Concept of complex stiffness applied to problems of oscillations with viscous and hysteretic damping

Abstract

The concept of complex stiffness in problems of oscillations with viscous, or structural (hysteretic) damping is often used in a wrong way, leading to erroneous solutions. It is shown in the Paper that correct expressions for complex stiffness are different in the cases of forced and free oscillations. All fundamental cases for a single degree of freedom are critically re-examined and compared, and fallacious solutions eliminated. The law of hysteretic damping being only known for a simple harmonic oscillation, all problems involving decaying oscillations, or more than one oscillatory mode, can only be treated tentatively at present, until the general law is found. This requires further experimental work.