5.1 Random Vibration

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The discipline of random vibration of structures was borne of the need to understand how structures

respond to dynamic loads that are too complex to model deterministically. Examples include aerodynamic

loading on aircraft and earthquake loading of structures. Essentially, the question that must be answered is:

given the statistics (read: uncertainties) of the loading, what are the statistics (read: most likely values with

bounds) of the response? Generally, for engineering applications the statistics of greatest concern are the

mean, or average value, and the variance, or scatter. These concepts are discussed in detail subsequently.

Suppose that we are aircraft designers currently working on the analysis and design of a wing for a new

airplane. As engineers, we are very familiar with the mechanics of solids and can size the wing for static

loads. Also, we have vibration experience and can evaluate the response of the wing to a harmonic

5-1

© 2005 by Taylor & Francis Group, LLC

or impulsive forcing. However, this wing provides

lift to an airplane flying through a turbulent

atmosphere. Even though we are not fluid

dynamicists, we know that turbulence is a very

complicated physical process. In fact, the fluid

(air) motion is so complicated that probabilistic

models are required to model the behavior. Here, a

plausibly deterministic but very complicated

dynamic process is taken to be random for the

purposes of modeling. Wing design requires force

data resulting from the interaction between fluid

and structure. Such data can be shown as the time history in Figure 5.1.

The challenge is to make sense of such intricate fluctuations. The analyst and designer must run scale

model tests. A wing section is set up in the wind tunnel and representative aerodynamic forces are

generated. Data on wind forces and structural response are gathered and analyzed. With additional data

analysis, it is possible to estimate the force magnitudes. Estimates of the mean values of these forces can be

calculated, as well as of the range of possible forces. With these estimates, it is possible to study the behavior

of the wing under a variety of realistic loading scenarios using the tools of probability and statistics to

model this complex physical problem. This text introduces the use of probabilistic information in

mechanical systems, primarily structural and dynamic systems. These tools are applicable to all the sciences

and engineering, even though this text focuses on the mechanical sciences and engineering.

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