Part 5 – Dynamic Analysis with FEM-System MEANS V11 91

Part 5 - Dynamic Analysis with FEM-SystemMEANS V11

This is a FEM calculation with FEM-System MEANS V10 of a 440 Hz Tuning Forkwith which you can adjust the musical instruments according to the reference toneor it are also used in the medicine for hearing tests.

The dimensions and material data must first be converted to metric units by USAmeasurement units. The tuning fork model is produced in MEANS V10 without footand connection as follows:

US Measurement:

E-Modulus = 29 msi = 29 000 psiPoisson ratio = 0.29Density = 0.283 lb/in³Thickness = 0.155 in

Metric Measurement:

E-Modulus = 200 000 N/mm²Poisson ratio = 0.29Density = 7850 kg/m³Thickness = 3.937 mm

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Create Arcs

Start the program "MEANS V11" using the desktop icon, select the „View“ tab andmenu „3. Line-Modus“ to switch to the Line Modus.

A new menu will appear on the right, select menu "Create Arcs" to create two arcs:

Circular Arc 1:Center: xm = 0, ym = 0, zm = 0Radius = 8.09Number of Nodes = 16Start Angle = 270End Angle = 90

Circular Arc 2:Center: xm = 0, ym = 0, zm = 0Radius = 4,153Number of Nodes = 16Start Angle = 270End Angle = 90

Also, in Node Modus, switch on the node numbering to see the 34 nodes better:

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Enter 4 single nodes

In line mode, enter the 4 single nodes of the left side one by one with "New" and"Create Nodes":

Node 35 = X = -75.17 Y = 8.09Node 36 = X = -75.17 Y = 4.15Node 37 = X = -75.17 Y = - 4.15Node 38 = X = -75.17 Y = - 8.09

Line

In Lines Modus select menu "Create Lines" menu and create the lines by firstclicking on the first node, then clicking on the end node, and selecting "CreateLines“ and creating the following 6 lines:

Line 17-35, line 35-36, line 36-34, and line 18-37, line 37-38, line 38-1

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2D Mesh Generator

In Line Modus, select the "2D Mesh Generator" menu to start MEANS-SHELL, thetuning fork can be seen as a template for the mesh generation.

First select the icon in the view, then the icon and generate a triangle meshwith 355 nodes and 496 TRI3S elements.

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Then select menu "File" and "MEANS V10 for DirectX9 starting" to get back the userinterface of MEANS V10 with the new triangle mesh.

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QUAD Meshing

Select the „Mesh Generation“ tab and menu "QUAD-Meshes,Refine, Delete..“ togenerate a Quad-Mesh with the well-known Tetraeder Mesh Generator NETGEN.QUAD Meshing needs a STEP file from your CAD System or a triangle mesh fromMEANS-SHELL. Now select a Mesh granularity „very fine“ und generate a QUADmesh of 5157 QUA4S elements and 5124 nodes.

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Use menu "File" and "Export Mesh" to export the FEM mesh under the name"test.fem" to the default debug quadmesh directory so that it can be automaticallyconverted and imported into MEANS V10.

After the model check, a QUAD mesh with 6201 nodes is obtained.

Hexahedral model

Select menu "QUAD-Meshes, Refine, Delete...“ again and the register "Extrusion" togenerate a Hexaeder mesh with 39944 HEX8 elements and 43407 nodes. Use thefollowing setting:

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Create Boundary Conditions

In the Node Modus, create the following Range of Node

And choose menu "Step 2: Create Boundary Conditions" as well as the Selection"Select Nodes" to clamp the tuning fork with 7 nodes in the X, Y and Z directions.

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Dynamic Analysis

Select the „FEM Analysis" tab and "2. Dynamics" and calculate the lowest 15eigenfrequencies with the Quick Solver with the following setting.

Calculate the eigenvalue with the quick quick solver:

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Results comparison

The eigenfrequencies calculated with different meshes and element types arecompared with the eigenfrequencies of the FEM system LS-DYNA. The resultcomparison shows good agreement with almost all element types. The greatestdeviations occur with the linear tetrahedral element TET4. But if the same TET4mesh is calculated with the TET4X8 developed by HTA software, the results willimprove over 30%

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Eigenfrequency No. 4 = 449 Hz (first bending Eigenfrequency)

Eigenfrequency No. 8 = 2817 Hz (second bending Eigenfrequency)

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Eigenfrequency No. 12 = 7382 Hz (third bending Eigenfrequency)

Eigenfrequency No. 13 = 8398 Hz (first torsion Eigenfrequency)