Civil Engineering Reference
In-Depth Information
CHAPTER 7
Statistical energy analysis (SEA)
7.1
INTRODUCTION
We have several times referred to statistical energy analysis, SEA for short, which is a
general prediction model for complex continuous systems comprising both acoustic and
structural members. It has found many applications in building acoustics (see e.g. Craik
(1996)), which warrants an introductory chapter giving a background for the examples
being presented in the remaining two chapters.
One could argue against the notion of a “method” due to the fact that the user has
the choice on how SEA should be applied to a specific system, but we shall not go into
that discussion here. SEA originated in connection with the US space programme in the
1960. The problem addressed was the prediction of the response, both of the complete
structure and of single components, to the enormous sound and vibration forces released
during takeoff. Later applications include the transmission of sound and vibration
onboard ships, airplanes and other means of transport and also, as mentioned above, in
buildings. The literature covering the field is quite extensive, and the list of references is
by no means complete. We shall, however, give reference to a couple of general topics
on the subject, Lyon (1975) and Craik (1996), together with a review article, Fahy
(1994). The last few years have seen a lot of work into the subject of estimating the
uncertainty of the method. This, together with the advent of quite a number of
commercially available computer programs (see section 2.5.3.1) has opened up SEA for
more general use.
SEA is used to model complex
resonant
systems, which may contain structural
members such as beams, plates and shells together with acoustical members such as air
ducts and rooms. The response, represented by vibration levels (of velocity, acceleration
or displacement) and sound pressure levels are calculated for the given excitation
(mechanical force, acoustic pressure). The term
statistical
implies that the analysis,
contrary to finite element methods (FEM, BEM), does not give any exact information on
the behaviour of the system, e.g. how the system responds to an excitation of a single
frequency. The calculated data will represent averaged values, not only over given
frequency bands, but which also represents averaged values for an ensemble of systems
which are nominally identical to the actual one but with a certain statistical spread. The
latter is easy to forget because one normally observes, let alone makes measurements on,
a given single system.
In the context of building acoustics the aforementioned consideration represents a
strength due to the fact that the building components themselves and how they are
interconnected, are not in every detail the same for nominally identical systems. Also,
one is seldom interested in a detailed frequency description. Rough estimates on how the
