USING STATISTICAL ENERGY ANALYSIS TO PREDICT SOUND INSULATION IN BUILDNGS

USING STATISTICAL ENERGY ANALYSIS TO PREDICT
SOUND INSULATION IN BUILDINGS
C Hopkins Acoustics Research Unit, School of Architecture, University of Liverpool, UK
1 INTRODUCTION
Sound insulation in the eld is determined by both direct and anking transmission; hence a
prediction model such as Statistical Energy Analysis (SEA) is useful at the design stage to
determine the overall transmission. This paper gives an overview of classical SEA models which
are commonly used to predict airborne and impact sound insulation. Such models sometimes need
to incorporate data from measurements or deterministic models (e.g. nite element methods) to
give accurate predictions For example, this occurs when building components, or the
coupling/connections between them, are too complex to model with simple idealizations of beams, plates and springs. This is sometimes considered in the low-frequency range because heavyweight walls and oors often have low modal density and low modal overlap which increases the
uncertainty in coupling loss factors predicted using wave theory. In this paper, experimental and
numerical examples are used to illustrate aspects relating to the inclusion of laboratory
measurements in SEA models. Whilst classical SEA gives predictions of steady-state sound and vibration (i.e. L☜ values) it is also useful to be able to predict Fast time-weighted sound pressure
levels inside buildings. Hence examples are given to show that when the principles of classical SEA
are applied in short♥time periods using Transient SEA (TSEA) it is possible to predict Lpfm from
transients such asfootsteps on heavyweight oors.
2 STATISTICAL ENERGY ANALYSIS (SEA)
2.1 Overview of SEA
A brief summary of SEA is given here because detailed descriptions of its application to buildings
are given in monographs on building acoustics☝. The rst step in making the model is to dene
SEA subsystems that form parts of a building; these are either space subsystems such as rooms, or structural subsystems such as plates or beams. These subsystems need to be dened by their
ability to store modal energy; therefore, the boundaries of a subsystem must cause reections so
that the sound or vibration eld is reverberant for the specic wave type considered in the
subsystem. Reections occur when there is an impedance change at a boundary. Hence for space
subsystems where there is only one wave type, the surfaces that dene a room or cavity usually dene the subsystem. For structural subsystems it can be slightly more complex. Although bending
waves are of primary importance for sound radiation, in-plane waves can be important for structure
borne sound transmission. As these waves have different modal energies, they need to be
represented as separate subsystems. For example, a plate can be represented by three
subsystems using a separate subsystem for bending, transverse shear and quasi-longitudinal
waves. Conversion between these wave types at a junction can therefore be included in an SEA model using coupling loss factors from one subsystem to another. The subsystem boundaries may vary depending upon the wave type under consideration. A plate or beam can be represented by
one subsystem for each wave type, although in many situations it is only necessary to consider
bending waves and a single subsystem will be sufcient. The analysis is carried out in frequency
bands such that the statistical modal density can be used. In building acoustics. it is common to use