude. These rheological parameters represent material properties and are shown to be independent of the sample dimensions. A method for determining the strain dependent functions from observations of the force and corresponding displacement on a sample is described. The method can be used even when the strain is not uniform throughout the sample. As an example of the use of this method a single pair of functions, defining the dependence of the storage and loss moduli on strain amplitude, have been obtained for a sample of a non-linear viscoelastic material sheared longitudinally between concentric cylinders. These functions are consistent with all the experimental data obtained over a wide range of ratio of cylinder diameters and a wide range of displacement amplitudes.

Time-Dependent Response in the Flow Between Eccentric Rotating Disks

The stress-growth phenomenon in the eccentric rotating disk (ERD) geometry is analyzed using a linearized Bird-Carreau integral model. Good agreement is found between experimental observations and predicted responses for a low-density polyethylene melt. Transient stress response is reported as time- and frequency-dependent moduli. In start-up, the approach of the viscous and elastic stresses to their steady-state values at angular velocity Ω is found to be directly related to the decay of the storage modulus in stress relaxation after steady rotation.

Stimulated Brillouin Scattering: Effect of Sound Absorption on Hypersonic Velocity Measurements

The frequency spectrum of a sound wave generated by photon-phonon interactions is that of a damped harmonic oscillator with the shifted peak sharpened but not displaced by nonlinear amplification. Hence, the frequency of this line must differ from that given by the Mandelstam-Brillouin formula. The correction formula is given for a general case of a dispersive viscoelastic medium in terms of the frequency-dependent modulus and viscosity.

Calculation of the Complex Modulus of Linear Viscoelastic Materials from Vibrating Reed Measurements

Two methods of determining the variation of real and complex modulus with frequency from vibrating reed test results are detailed. One is based on measurements of the relative amplitude and phase lag of the motion of the free and driven ends of the reed, the other on amplitude resonance measurements only. The analysis is based on a general linear viscoelastic law, and takes into account the influence of the frequency dependent moduli of the material on the frequency and amplitude of the resonance peaks. This influence has not been correctly accounted for in previous analyses which have included the assumption that the material behaves according to a particular, simple viscoelastic law, which will in general not be borne out by the final results. The method is applied to a series of tests. For the material and frequency range used the imaginary part of the complex modulus was small compared with the real part, and the influence mentioned in the foregoing was small. A simpler method of analysis might thus be justified, but in other cases it will be necessary to carry out the complete analysis in order to obtain a satisfactory interpretation of test results.