STATISTICAL STATISTICAL ENERGY ANALYSISENERGY ANALYSIS

Semra Özkök

Hasan Barış Karayel

ENERGY BASED METHODS

• Energy based methods are the best methods to solve the vibration and acoustics problems using energy quantities like energy, energy density, power, etc...

• Finite Element Analysis and Boundary Element Analysis are the best CAE(computer aided eng.) tools.

• But they cannot achieve to predict high frequency problems effectively

ENERGY BASED METHODS

• Example:

if the frequency increases, wavelengths get smaller and the complexity of the system dynamics increases. And then, acoustic cavity gets as the third power of frequency.

ENERGY BASED METHODS

• One possible CAE solution to solve these challenges is Statistical Energy Analysis (SEA).

• SEA has the capability to solve this problem and to identify how vibrations are distributed in the structure of a system described as a set of subsystems.

ENERGY BASED METHODS

DEVELOPMENT OF SEA

• In these days, the most famous energy-based method is the statistical energy analysis.

• Similar approaches of SEA were used in room acoustics, before the actual development of SEA.

• Then it was used in the early 1960 with the application to vibro acoustic problems in aerospace engineering.

DEVELOPMENT OF SEA

• In last few years, this method is mostly used in automotive industry and aerospace engineering. At the same time, it is started to use in commercial software like the other analysis methods.

WHERE SEA IS USED

• Today, it is very common to use for interior noise design of automobiles, air- and motor-craft, ships, rail cars and other transport vehicles.

• The space industry uses SEA to predict random vibration response of sensitive equipment on space structures subjected to harsh vibro-acoustic launch loads.

WHERE SEA IS USED

Thermo gram display using color to denote the modal energy distribution under the applied structural and acoustic loads.

WHERE SEA IS USED

Automotive: in automobiles, trucks, buses, etc.

Ship: in ships, luxury yachts, and submarines.

Aircraft: in commercial, executive and military aircraft.

WHERE SEA IS USED

Space: in spacecraft and launch vehicles.

Architecture: in office buildings, hotels, etc.

Sonar: for Navy projects and sonar systems

Rail: for commuter and high speed trains.

WHERE SEA IS USED

Graphical representation of an SEA model of a car body shell: plate (top) and beam (bottom) subsystems

SEA FUNDAMENTALS

Power Balance Equation:

Pi = whiE

• Where hi is damping loss factor.

• Based on the assumption of conservation of energy.

SEA FUNDAMENTALS

Power Balance Equation:

Pij = whijEi

• Where hij is coupling loss factor.

SEA FUNDAMENTALS

Model Density:

• In SEA, modal density is an important variable.

• It means the number of modes per frequency bandwidth.

SEA FUNDAMENTALS

• For plates to find modal density,let us look at the following figure.

SEA FUNDAMENTALS

• To find number of modes, two circles which their radiuses are equal to the freely propagating wave number of lower and upper frequencies are drawn.

• Then the modes are counted between these circles.

• Lastly, modes divided to the given frequency interval give the modal density.

SEA FUNDAMENTALS

SEA MODELING PROCEDURES

• First of all, structure is converted to a SEA model. In SEA, system is divided into subsystems.

• After modeling SEA, the interactions between subsystems, input powers and subsystem energies are defined.

SEA MODELING PROCEDURES

• When power balance equations solved for the unknowns within it, energies of subsystem are found.

• In SEA, there is two main methods to reach the solution:

- Experimental SEA

- Predictive SEA

SEA MODELING PROCEDURES

• Before begining these method, let us examine the substructuring process which is same for these two method.

• A subsystem is a physical element of the structure that is to be analyzed.

• A subsystem is a group of “similar” energy storage modes.

SEA MODELING PROCEDURES

• To illustrate this, some examples of vibro/acoustic elements that may be treated as subsystems shall be given here together with the necessary input data to characterize them:

• an acoustic cavity (a room): longitudinal waves –only one subsystem needed, characterized by volume, fluid parameters, absorption

SEA MODELING PROCEDURES

• a plate: bending, compression and shear waves modeled by three subsystems, characterized by area, thickness, material parameters, damping

• a beam: four wave types – four subsystems, characterized by length, shape of cross-section, material parameters, damping

• shells, non-isotropic plates, ...

SEA MODELING PROCEDURES

Experimental SEA:

• Experimental SEA based on determining all quantities in the following equation by experiment .

SEA MODELING PROCEDURES

• To do this firstly, power is injected to each subsystem in the structure in turn.

• Then, each time the energy in each subsystem is measured.

