Aeroelastic flutter solution based on dynamic modes interpolation
Aeroelastic flutter solution based on dynamic modes interpolation
University of Liège, 2021
University of Liège, 2021
:warning:
This code is a partial transcription of the method discribed in [this PhD thesis](https://hdl.handle.net/2268/245578) for calculating flutter using high-fidelity aerodynamics. It is given as a reference and is not intented for general purpose analysis and optimization. Users interested in practical flutter-constrained optimization problems should explore the following codes:
aedmi computes the solution of the aeroelastic equation `u/l * M * p^2 + K - 1/2*r*u^2 * Q(k) = 0`, where `M` and `K` are the modal mass and stiffness matrices of the structure, `Q` is the modal aerodynamic loads matrix, `u` and `r` are the freestream fluid velocity and density, and `l` is a reference length. `p` is a non-dimensional parameter defined as `p = (g+1i)*k`, where `g` is the true damping and k is the reduced frequency.
aedmi computes the solution of the aeroelastic equation `u/l * M * p^2 + K - 1/2*r*u^2 * Q(k) = 0`, where `M` and `K` are the modal mass and stiffness matrices of the structure, `Q` is the modal aerodynamic loads matrix, `u` and `r` are the freestream fluid velocity and density, and `l` is a reference length. `p` is a non-dimensional parameter defined as `p = (g+1i)*k`, where `g` is the true damping and k is the reduced frequency.
The flutter solution is obtained using a kind of reduced order modeling technique called dynamic mode interpolation. This technique was originally developed by Hüseyin Güner during his [doctoral thesis](http://hdl.handle.net/2268/245578). Practically, the mode shapes of the structure are first pre-computed. Then, the aerodynamic loads at some reference Mach numbers and reduced frequencies are pre-computed by imposing the motion for each structural mode shape. Finally, aedmi will compute the modal load matrix `Q` for each Mach number and reduced frequency, and solve the aeroelastic system by interpolating this matrix for any reduced frequency.
The flutter solution is obtained using a kind of reduced order modeling technique called dynamic mode interpolation. This technique was originally developed by Hüseyin Güner during his [doctoral thesis](http://hdl.handle.net/2268/245578). Practically, the mode shapes of the structure are first pre-computed. Then, the aerodynamic loads at some reference Mach numbers and reduced frequencies are pre-computed by imposing the motion for each structural mode shape. Finally, aedmi will compute the modal load matrix `Q` for each Mach number and reduced frequency, and solve the aeroelastic system by interpolating this matrix for any reduced frequency.
## Requirements
## Requirements
aedmi needs a python3 interpreter and its libraries, as well the `numpy`, and `scipy`. The `vtk` packages is also needed to read VTK formatted date, and the `matplotlib` package is optional (needed to save the graphical solution to disk).
aedmi needs a Python3 interpreter and its libraries, as well the `numpy`, and `scipy`. The `vtk` packages is also needed to read VTK formatted data, and the `matplotlib` package is optional (needed to save the graphical solution to disk).
### Linux
### Linux
If you are using Linux, you can install python and the packages using Aptitude.
If you are using Linux, you can install python and the packages using Aptitude.
