Page 23 - Fluid-Structure Interactions Slender Structure and Axial Flow (Volume 1)

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Concepts, Definitions and

Methods

As the title implies, this also is an introductory chapter, where some of the basics of the
dynamics of structures, fluids and coupled systems are briefly reviewed with the aid of a
number of examples. The treatment is highly selective and it is meant to be a refresher
rather than a substitute for a more formal and complete development of either solid or
fluid mechanics, or of systems dynamics.
Section 2.1 deals with the basics of discrete and distributed parameter systems, and the
classical modal techniques, as well as the Galerkin method for transforming a distributed
parameter system into a discrete one. Some of the definitions used throughout the book
are given here. A great deal if not all of this material is well known to most readers;
yet, some unusual features (e.g. those related to nonconservative systems or systems with
frequency-dependent boundary conditions) may interest even the cognoscenti.
The structure of Section 2.2, dealing with fluid mechanics, is rather different. Some
generalities on the various flow regimes of interest (e.g. potential flow, turbulent flow)
are given first, both physical and in terms of the governing equations. This is then followed
by two examples, in which the fluid forces exerted on an oscillating structure are calcu-
lated, for: (a) two-dimensional vibration of coaxial shells coupled by inviscid fluid in
the annulus; (b) two-dimensional vibration of a cylinder in a coaxial tube filled with
viscous fluid.
Finally, in Section 2.3, a brief discussion is presented on the dynamical behaviour of
fluid-structure-interaction systems, in particular the differences when this is obtained via
nonlinear as opposed to linear theory.

2.1 DISCRETE AND DISTRIBUTED PARAMETER SYSTEMS

Some systems, for example a mathematical simple pendulum, are sui getieris discrete;
i.e. the elements of inertia and the restoring force are not distributed along the geometric
extent of the system. However, what distinguishes a discrete system more precisely is that
its configuration and position in space at any time may be determined from knowledge of
a numerable set of quantities; i.e. the system has a finite number of degrees of freedom.
Thus, the simple pendulum has one degree of freedom, even if its mass is distributed
along its length, and a double (compound) pendulum has two.
The quantities (variables) required to completely determine the position of the system
in space are the generalized coordiwates, which are not unique, need not be inertial, but
must be equal to the number of degrees of freedom and mutually independent (Bishop &

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