Numerical techniques

Abstract

This chapter gives an overview of numerical techniques for vibration analysis. The centered difference approximation for the first, second, and fourth derivative are given. These form the basis for the finite difference approximation of both spring-mass systems and the continuous problem. The fourth-order Runge-Kutta method is presented. Both of these approaches are used to solve the single-degree-of-freedom (single-DoF) system. In order to demonstrate these techniques for the multiple-degree-of-freedom (multi-DoF) system a two-degree-of-freedom (two-DoF) system is explored. Finite element and finite difference methods are presented as solution techniques for the continuous problem (also see Chapter 9). The bar and beam are used for examples. The Rayleigh method and Dunkerley's formula are presented. These are methods for computing the fundamental frequency.