Vibrations of Continuous Structures

Abstract

Starting in this chapter, we will focus on continuous structures and study their interactions with flow. A continuous structure such as a beam or a string is a structure in which the response is a function of time and space. If we consider a string (for example, a guitar string) as it oscillates, different points on the string move differently. The motion at each point is a function of time, but it is not necessarily the same function for different points along the length of the string. Therefore, the response of a string is a function of time and space. The equations that represent such systems are called Partial Differential Equations (PDEs). PDEs include derivatives with respect to both time and space. Before we study how continuous structures interact with flow, we focus on continuous structures with no flow around them. In this chapter, we will study beams and strings, since they are the continuous structures that are widely used in fluid-structure interaction systems. We also discuss the Galerkin method, which is a widely used method to solve PDEs that represent continuous structures.