Resonance frequencies and loss factors of various single-degree-of-freedom systems

Abstract

A single-degree-of-freedom(SDOF) system with a mass(m), a spring(k), and a damping(c) is a basic mechanical system.It is well known that a complex mechanical system is represented by a combination of infinite number of SDOF systems.The modal analysis theory is based on this principle, but only one type among various types of SDOF systems is presently employed for a modeling of complex systems.When one needs to estimate m, k, and c of a SDOF system from the measurement of the resonance frequency and the loss factor, the relationships between them must be exactly known.Those relationships are known for commonly used SDOF systems, but those for rather unfamiliar types are not known.In this technical report, various types of SDOF systems and their equivalent electrical circuits are listed, and equations that relate the resonance frequencies to the undamped resonance(natural) frequencies and the loss factors are given.It is also shown that, for some type of SDOF systems, some cares must be taken how to interpret the loss factor.