COMSOL 6.4 - Optimization of a Tuning Fork

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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/Design_Optimization/tuning_fork_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

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.

1

In the window, click .

2

In the window for , type Study 1: Sweep in the text field.

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

Study 2: Optimization

1

In the window, click .

2

In the window for , type Study 2: Optimization in the text field.

Parameter Optimization

1

In the toolbar, click

and choose .

2

In the window for , locate the section.

3

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 prong length.

4

Locate the section. Click

.

Specify a length scale and suitable bounds.

5

In the table, enter the following settings:


Parameter	Initial value	Lower bound	Upper bound	Unit
L (Cylinder length)	7.8[cm]	7[cm]	9[cm]	m

The setup is now complete.

6

In the toolbar, click

.

Mode Shape (solid) 1

1

button in the toolbar.

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

Objective 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.

Mode Shape (solid) 1

1

button in the toolbar.

2

In the window, expand the > node.

Eigenfrequencies (Study 1), Mode Shape (solid)

1

In the window, under , Ctrl-click to select and .

2

Right-click and choose .

In the window for , type Sweep in the text field.

Eigenfrequencies (Study 2: Optimization), Mode Shape (solid) 1

1

In the window, under , Ctrl-click to select and .

2

Right-click and choose .

In the window for , type Optimization in the text field.

Length vs. Frequency

1

In the toolbar, click

.

2

In the window for , type Length vs. Frequency in the text field.

3

Locate the section. From the list, choose .

1

Right-click and choose .

2

In the window for , locate the section.

3

In the table, enter the following settings:


Expression	Unit	Description
freq	Hz	Sweep

4

Locate the section. From the list, choose .

5

Click to expand the section. Find the subsection. Clear the checkbox.

1

Right-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	Unit	Description
freq	Hz	Optimization

5

Locate the section. From the list, choose .

6

In the text field, type L.

7

Click to expand the section. Find the subsection. From the list, choose .

8

In the toolbar, click

.

9

button in the toolbar.