COMSOL 6.4 - Shape Optimization of a Tuning Fork

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Shape Optimization of a Tuning Fork

This model extends the model Tuning Fork in the COMSOL Multiphysics Application Library by adding a second study, in which the Parametric Sweep is replaced by an Optimization study node. The prong length Lp = L + πRb/2, where L is the straight cylindrical part and Rb is the prong base radius, is determined by minimizing the objective function (f − 440 Hz)2, where f is the fundamental frequency of the fork. The result agrees with that found in the original model version. For a detailed description of the model geometry and setup, see Tuning Fork in the COMSOL Multiphysics Application Library.

Optimization_Module/Shape_Optimization/tuning_fork_shape_optimization

Modeling Instructions

In this model version you determine the prong length by using an study node.

Application Libraries

1

From the menu, choose .

2

In the window, select > > in the tree.

3

Add a parameter for scaling the prong length using the interface, so that the problem can be solved using gradient based optimization.

Global Definitions

1

In the window, under click .

2

In the window for , locate the section.

3

In the table, enter the following settings:


Name	Expression	Value	Description
scaleZ	1	1	Z scaling

Component 1 (comp1)

Prescribed Deformation 1

1

In the toolbar, click

and choose .

2

Select Domains 1 and 3 only.

3

In the window for , locate the section.

4

Specify the dx vector as


0	X
0	Y
Zg*(scaleZ-1)	Z

The Zg variable refers to the z-component in the geometry frame.

Define a to keep track of the prong length in the material frame.

Scaled Prong Length

1

In the toolbar, click

and choose .

2

In the window for , type Scaled Prong Length in the text field.

3

In the text field, type scaledL.

4

Locate the section. In the text field, type L*scaleZ.

To keep the results of the parametric study, add a second study with an step set up the same way as before.

1

In the toolbar, click

to open the window.

2

Go to the window.

3

Find the subsection. In the tree, select > .

4

Click the button in the window toolbar.

5

In the toolbar, click

to close the window.

Step 1: Eigenfrequency

1

In the window for , locate the section.

2

Select the checkbox. In the associated text field, type 1.

3

In the text field, type 440.

Now, add optimization. The solver is generally the fastest of the derivative-free solvers when the objective function is smooth.

General Optimization

1

In the toolbar, click

and choose .

2

In the window for , locate the section.

3

From the list, choose .

4

Locate the section. In the table, enter the following settings:


Expression	Description	Evaluate for
(freq-440[Hz])^2		Eigenfrequency

Next, add the control parameter. You can choose between the global parameters defined in your model. In this case, use the scaling parameter.

5

Locate the section. Click

.

Specify a length scale and suitable bounds.

6

In the table, enter the following settings:


Parameter	Initial value	Scale	Lower bound	Upper bound	Unit
scaleZ (Z scaling)	1	1	0.8	1.2

The setup is now complete.

7

In the toolbar, click

.

Probe Plot Group 2

1

button in the toolbar.

The default plot shows the eigenmode that corresponds to the optimized value of the cylinder length L.

Objective Probe Table 3

The optimized value of the cylinder length can be seen in the Objective Table:

The resulting cylinder length is close to 7.91 cm, which agrees with the value determined using a parametric sweep.

Probe Plot Group 2

button in the toolbar.