https://github.com/krproject-tech/membrane_vibration_fdm
Finite difference method to solve the membrane vibration problem
https://github.com/krproject-tech/membrane_vibration_fdm
finite-difference-method matlab wave-equation
Last synced: 8 months ago
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Finite difference method to solve the membrane vibration problem
- Host: GitHub
- URL: https://github.com/krproject-tech/membrane_vibration_fdm
- Owner: KRproject-tech
- License: mit
- Created: 2024-05-05T11:36:58.000Z (almost 2 years ago)
- Default Branch: main
- Last Pushed: 2024-05-07T15:54:13.000Z (almost 2 years ago)
- Last Synced: 2025-02-01T05:41:57.553Z (about 1 year ago)
- Topics: finite-difference-method, matlab, wave-equation
- Language: MATLAB
- Homepage:
- Size: 78.1 KB
- Stars: 0
- Watchers: 1
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- License: LICENSE
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README
# Membrane_vibration_FDM
Finite difference method (FDM) to solve the membrane vibration problem
**Communication**
**Language**
## Directory
└─membrane_PDE
├─save
│ └─fig
└─ToolBoxes
## Preparation before analysis
__[Step 1] Install the ToolBoxes__
The following ToolBoxes in “./cores/ToolBoxes/” are required,
__For plotting results:__
* __“mmwrite”__ by Micah Richert:
https://jp.mathworks.com/matlabcentral/fileexchange/15881-mmwrite
## Governing equation
$$
\begin{aligned}
\mathrm{PDE}&: \partial^2_t u(x,y,t) - t_x \partial^2_x u(x,y,t) - t_y \partial^2_y u(x,y,t) = 0, \ (x,y) \in [0, L_x] \times [0, L_y], \\
\mathrm{BC} &: u(x,y,t) = 0, \ (x,y) \in ([0, L_x] \times \\{0, L_y \\}) \cup (\\{0, L_x \\} \times [0, L_y]), \\
\mathrm{IC} &: u(x,y,0) = \left( \sin{\pi \frac{x}{L_x}}\sin{\pi \frac{y}{L_y}} \right)^3.
\end{aligned}
$$
## Demonstration movie
[](https://www.youtube.com/watch?v=_kEdkMvdkE4)