Modal Analysis
Problem Description
Modal analysis of a cantilever beam having uniform cross section is performed to calculate the mode shapes and natural frequencies of the beam.
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Geometry
A cantilever beam of length 1m , having rectangular cross section is studied.
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Mesh Generation
We model the beam using 2D plane stress quadrilateral element and 8 node hexahedral element.
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Import Mesh
Now import the mesh file saved in file 2DPlaneBeam.m which is exported from GMSH.
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Define Analysis Settings
Select type of analysis as modal and using the analysis settings dialog box , define mode extraction method for the analysis.
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Define Material Properties
Select material of torque arm from material editor. We can also add new materials from the editor.
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Define Element Properties
We define the behavior of 2D 4 node quadrilateral elements as plane stress.
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Now we define the formulation of quadrilateral elements as Enhanced Strain method.
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Select the stiffness matrix integration rule as 2x2.
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Select the mass matrix integration rule as 3x3 for higher accuracy.
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Specify the thickness as 20 mm.
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Apply Boundary Conditions
The beam is fixed at its left end using boundary ID 4.
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Solve
Start Modal solver to solve the model.
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Results
Using the post processor tab, we plot the required Mode shapes.
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3D Model
Using the same procedure we solve for 3D model of the beam using Hexahedral elements .
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Results
In 3D analysis, the order of mode shapes change as degree of freedom of the model increases.
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Lateral Bending Mode
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Vertical Bending Mode
Summary
In this tutorial we have prepared the geometry and generated the mesh in GMSH. The mesh is then imported in SCIFESOL to perform modal analysis.
Watch video tutorial
note:Script file for above analysis is available in the SCIFESOL package.