1 - Introduction to Mechanical Vibrations

Abstract

This chapter provides an introduction to mechanical vibrations. Terminology is discussed that is used in analyzing the vibratory response of mechanical systems. Mathematical methods are described for the linear response of vibrating systems. The equations of motion and linear behavior of single-degree-of-freedom systems are outlined for both free and forced response. All vibrations in realistic systems occur with some form of damping mechanism, where the energy of vibration is dissipated during a cycle of motion. The inclusion and characteristics of damping are very important to active control methods since it represents a process by which the response of a system can also be reduced by passive means. The chapter shows typical response versus time curves for an SDOF system with light, critical and heavy damping. The use of the Laplace transform to solve for transient response is reviewed. The extension to multi-degree-of-freedom systems and the use of finite element analysis are introduced. These approaches are valid for lightly damped structures or elements that are small relative to the wavelength of motion.