Vibration of Continuous Systems, 2nd Edition

5Derivation of Equations: Integral Equation Approach

5.1 INTRODUCTION

In this chapter we describe the integral formulation of the equations of motion governing the vibration of continuous systems. An integral equation is an equation in which the unknown function appears under one or more signs of integration. The general form of an integral equation is given by

(5.1)

where is a known function of the variables t and and is called the kernel or nucleus, is an unknown function, and are known functions, and a and b are known limits of integration. The function which satisfies Eq. (5.1) is called the solution of the integral Eq. (5.1). Physically, Eq. (5.1) relates the present value of the function to the sum or integral of what had happened to all its previous values, , from the previous ...