SEA MODELING PROCEDURES

• For each subsystem a set of energies is ready and the previous equation can be set up using the following equation.

• By inverting the matrix of energies, this system may be solved to get the coupling and damping loss factors.

SEA MODELING PROCEDURES

Predictive SEA:

• The basic idea of predictive SEA is to assess the coupling loss factors.

• So, it is possible to predict the behavior of a structure even in an early stage of its design without requirements of any measurement after built.

SEA MODELING PROCEDURES

• This procedure firstly starts with estimating of the damping loss factors either from measurement, from tables, from calculations or simply from “experience”.

• Then, the input power is determined.

SEA MODELING PROCEDURES

• The coupling loss factors may be estimated by lots of different methods:

• From radiation or transmission efficiencies (wave approach).

• using modal approaches

SEA MODELING PROCEDURES

• using numerical methods (e.g. Finite Element Method)

• coupling power proportionality hij = hjihj/hi (hi, hj are the modal densities of subsystems i and j)

• ...

SEA MODELING PROCEDURES

• With all necessary input parameters available, the SEA equations may be solved and the response of the structure may be predicted.

• As in experimental SEA this enables lots of useful possibilities for analysis.

MODELING SOFTWARES

• Nearly all of the industries have started to use SEA as a CAE tool and some of the organizations have prepared SEA computer codes.

• Two of these codes have been developed commercially. • SEAM was developed by Cambridge Colloborative Inc.,

was the first SEA computer code to become commercially available.

• AutoSEA2 was developed by Vibro- Acoustic Sciences Ltd., has been made commercially available.

MODELING SOFTWARES

• Dynamic response of complex structures at mid and high frequencies can be measured by SEAM software.

• SEAM is used to predict interior noise and

vibration in automobiles, aircraft, shipbuilding and construction equipment cabs as well as the radiated noise from ships and the vibro-acoustic environments for spacecraft.

Seam Acoustic and Vibration Prediction Software

MODELING SOFTWARES

*many of the standard features come with SEAM. Some of them:

• Ability to develop very large models with thousands of SEA subsystems

• Transverse shear deformation corrections for bending of all structural elements

Seam Technical Features

MODELING SOFTWARES

• Prediction of input power and response mean and variance

• Automatic calculation of properties for beam, plate and shell elements from cross-section dimensions and materials

Seam Technical Features

MODELING SOFTWARES

• Choice of several different metric and English units, including mixed units

• On-line context sensitive help

• Quick-look plotting for subsystem SEA parameters: modal energy, energy flow, response, transfer functions, acoustic noise reduction, vibration reduction, and sound transmission loss

Seam Technical Features

MODELING SOFTWARES

• SEAM is appropriate for both UNIX and PC-compatible computers. Sun, Silicon Graphics, and Hewlett Packard workstations are supported

Application Platforms

MODELING SOFTWARES

• In AutoSEA2, an analytical method is used to approach noise and vibration reduction in design.

• With AutoSEA2, noise and vibration problems can be modeled earlier in the design process, eliminating costly mistakes before they go too far.

AutoSEA2

MODELING SOFTWARES

• AutoSEA2 is applied to predict interior noise levels in automobiles, trucks, trains, aircraft, ships, construction and agricultural equipment, and even the Space Station Freedom!

Using of AutoSEA2

MODELING SOFTWARES

*Dimensional Modeling Features

- Models built faster

- Time saved and errors avoided updating models

MODELING SOFTWARES

* Computation Engine Features

-Reliability of the proven industry standard

-Accuracy of full wave transmission theory

MODELING SOFTWARES

* Open-Architecture Features

AutoSEA2 is built on an open-architecture platform designed with flexibility and expandability in mind

MODELING SOFTWARES

* Auto-Connect Features

Common boundary geometry is shared by point, line and area junctions between all structural and acoustic subsystems and, the junction is automatically detected and computed.

SEA IN SHIP INDUSTRY

• The usage of SEA has begun to spread over the ship industry for last years.

• The most crucial reason of this, undoubtedly, is the importance of preliminary calculations of vibrations caused by main diesel engines and their auxiliary machines (Electric Generators) and pumps.

SEA IN SHIP INDUSTRY

• Great noise problems, which are the reason of the vibration of machines, affect the living places on ship negatively.

• So, for ship design, these calculations -made before- are important.

SEA IN SHIP INDUSTRY

• It is same with yacht industry.

• Especially, motor-yachts use high speed engines –diesel or water jet.

• These machines make great noise and passengers may be disturbed.

• SEA is used to predict this noise before and comfort of passengers can be supplied.

THANKS VERY MUCH!