CHAPTER 2 - Systems with Several Degrees of Freedom

Abstract

This chapter provides an overview of the systems with several degrees of freedom. It discusses vibration analysis of multi-degree-of-freedom systems with emphasis on determining their response for various types of excitation. From the figures used to illustrate them, these systems might represent a limited class of practical structures. The general analysis of multi-degree-of-freedom systems can be handled only in matrix form. Before considering this general analysis, some new vibration concepts have been introduced by analyzing the systems with two degrees of freedom, where matrix algebra is not essential. Free undamped vibrations, the steady-state response to harmonic excitation and the response to a general exciting force of systems with two degrees of freedom are considered. Harmonic applied forces occur frequently. As small changes in damping values cause large changes in response at or near resonant conditions, the restriction on damping with the normal mode method is a disadvantage when the excitation is harmonic.