Page 21 - Fluid-Structure Interactions Slender Structure and Axial Flow (Volume 1)

4 SLENDER STRUCTURES AND AXIAL FLOW

structural motions, and hence only half of this matrix is of direct interest. The struc-
ture, or ‘body oscillator’, is any component with a certain inertia, either elastically
supported or flexible (e.g. a flexibly supported rigid mass, a beam, or a shell). Thus,
in a one-degree-of-freedom system, the equation of which may generally be written as
i + mix + g(x, i, x) = f(t), the first two terms must be present, i.e. the structure, if
appropriately excited, must be able to oscillate!
Extraneously induced excitation (EIE) is defined as being caused by fluctuations in
the flow or pressure, independently of any flow instability and any structural motion. An
example is the turbulence buffeting, or turbulence-induced excitation, of a cylinder in flow,
due to surface-pressure fluctuations associated with turbulence in the flow. Instability-
induced excitation (IIE) is associated with a flow instability and involves local flow
oscillations. An example is the alternate vortex shedding from a cylindrical structure.
In this case it is important to consider the possible existence of a control mechanism
governing and perhaps enhancing the strength of the excitation: e.g. a fluid-resonance or
a fluidelastic feedback. The classical example is that of lock-in, when the vortex-shedding
frequency is captured by the structural frequency near simple, sub- or superharmonic reso-
nance; the vibration here further organizes and reinforces the vortex shedding process.
Finally, in movement-induced excitation (MIE) the fluctuating forces arise from move-
ments of the body; hence, the vibrations are self-excited. Flutter of an aircraft wing and
of a cantilevered pipe conveying fluid are examples of this type of excitation. Clearly,
certain elements of IIE with fluidelastic feedback and MIE are shared; however, what
distinguishes MIE is that in the absence of motion there is no oscillatory excitation
whatsoever.
A similar classification, related more directly to the nature of the vibration in each
case, was proposed earlier by Weaver (1976): (a) forced vibrations induced by turbulence;
(b) self-controlled vibrations, in which some periodicity exists in the flow, independent of
motion, and implying some kind of fluidelastic control via a feedback loop; (c) self-excited
vibrations. Other classifications tend to be more phenomenological. For example, Blevins
(1990) distinguishes between vibrations induced by (a) steady flow and (b) unsteady
flow. The former are then subdivided into ‘instabilities’ (i.e. self-excited vibrations) and
vortex-induced vibrations. The latter are subdivided into: random, e.g. turbulence-related;
sinusoidal, e.g. wave-related; and transient oscillations, e.g. water-hammer problems.
All these classifications, and others besides, have their advantages. Because this book
is essentially a monograph concerned with a subset of the whole field of flow-induced
vibrations, adherence to a single classification scheme is not so crucial; nevertheless, the
phenomenological classification will be used more extensively. In this light, an important
aim of this section is to sensitize the reader to the various types of phenomena of interest
and to some of the physical mechanisms causing them.

1.3 SCOPE AND CONTENTS OF VOLUME 1

Chapter 2 introduces some of the concepts and methods used throughout the book, both
from the fluids and the structures side of things. It is more of a refresher than a textbook
treatment of the subject matter, and much of it is developed with the aid of examples.
At least some of the material is not too widely known; hence, most readers will find
something of interest. The last part of the chapter introduces some of the differences in