Statistical Energy Analysis
Encyclopedia
Statistical energy analysis (SEA) is a method for predicting resonant sound
and vibration
transmission in dynamical system
s made up of coupled acoustic cavities and structural parts. The vibrational behavior of the system is defined in terms of energy. The energy is here the potential
and kinetic energy
of the modal resonance
s (eigenmodes)of the dynamical system.
To solve a sound or vibration problem with SEA, the system is partitioned into components (like plates, shells, beams or cavities) which in turn are represented by one or more modal "subsystems", for whom the vibrational energy is shared among modes with similar dynamic properties. A plate may thus be modeled by three subsystems, one for each type of waves possible (bending,longitudinal and shear). A number of practical prerequisites have to be fulfilled:
1) The subsystems, when the component is isolated, shall have at least a few eigenmodes in each frequency band of interest.
2) The damping of the modes shall not be too high, so that non-resonant transmission becomes significant
3) The coupling strength between subsystems should not be too strong
This means in practice that SEA is useful only at sufficiently high frequencies, e.g. it can by default not predict response of low frequency "global modes".
The core of SEA calculations consists of a relatively small set of energy-balance equations that uses modal densities and internal loss factors (damping) of the subsystems, coupling loss factors between these and the vibrational power injected by the external sources to calculate the vibrational energies of the various subsystems. Engineering response for the subsystems are then expressed as spatial average quantities (sound pressure, vibration velocite etc.), derived from these energies.
SEA is popular in aerospace
and automotive
industries where various mid- and high frequency sound and vibration transmission properties can be predicted at low cost and for a wide frequency range: random vibration levels of rockets and payloads structures at lift-off, sound transmission into car passenger cabins due to various noise sources (exhaust, engine...). For mechanical engineers, vibrations are a ubiquitous problem which not only cause noise but also reduce life of machinery. Statistical energy analysis is a statistical method to predict multi-modal resonant vibrational levels of components of structures without solving elaborated equations or using finite element software.
SEA was originally stated by Lyon and Maidanik in the early 60s where they found the power exchange relationship between two coupled spring-mass oscillators . Further on, the theory has been extended to the coupling of continuous dynamic systems (beams, plates, shells) . More recently, vibrational entropy has been recognized as being part of SEA with equal importance as energy
SEAM, SEAM 3D from Cambridge Collaborative Inc. USA, http://www.seam.com/software.htm
VA One SEA Module (previously AutoSEA) from ESI group, France, http://www.esi-group.com/products/vibro-acoustics/va-one/core-modules/sea-module
GSSEA-Light from Gothenburg Sound AB, Sweden, http://www.gothenburgsound.se/products/Software/GSSEA-Light/index.html
http://www.free-sea.de/
SEAlab - open code in Matlab/Octave from Applied Acoustics, Chalmers, Sweden, http://www.ta.chalmers.se/research.php?page=sealab
Sound
Sound is a mechanical wave that is an oscillation of pressure transmitted through a solid, liquid, or gas, composed of frequencies within the range of hearing and of a level sufficiently strong to be heard, or the sensation stimulated in organs of hearing by such vibrations.-Propagation of...
and vibration
Vibration
Vibration refers to mechanical oscillations about an equilibrium point. The oscillations may be periodic such as the motion of a pendulum or random such as the movement of a tire on a gravel road.Vibration is occasionally "desirable"...
transmission in dynamical system
Dynamical system
A dynamical system is a concept in mathematics where a fixed rule describes the time dependence of a point in a geometrical space. Examples include the mathematical models that describe the swinging of a clock pendulum, the flow of water in a pipe, and the number of fish each springtime in a...
s made up of coupled acoustic cavities and structural parts. The vibrational behavior of the system is defined in terms of energy. The energy is here the potential
Potential energy
In physics, potential energy is the energy stored in a body or in a system due to its position in a force field or due to its configuration. The SI unit of measure for energy and work is the Joule...
and kinetic energy
Kinetic energy
The kinetic energy of an object is the energy which it possesses due to its motion.It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its acceleration, the body maintains this kinetic energy unless its speed changes...
of the modal resonance
Resonance
In physics, resonance is the tendency of a system to oscillate at a greater amplitude at some frequencies than at others. These are known as the system's resonant frequencies...
s (eigenmodes)of the dynamical system.
To solve a sound or vibration problem with SEA, the system is partitioned into components (like plates, shells, beams or cavities) which in turn are represented by one or more modal "subsystems", for whom the vibrational energy is shared among modes with similar dynamic properties. A plate may thus be modeled by three subsystems, one for each type of waves possible (bending,longitudinal and shear). A number of practical prerequisites have to be fulfilled:
1) The subsystems, when the component is isolated, shall have at least a few eigenmodes in each frequency band of interest.
2) The damping of the modes shall not be too high, so that non-resonant transmission becomes significant
3) The coupling strength between subsystems should not be too strong
This means in practice that SEA is useful only at sufficiently high frequencies, e.g. it can by default not predict response of low frequency "global modes".
The core of SEA calculations consists of a relatively small set of energy-balance equations that uses modal densities and internal loss factors (damping) of the subsystems, coupling loss factors between these and the vibrational power injected by the external sources to calculate the vibrational energies of the various subsystems. Engineering response for the subsystems are then expressed as spatial average quantities (sound pressure, vibration velocite etc.), derived from these energies.
SEA is popular in aerospace
Aerospace
Aerospace comprises the atmosphere of Earth and surrounding space. Typically the term is used to refer to the industry that researches, designs, manufactures, operates, and maintains vehicles moving through air and space...
and automotive
Automotive industry
The automotive industry designs, develops, manufactures, markets, and sells motor vehicles, and is one of the world's most important economic sectors by revenue....
industries where various mid- and high frequency sound and vibration transmission properties can be predicted at low cost and for a wide frequency range: random vibration levels of rockets and payloads structures at lift-off, sound transmission into car passenger cabins due to various noise sources (exhaust, engine...). For mechanical engineers, vibrations are a ubiquitous problem which not only cause noise but also reduce life of machinery. Statistical energy analysis is a statistical method to predict multi-modal resonant vibrational levels of components of structures without solving elaborated equations or using finite element software.
SEA was originally stated by Lyon and Maidanik in the early 60s where they found the power exchange relationship between two coupled spring-mass oscillators . Further on, the theory has been extended to the coupling of continuous dynamic systems (beams, plates, shells) . More recently, vibrational entropy has been recognized as being part of SEA with equal importance as energy
Software links
Software for Statistical Energy Analysis is commercially available from the following companies:SEAM, SEAM 3D from Cambridge Collaborative Inc. USA, http://www.seam.com/software.htm
VA One SEA Module (previously AutoSEA) from ESI group, France, http://www.esi-group.com/products/vibro-acoustics/va-one/core-modules/sea-module
GSSEA-Light from Gothenburg Sound AB, Sweden, http://www.gothenburgsound.se/products/Software/GSSEA-Light/index.html
Freeware links
Statistical Energy Analysis Freewarehttp://www.free-sea.de/
SEAlab - open code in Matlab/Octave from Applied Acoustics, Chalmers, Sweden, http://www.ta.chalmers.se/research.php?page=sealab