Mechanical Systems with One Degree of Freedom

Abstract

In noise reducing engineering, the consequences of changes made to a system must be understood. Questions posed could be on the effects of changes to the mass, stiffness, or losses of the system and how these changes can influence the vibration of or noise radiation from some structures. Real constructions certainly have many or in fact infinite modes of vibration. However, to a certain extent, each mode can often be modeled as a simple vibratory system. The most simple vibratory system can be described by means of a rigid mass, mounted on a vertical mass less spring, which in turn is fastened to an infinitely stiff foundation. If the mass can only move in the vertical direction along the axis of the spring, the system has one degree of freedom (1-DOF). This is a vibratory system never actually encountered in practice. However, certain characteristics of systems with many degrees of freedom, or rather, continuous systems with an infinite degree of freedom, can be demonstrated by means of the very simple 1-DOF model. For this reason, the basic mass–spring system is used in this chapter to illustrate some of the basic concepts concerning free vibrations, transient, harmonic, and other types of forced excitation. Kinetic and potential energies are discussed as well as their dependence on the input power to the system and its losses.