Non-Linearity in Dynamic Tests. I. Vibration Test Methods

Abstract

Abstract In those cases where dynamic tests are to be interpreted in terms of the molecular structure of rubber, there is a definite need for a method of analysis which is wholly free from mathematical assumptions. Such a method of analysis is possible by the use of phase planes of velocity plotted against displacement. This is so because the slope of the trajectory at any point of the motion of any single degree of freedom system can be written solely in terms of physical quantities, namely, driving force, viscoelastic reaction and momentum. The analysis involves no hidden mathematical assumption. Methods of deriving stress strain relationships from phase plane trajectories are described. This phase plane method is discussed in some detail. Examples are given showing the inadequacy of the usual linear analysis in the case of rubberlike materials. Analysis shows that dynamic test machines should either apply a known motion and record a force-deflection curve or apply a force of known wave form and record the resulting motion as a phase plane trajectory. If force and motion are not kept independent of each other in this manner there is an inbuilt mathematical relationship which, more often than not, influences and falsifies the results. An important conclusion is that only when the nature of the non-linearities, or what is the same thing, the character of the functions which correctly describe the actual behavior of a vibrating system have been established by sound analysis of test data, should the phenomena be ascribed to the physical properties of the material. Because of the important consequence of the acceptance of some common mathematical steps in any analysis, certain of these are critically examined and their relevance discussed.