IDENTIFICATION OF COMPLEX MODULUS FROM MEASURED STRAINS ON AN AXIALLY IMPACTED BAR USING LEAST SQUARES

Abstract

The complex modulus of a material with linearly viscoelastic behaviour is identified on the basis of strains which are known, from measurements and sometimes from a free end boundary condition, at three or more sections of an axially impacted bar specimen. The aim is to improve existing identification methods based on known strains at three uniformly distributed sections by increasing the number of sections considered and by distributing them non-uniformly. The increased number of sections results in an overdetermined system of equations from which an approximate solution for the complex modulus is determined using the method of least squares. Through the non-uniform distribution of sections, critical conditions with accompanying large errors at certain frequencies are largely eliminated. Experimental tests were carried out at room temperature with two materials, viz., polypropylene and polymethyl methacrylate, five strain gauge configurations and two kinds of impact excitation. Substantial improvement in the quality of the results for complex modulus was obtained.