Viscoelastic Response of PMMA due to Lateral Impact

Abstract

Viscoelastic constants of PMMA under dynamic load have been determined in the past with several methods based on the theories of longitudinal vibration, lateral vibration and longitudinal wave propagation. In this paper, the values of these constants used in the 3-elements linear viscoelastic solid model were employed to make the numerical prediction of impact response of PMMA.
The theoretical results were obtained by using the one-dimensional longitudinal viscoelastic wave propagation theory and Bernoulli-Euler theory for viscoelastic beam. The impact load history was calculated numerically by using the nonlinear integral equation derived from the Hertz theory of contact. The time histories of strains and deflection were obtained from the numerical values of impact load. The strains on a rod and a beam were measured with strain gauges, and the deflection of a beam was obtained from the output of an optical follower measured in a short period after lateral impact of a rod on a beam.
The theoretical predictions were in good agreement with the experimental results. It was shown that the time history of strain on a rod was more sensitive to viscoelastic constants than that on a beam or the deflection history of a beam, and the short time response of deflection of a beam after impact was scarcely affected by viscoelastic constants. This should be a useful knowledge when the method for determining viscoelastic constants is evaluated.