FEATool Multiphysics
v1.10 Finite Element Analysis Toolbox |

Vibrations of a Circular Membrane

This example computes the the vibration modes, eigenvalues, and frequencies for a circular drum or membrane. The membrane is modeled by the unit circle and assumed to be attached to a rigid frame. The Poisson PDE equation is used with the *Eigenvalue* solver to compute the solution.

This model is available as an automated tutorial by selecting **Model Examples and Tutorials...** > **Classic PDE** > **Vibrations of a Circular Membrane** from the **File** menu. Or alternatively, follow the step-by-step instructions below.

- To start a new model click the
**New Model**toolbar button, or select*New Model...*from the*File*menu. - Select the
**Poisson Equation**physics mode from the*Select Physics*drop-down menu. - Press
**OK**to finish the physics mode selection. - To create a circle or ellipse, first click on the
**Create circle/ellipse***Toolbar*button. Then left click in the main plot axes window, and hold down the mouse button. Move the mouse pointer to draw the shape outline, and release the button to finalize the shape. - Select
**E1**in the geometry object*Selection*list box. - To modify and edit the selected ellipse, click on the
**Inspect/edit selected geometry object***Toolbar*button to open the*Edit Geometry Object*dialog box. - Enter
`0 0`

into the*center*edit field. - Enter
`1`

into the*x*edit field._{radius} - Enter
`1`

into the*y*edit field._{radius} - Press
**OK**to finish and close the dialog box. - Switch to
**Grid**mode by clicking on the corresponding*Mode Toolbar*button. - Enter
`0.1`

into the*Grid Size*edit field. - Press the
**Generate**button to call the grid generation algorithm. - Switch to
**Equation**mode by clicking on the corresponding*Mode Toolbar*button. - Press
**OK**to finish the equation and subdomain settings specification. - Switch to
**Boundary**mode by clicking on the corresponding*Mode Toolbar*button. - Select
**1**,**2**,**3**, and**4**in the*Boundaries*list box. - Select
**Dirichlet boundary condition**from the*Poisson Equation*drop-down menu. - Enter
`0`

into the*Dirichlet coefficient*edit field. - Press
**OK**to finish the boundary condition specification. - Switch to
**Solve**mode by clicking on the corresponding*Mode Toolbar*button.

Open the *Solver Settings* dialog box, and select the **Eigenvalue** solver which per default will try to find the *6* smallest eigenvalues with corresponding eigenvectors.

- Press the
**Settings***Toolbar*button. - Select
**Eigenvalue**from the*Solution and solver type*drop-down menu. Press the

**Solve**button.

Plot the first, second, and fourth modes and confirm that they feature a corresponding number of peaks and troughs.

- Press the
**Plot Options***Toolbar*button. - Select the
**Height Expression**check box. - Select
**25.9617 (0.810936 Hz)**from the*Available solutions/eigenvalues (frequencies)*drop-down menu. - Press
**OK**to plot and visualize the selected postprocessing options.

The frequency of the second and third mode the to first one should be a factor *1.59* times higher, fourth and fifth *2.14*, and sixth *2.30*.

The *vibrations of a circular membrane* classic pde model has now been completed and can be saved as a binary (.fea) model file, or exported as a programmable MATLAB m-script text file, or GUI script (.fes) file.