Dynamic restoring and dissipative parameters of non-linear systems

Abstract

Elastometer vibration and shock absorbing machinery mountings and package cushioning cannot be accurately modeled as linear Voigt type systems, since most of them exhibit stiffening or softening elasticity in conjunction with friction and viscous damping. Improved accuracy may be achieved by a non-linear shock or vibration loaded model, incorporating linear with non-linear elasticity and combined Coulomb and viscous damping. Formulae of such a model are compiled whereby optimal cushioning systems and mounts in shock and vibration loading may be designed. The use of these formulae requires experimental evaluation of two pairs of restoring and dissipative parameters in shock and vibration loading. Equations and test procedures for evaluating these parameters by means of shock and vibration machine tests are presented, along with a detailed discussion of properties of hysteresis loops of non-linear single degree of freedom systems in shock and vibration loading. A special test jig is described comprising a non-linear system with adjustable non-linear elasticity as well as variable Coulomb and viscous damping. This jig was used to evaluate the validity of the mathematical model by means of extensive tests on a shock and vibration machine. Programs developed for an Apple II microcomputer facilitated rapid and accurate computations whereby a numerical example is presented as an illustration of the procedure for evaluating restoring and dissipative parameters. This mathematical model and test procedures are believed to closely approximate shock and vibration isolation systems. As such, they may be conducive to developing better cushioning material and improved machinery mounts.