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# solvepdeeig

Solve PDE eigenvalue problem specified in a PDEModel

## Syntax

``result = solvepdeeig(model,evr)``

## Description

example

````result = solvepdeeig(model,evr)` solves the PDE eigenvalue problem in `model` for eigenvalues in the range `evr`.```

## Examples

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Solve for several vibrational modes of the `BracketTwoHoles` geometry.

The equations of elasticity have three components. Therefore, create a PDE model that has three components. Import and view the `BracketTwoHoles` geometry.

```model = createpde(3); importGeometry(model,'BracketTwoHoles.stl'); pdegplot(model,'FaceLabels','on','FaceAlpha',0.5)```

Set F1, the rear face, to have zero deflection.

`applyBoundaryCondition(model,'dirichlet','Face',1,'u',[0;0;0]);`

Set the model coefficients to represent a steel bracket. For details, see 3-D Linear Elasticity Equations in Toolbox Form.

```E = 200e9; % elastic modulus of steel in Pascals nu = 0.3; % Poisson's ratio specifyCoefficients(model,'m',0,... 'd',1,... 'c',elasticityC3D(E,nu),... 'a',0,... 'f',[0;0;0]); % Assume all body forces are zero```

Find the eigenvalues up to `1e7`.

`evr = [-Inf,1e7];`

Mesh the model and solve the eigenvalue problem.

```generateMesh(model); results = solvepdeeig(model,evr);```
``` Basis= 10, Time= 20.76, New conv eig= 0 Basis= 11, Time= 20.99, New conv eig= 0 Basis= 12, Time= 21.18, New conv eig= 0 Basis= 13, Time= 21.38, New conv eig= 0 Basis= 14, Time= 21.61, New conv eig= 1 Basis= 15, Time= 21.82, New conv eig= 2 Basis= 16, Time= 22.03, New conv eig= 2 Basis= 17, Time= 22.21, New conv eig= 2 Basis= 18, Time= 22.37, New conv eig= 4 End of sweep: Basis= 18, Time= 22.38, New conv eig= 4 Basis= 14, Time= 24.30, New conv eig= 0 End of sweep: Basis= 14, Time= 24.31, New conv eig= 0 ```

How many results did `solvepdeeig` return?

`length(results.Eigenvalues)`
```ans = 3 ```

Plot the solution on the geometry boundary for the lowest eigenvalue.

```V = results.Eigenvectors; subplot(2,2,1) pdeplot3D(model,'ColorMapData',V(:,1,1)) title('x Deflection, Mode 1') subplot(2,2,2) pdeplot3D(model,'ColorMapData',V(:,2,1)) title('y Deflection, Mode 1') subplot(2,2,3) pdeplot3D(model,'ColorMapData',V(:,3,1)) title('z Deflection, Mode 1')```

Plot the solution for the highest eigenvalue.

```figure subplot(2,2,1) pdeplot3D(model,'ColorMapData',V(:,1,3)) title('x Deflection, Mode 3') subplot(2,2,2) pdeplot3D(model,'ColorMapData',V(:,2,3)) title('y Deflection, Mode 3') subplot(2,2,3) pdeplot3D(model,'ColorMapData',V(:,3,3)) title('z Deflection, Mode 3')```

## Input Arguments

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PDE model, specified as a `PDEModel` object. The model contains the geometry, mesh, and problem coefficients.

Example: `model = createpde(1)`

Eigenvalue range, specified as a two-element real vector. `evr(1)` specifies the lower limit of the range of the real part of the eigenvalues, and may be `-Inf`. `evr(2)` specifies the upper limit of the range, and must be finite.

Example: `[-Inf;100]`

Data Types: `double`

## Output Arguments

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Eigenvalue results, returned as an `EigenResults` object.

## Tips

• The equation coefficients cannot depend on the solution `u` or its gradient.