Hello. Sign In
Standards Store




THE DUFFING EQUATION: NONLINEAR OSCILLATORS AND THEIR BEHAVIOUR

2011 Edition, 2011

Complete Document



Detail Summary

Active, Most Current

Additional Comments:
ISBN: 9780470715499
Format
Details
Price (USD)
Print
Backordered
$213.00
Add to Cart

Product Details:

  • Revision: 2011 Edition, 2011
  • Published Date: January 2011
  • Status: Active, Most Current
  • Document Language:
  • Published By: John Wiley and Sons (WILEY)
  • Page Count: 390
  • ANSI Approved: No
  • DoD Adopted: No

Description / Abstract:

Introduction

It is possibly the dream of many researchers to have an equation named after them. One person who achieved this was Georg Duffing, and this book is devoted to various aspects of his equation. This equation is enigmatic. In its original form, it essentially has only one extra nonlinear stiffness term compared to the linear second-order differential equation, which is the bedrock of vibrations theory, and this opens the door to a whole new world of interesting phenomena. Much of this was not known at the time of Georg Duffing, and is described in this book. The story behind the equation is also very interesting, because Georg Duffing was not an academic; he was an engineer, who carried out academic work in his spare time, as will be described later. In the present day when academics are being constantly reminded about the impact of their research work, and are constantly being judged by their output, in terms of publications, it is also interesting to look at the academic output from Georg Duffing and the impact of his work. Rarely is a paper or textbook written on nonlinear dynamics today without some reference to the Duffing equation, such is the impact of his work, yet he wrote less than ten publications in his life.

The aim of this book is twofold. The first is to give a historical background to Duffing's work, and to track the evolution of his work to the present day. This is done in this chapter. The second aim is to provide a thorough treatment of the different forms of his equation through the various chapters written by the contributing authors. This will involve qualitative and quantitative analysis coupled with descriptions of the many physical phenomena that are described by the various forms of his equation. Nowadays, the term ‘Duffing equation' is used for any equation that describes an oscillator that has a cubic stiffness term, regardless of the type of damping or excitation. This, however, was not the case in Duffing's original work, in which he restricted his attention to the free and forced harmonic vibration of an oscillator in which the stiffness force had quadratic and cubic terms, and the damping considered was of the linear viscous type. In this book the contemporary view is taken and many forms of the Duffing equation are studied, with the notable exceptions of a randomly or parametrically excited oscillator.