# Guyan reduction for dynamic analysis

1. Dec 1, 2011

### svishal03

Please cana nyone physically explain the meaning of Guyan reduction for dynamic analysis? I have an ide that it relates to the erduction in the degreeso f freedom of the structure for FE analsysis such that the model is still accurate but performs (in relation to the time required for completing the analysis) much better.

Can anyon explain how Guyan reduction is carried out principally ? (without going into the math part)? Please help

2. Dec 1, 2011

### AlephZero

The basic idea is

1. You choose a subset of the degrees of freedom in the FE model that are enough to (approximately) represent the motions of the structure that you are interested in.

2. You then redistribute the mass properties of the model onto the selected degrees of freedom, by assuming you can "interpolate" the motion for the other degrees of freedom based only on the static behaviour of the structure, or in other words using only the stiffness matrix.

3. You solve the "reduced" model using the selected degrees of freedom

4. You then approximate the response of the "full" model using the same assumptions as in step 2.

I think it's pretty much impossible to explain "how to do it " in any more detail without writnig down the math.

There are algorithms that automatically select which variables to keep in the reduced model in step 1 (actually, it would be more accurate to say the algorithms select which variables NOT to keep), but the general idea is the same whether the selection is made manually by the user or automatically by the software. Either way, the quality of the answers depends (obviously) on choosing an appropriate set of variables to keep.

3. Dec 1, 2011

### svishal03

Dear Sir,

Thanks for the response.

That means the number of mode shapes you solve in Guyan reduction only corresponds to the reduced degrees of freedom ? (because number of mode shapes = number of degrees of freedom)

Vishal

4. Dec 1, 2011

5. Dec 1, 2011

### AlephZero

That's right.

6. Dec 2, 2011

### svishal03

Why are Guyan models not aplicable to structures with cyclic symmetry?

7. Dec 3, 2011

### AlephZero

There is no reason why you can't use it if you want, provided you keep all the variables on the cyclic boundaries in the reduced model.

8. Dec 3, 2011

### svishal03

Thanks sir-can you give an example of what you mentioned with reference to analysis of bladed disc which was discussed in cyclic symmetry post (wherein you put your inputs to the question)

With respects,
Vishal

9. Dec 3, 2011

### AlephZero

I learned this stuff about 25 years ago, partly by figuring it out for myself. I don't have any references to current books or website with the theory. The documents I do have are not in the public domain.

Commercial FE software like Ansys, Abaqus, Nastran etc that have these capabilities shouldl have the basic equations somewhere in the documentation, e.g.
http://www.ansys.spb.ru/pdf/present/cyclic_symmetry_analysis.pdf

I don't mind answering questions in general terms, but I'm not going to spend time doing Google searches for you, sorry!

10. Dec 4, 2011

### svishal03

Sir-I'm sorry if I overdid with the queries.

Thanks for your help, it was very useful.

Yes, shall keep in mind what you said below.

Again-I'm sorry.

Vishal