Abstract
The unsteady behaviour of an infinitely long fluid-loaded elastic plate
which is driven
by a single-frequency point-force excitation in the presence of mean flow is known
to exhibit a number of unexpected features, including absolute instability when the
normalized flow speed, U, lies above some critical speed
U0, and certain unusual
propagation effects for U<U0. In the latter
respect Crighton & Oswell (1991) have
demonstrated most significantly that for a particular frequency range there exists
an anomalous neutral (negative energy) mode which has group velocity pointing
towards the driver, in violation of the usual radiation condition of outgoing waves
at infinity. They show that the rate of working of the driver can be negative, due
to the presence of other negative-energy waves, and can also become infinite at a
critical frequency corresponding to a real modal coalescence. In this
paper we attempt
to extend these results by including, as is usually the case in a
practical situation,
plate curvature in the transverse direction, by considering a fluid-loaded cylinder
with axial mean flow. In the limit of infinite normalized cylinder radius,
a, Crighton
& Oswell's results are regained, but for finite a very significant
modifications are
found. In particular, we demonstrate that the additional stiffness introduced by the
curvature typically moves the absolute-instability boundary to a much higher flow
speed than for the flat-plate case. Below this boundary we show that Crighton &
Oswell's anomalous neutral mode can only occur for
a>a1(U), but in practical
situations it turns out that a1(U) is exceedingly
large, and indeed seems much larger
than radii of curvature achievable in engineering practice. Other negative-energy
waves are seen to exist down to a smaller, but still very large, critical
radius a2(U),
while the existence of a real modal coalescence point, leading to a divergence in
the driver admittance, occurs down to a slightly smaller critical radius
a3(U). The
transition through these various flow regimes as U and a vary is
fully described by
numerical investigation of the dispersion relation and by asymptotic analysis in the
(realistic) limit of small U. The inclusion of plate dissipation is
also considered,
and, in common with Abrahams & Wickham (1994) for the flat plate, we show
how the flow then becomes absolutely unstable at all flow speeds provided that
a>a2(U).
Publisher
Cambridge University Press (CUP)
Subject
Mechanical Engineering,Mechanics of Materials,Condensed Matter Physics
Cited by
38 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献