Theoretical and Experimental Studies of Wave Propagation in Viscoelastic Materials

Author: Arenz, Robert James

Year: 1964

Degree: Dissertation (Ph.D.)

Advisor: Williams, Max L.

Committee Member: Unknown, Unknown

Option: Aeronautics

DOI: 10.7907/E8KM-6M98

Abstract

The phenomenon of wave propagation in viscoelastic materials is investigated both theoretically and experimentally, with attention directed to two areas. First, analytical methods of solution are developed for certain wave propagation problems in one and two dimensions utilizing realistic material properties. This is accomplished by use of time-dependent material property characterization through a Dirichlet series representation to overcome the limitations of the widely-used simple spring and dashpot models involving two or three elements. The Laplace transformed solutions are then inverted by an extension of the Schapery collocation method to dynamic situations. The second topic deals with dynamic photoelasticity applied to viscoelastic materials. It is shown that the relationships between stress optic and strain optic coefficients for linearly viscoelastic materials can be formulated. Then the time-dependent birefringence characteristics of a typical low modulus polymer material are determined from constant strain rate tests for a full range of dynamic loading rates by taking advantage of the time-temperature shift phenomenon. Much recent work in dynamic photoviscoelasticity has been based on static calibrations only. Hence to put the technique on a firm foundation and indicate the general necessity of including the time dependency in treatment of material properties, a comparison is made of predicted fringe patterns with experimental results for both one- and two-dimensional situations. The cases considered are the rod and semi-infinite plate geometries under quasistep pressure inputs, for which viscoelastic solutions are obtained from the wave propagation analysis in the first part of the thesis. The results indicate the feasibility of quantitative photoviscoelasticity for dynamic stress analysis.

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