Analysis of a one-dimensional nonlinear mechanical model and its application to the qualitative explanation of the visco-elastic behavior of aluminum from sonic tests

The sonic testing method employed in this thesis provides data for the calculation of several of the mechanical properties or aluminum and for a qualitative analysis of the visco-elastic behavior of this material.

Young's modulus of elasticity is determined for aluminum bars with various lengths and cross sections using the resonant frequency (in flexure) of each bar. This property varies linearly with the length to depth ratio of the test specimens, decreasing as the L/D ratio decreases. Certain nonlinear relationships exist between the length to depth ratios, resonant frequencies and Young's modulus, and are depicted in figures 8 and 9.

In addition, the logarithmic decrement, a measure or the internal damping of the material, is computed from the nondimensional amplitude-frequency response curves and is observed to increase as the test specimens become shorter. This is an indication that the internal damping increases as the lengths of the test specimens become shorter.

Due to the visco-elastic nature or aluminum, the manner in which this damping varies is unknown. An attempt to qualitatively analyze this phenomena is made by analyzing a one-dimensional mechanical model incorporating both a nonlinear restoring force and nonlinear viscous damping in its system. Observations of the test results show that the restoring force is best described by a linear spring, but that the damping can indeed be described, at least qualitatively, by a nonlinear dashpot.

This qualitative analysis of aluminum can at best provide only a concept of the physical characteristics of this material in the light of experimental results.