13.4 Vibrations Due to Fluid – Structure Interaction

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The principles of vibration due to fluids such as water are very similar to those of wind action presented

in the previous section. The fluid flow can significantly affect the vibrational characteristics of a structure.

The presence of a quiescent fluid decreases the natural frequencies and increases the damping of the

structure. Similar to wind, a turbulent fluid flow exerts random pressures on a structure, and these

random pressures induce a random response leading to large structural deformations or failure. More

details on fluid – structure interaction can be found in text books (e.g., Tiejens and Prandtl, 1957;

Milne-Thompson, 1968).

13.4.1 Added Mass and Inertial Coupling

A real fluid is viscous and compressible. In contrast, a perfect fluid is nonviscous and incompressible.

Fluid damping is absent in perfect fluids, and therefore, for a structure oscillating in a quiescent perfect

fluid, the fluid-force component is associated with the fluid inertia called the added mass. This is of

practical importance when the fluid density is comparable to the density of the structure, because then

the added mass becomes a significant fraction of the total mass in dynamic motion. Added mass and fluid

damping associated with single and multiple cylindrical structures are discussed in detail by Chen (1987).

For example, the added mass for a circular cylinder of radius a and height h is equal to pa2h: Added

masses for different cross-sectional shapes are presented by Milne-Thompson (1968).

13.4.2 Wave-Induced Vibration of Structure

This effect is similar to wind; however, the density is very much larger than wind, thus making

the structural damping less effective. Therefore, it is essential to ensure that resonance does not occur.

TABLE 13.6 Main Differences between Wind and Earthquake Loading

Characteristic Wind Earthquake

Source of loading External force due to wind pressures Applied base motion from

ground vibration

Type and duration

of loading

Wind storm of several hours duration.

Loads fluctuate, but are

predominantly in one direction

Transient cyclic loads of at most

a few minutes total duration.

Loads change repeatedly in direction

Predictability Good statistical basis is

generally available

Poor

Sensitivity of loading to

return period

Moderate; þ15% typical for

£ 10 on return period

High; maximum credible earthquake

often greatly in excess of “design” values

Influence of local

soil conditions

Little effect on dynamic sensitivity Soil conditions can be very important

Spectral peak input range Gust: , 0.1 Hz Usually 1 to 5 Hz

Main factors affecting

building response

External shape of building or structure.

Generally only global dynamic

properties are important.

Dynamic considerations affect

only a small fraction of

building structures

Response is governed by global dynamic

properties (fundamental period,

damping, and mass)

but plan and vertical regularity of

structure also important.

All structures are affected dynamically

Normal design basis Elastic response is required Inelastic response is usually permitted,

but ductility must be provided

Design of nonstructural

elements

Applied loading is concentrated

on external cladding

Entire building contents are shaken and

must be appropriately designed

Source: Data from Maguire, J.R. and Wyatt, T.A., 1999. Dynamics — An Introduction for Civil and Structural Engineers,

Thomas Telford, London.

Vibration and Shock Problems of Civil Engineering Structures 13-33

© 2005 by Taylor & Francis Group, LLC

The fluid forces which act in line with the

direction of wave propagation (Figure 13.19) can

be found using a generalized form of Morrison’s

equation comprising both drag (proportional to

area times velocity squared) and inertia forces

(proportional to immersed volume times acceleration).

More details can be found in Muga and

Wilson (1970).

Flexible structures will resonate with the wave if

the structural natural period equals the wave

period or a harmonic of the wave period. Since

the wave frequencies of importance are ordinarily

less than 0.2 Hz, such a resonance occurs only for

exceptionally flexible structures such as offshore platforms. The amplitude of structural response at

resonance is a balance between the wave force and the structural stiffness times the damping.

The above discussion considers only the in-line forces. These in-line forces produce an in-line

response. However, substantial transverse vibrations also occur for ocean flows around circular cylinders.

These vibrations are associated with periodic vortex shedding, which was discussed under wind-induced

vibration.

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