Derivation of Equations

This chapter describes 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. If the unknown function appears nonlinearly in the regular and/or exceptional parts, the equation is said to be a nonlinear integral equation. Based on the type of integral in the regular part, the integral equations are classified as Fredholm- or Volterra-type equations. If the regular part of the integral equation contains a singular integral, the equation is called a singular integral equation. Otherwise, the equation is called a normal integral equation. Several methods, both exact and approximate methods, can be used to find the solutions of integral equations. The chapter considers the method of undetermined coefficients and the Rayleigh-Ritz, Galerkin, collocation, and numerical integration methods.