On a Kind of Hysteretic Damping

Slightly nonlinear materials and structures with purely hysteretic damping, subjected to harmonic disturbances, are examined. It is shown that a load-deformation or stress-strain relation, on first loading, supplemented by a rule to obtain the curves on unloading and reloading, leads to a behavior similar to that of a linear viscoelastic material, but the equivalent damping ratio does not depend on frequency or amplitude. The relations between stress and strain in unloading and reloading can be obtained from a relation for first loading. It is contended that some materials that are considered viscoelastic actually possess this type of hysteretic behavior. Expressions are included for equivalent viscous damping and for the period of free vibration.