Chapter 1 - Some Basics of the Theory of Vibrations

Abstract

A good physical understanding of the behavior of vibrating structures can be achieved by analyzing the behavior of a single degree of freedom (SDOF) oscillator. The SDOF system is covered by an extremely large number of textbooks and is the basis for every academic course in vibration analysis in aerospace, mechanical, and civil engineering schools. The SDOF system can be excited either by a force acting on the mass or by a forced movement of the support. The first type of excitation is usually called “force excitation” and the latter is called base excitation These two major types of excitations are basic to the structural response analyses of both the SDOF and the continuous elastic systems. Duhamel's integral can also be performed analytically for harmonic excitations. The results of such an analysis are more general, as it expresses both the steady state and the transient response. A multiple-degrees-of-freedom (MDOF) system contains several masses, interconnected by springs and dampers and excited by several external forces and/or base excitations. It is essential to learn the behavior of MDOF systems and the methods used in order to analyze them. One of the main purposes of a practical structure is to support some kinds of payloads.