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Lecture 25: Large Scale Systems: 1. Guyan Reduction

This lecture discusses approaches for reducing the size of large dynamic systems when performing vibration analysis using finite element methods. It covers Guyan reduction which eliminates degrees of freedom to reduce the eigenvalue problem that is solved. It retains master degrees of freedom and eliminates slave degrees of freedom. It also covers inverse iteration, an iterative method to compute frequencies and mode shapes for multi-degree of freedom systems by rearranging the equations of motion and using the dynamic matrix. Examples are provided to demonstrate both methods.

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89 views6 pages

Lecture 25: Large Scale Systems: 1. Guyan Reduction

This lecture discusses approaches for reducing the size of large dynamic systems when performing vibration analysis using finite element methods. It covers Guyan reduction which eliminates degrees of freedom to reduce the eigenvalue problem that is solved. It retains master degrees of freedom and eliminates slave degrees of freedom. It also covers inverse iteration, an iterative method to compute frequencies and mode shapes for multi-degree of freedom systems by rearranging the equations of motion and using the dynamic matrix. Examples are provided to demonstrate both methods.

Uploaded by

ali381
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF, TXT or read online on Scribd
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53/58:153 Lecture 25 Fundamental of Vibration

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Lecture 25: Large scale systems


Reading materials: 10.1 and 10.2

1. Guyan Reduction

Finite element discretization results in a large dynamic system. Therefore,


computation is intensive.

One approach is reducing the size of the eigenvalue problem that must be
solved to compute the mode shapes and frequencies.

Generalized eigenvalue problem

In the reduction process, choosing an appropriate set of DOFs that are to be


retained. Those DOFs are called master DOFs while the ones eliminated are called
slave DOFs.

Relationship between the total DOFs (#n) and the master DOFs (#m)s

Static equilibrium equations

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53/58:153 Lecture 25 Fundamental of Vibration
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Example 1

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53/58:153 Lecture 25 Fundamental of Vibration
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Reduced matrices

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53/58:153 Lecture 25 Fundamental of Vibration
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For original problem

2. Inverse iteration

An iterative method to compute frequencies and modes shapes for multi-degree


freedom systems.

Rearrange

Dynamic matrix

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53/58:153 Lecture 25 Fundamental of Vibration
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Example 2

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53/58:153 Lecture 25 Fundamental of Vibration
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