Examples of Physical Systems Described by the Duffing Equation

Abstract

In this chapter several examples of physical systems whose dynamic behaviour can be approximated by several forms of the Duffing equation are given. The physical systems are chosen to illustrate the physical phenomena that result in different forms of this equation related to several types of geometric nonlinearity: hardening, softening, positive linear-negative cubic nonlinearity and pure nonlinearity. The equations of motion are derived and are then non-dimensionalised. The equations that describe these systems are subsequently investigated in more detail in later chapters. © 2011 John Wiley & Sons, Ltd. All rights reserved.