Estimation of dynamic paramaters for viscoelastic materials by longitudinal vibration testing using pulse method
In this paper, two methods based on longitudinal vibration testing of a thin bar are proposed for measuring the dynamic parameters of the viscoelastic materials in a wide frequency region. First, an inverse method by FEM based on resonance measurement is presented, in which the measured response of longitudinal vibration is asymptotically approached by the forward calculated response from the finite element computation, then the dynamic parameters can be obtained. Second, an improved wave propagation measurements based on free end longitudinal vibration signal is described. In which the dynamic parameters in the frequency range of 1kHz to 5kHz are calculated from the vibration velocity ratio between the long bar and the short bar.
Determination of the dynamic elastic moduli and internal friction using thin resonant bars
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.
Frequency response of a photo-viscoelastic material
AbstractAn electromagnetic shaker was used to apply sinusoidal axial displacements to one end of a column of Hysol 4364, an optically sensitive urethane rubber compound of low modulus. The nondriven end of the column was free. The column was excited at frequencies of 81, 244, 424, 603 and 783 cps, corresponding to the first five resonant frequencies of longitudinal vibration. Measurements were made of displacement mode shapes and phase angles, and birefringence modes and phase angles. Measured displacement modes and phase angles were shown to agree with predictions based on a linear one-dimensional viscoelastic theory. The measurements and theory were used to determine the mechanical and optical frequency response of the material for the experimental frequencies. This consisted of determining:1.the dynamic elastic modulus,2.the phase angle between stress and strain,3.the dynamic stress-optic coefficient, and4.the phase angle between stress and birefringence.
The elastic modulus increased continuously from the static value of 318 psi to 576 psi at 783 cps. The stress-strain phase angle increased from 9.3 deg at 81 cps to 11.9 deg at 783 cps.The stress-optic coefficient was essentially constant over the frequency range and equal to the static tension value, 1.03 psi/fringe/in. The stress-fringe phase angle appeared to be greater than the stress-strain phase angle by a constant 4 deg ±2 deg which indicated that birefringence lagged both stress and strain for this material.