Welcome to the Up2HF Project !
Welcome to the Up2HF Project, a website regrouping knowledge, programs and application around high frequency vibroacoustics.
We first and foremost wish to thank the Carnot Institute for sponsoring us.
Who we are
This website is part of a project created by researchers in Centrale Lyon (France) and INSA Lyon (France) aiming to facilitate the diffusion of knowledge about high frequency vibroacoustics.
Who this is for
This website is aimed at students, researchers and engineers willing to learn more on this subject. This will be most useful to you if you have a basic understanding of acoustics and vibration concepts along with some programming experience.
A word on vibroacoustics
Vibroacoustics is the study of vibrations of structures excited by an exterior force and/or an injected power.
Here, a plate of shape ratio is excited in its middle by a sinusoidal force at the natural frequency of the mode .
In order to study these vibrations and predict the behavior of a structure, we usually use the finite element method. This method consists of applying the governing equations on smaller elements in the system.
However, this method is limited: the higher the studied frequency, the higher the number of degrees of freedom are and thus the longer it takes to compute.
However, this method is limited: the higher the studied frequency, the higher the number of degrees of freedom are and thus the longer it takes to compute.
Observation of the fidelity of a discretized string depending of the mode observed and the mesh resolution.
Here, the static error obtained through calculations are neglected. Only the error due to non adapted mesh resolution are observed.
Here, the static error obtained through calculations are neglected. Only the error due to non adapted mesh resolution are observed.
As such, due to limited capabilities of computers, a high frequency calculation limit appears depending on the system’s structural complexity.
| Structure | Car | Aircraft | Ship |
|---|---|---|---|
| Frequency | ≈500 Hz | ≈50 Hz | ≈5 Hz |
Beyond this frequency, the calculation grows rapidly.
To reduce this caculation time, a new method has been developed by researchers based on the study of statistical variables of the structure called Statistical Energy Analysis (or SEA).
The initial derivation of SEA arose in 1959 by Richard Lyon and Preston Smith as part of work concerned with the development of methods for analyzing the response of large complex aerospace structures subjected to spatially distributed random loading.
The initial derivation of SEA arose in 1959 by Richard Lyon and Preston Smith as part of work concerned with the development of methods for analyzing the response of large complex aerospace structures subjected to spatially distributed random loading.
Lyon's calculation showed that under certain conditions, the flow of energy between two coupled oscillators is proportional to the difference in the oscillator energies (suggesting a thermal analogy exists in structural-acoustic systems).
However, these conditions greatly restrict the use of SEA. Indeed, as seen in the validity diagram below, the domain of application of SEA is restricted to low coupling and diffuse fields.
Validity diagram of SEA and RADIOSITY methods
Since then, other methods were created in order to extend this domain, such as radiative transfer energy method (noted RADIOSITY) where local energies can be obtained contrary to SEA with a discretization of the border or Statistical Modal Energy Deformation Analysis (SmEdA) which neglect the diffuse field condition of SEA (more on ___).
How to use this website ?
This website is composed of three main points:
- a presentation of the three theories for high frequency vibroacoustics for neophytes and those wishing to know a bit more.
- a jupyter notebook on the application of each theory on simple subsystems.
- a list of industrial applications for each theory.
