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# Modal Analysis: Mode Shape and Curve Fitting

## Modal Analysis: Mode Shape and Curve Fitting

(OP)

I hope someone can help me out. I am new in experimental modal analysis and trying to learn it. There are a few things I am having difficulty to undersatnd. These are:

1. Mode shape scaling: It is suggested that scaling the mode shape for Unity Modal Mass preserves the mass and stiffness characteristics of the system. I cannot understand the reasoning behind it. Is the mode shape scaled to Unity Modal Mass in experimental modal analysis? Yet again, it is said that mode shape scaling is critical for structural modification. I cannot understand how mode shape scaling relates to structural modification or why structural modification cannot be done without mode shape scaling.

2. When we do curve fitting for extracting modal parameters, modal order needs to be specified. Does modal order mean the maximum number of modes active in the response or double the maximum number of modes active in the response? If double, then what is the reason for doubling?

I apologize if the questions sound dumb. Thank you very much for your help.

IMHK

### RE: Modal Analysis: Mode Shape and Curve Fitting

Wow, it's a subtle question.

Suppose that Ai are the experimental mode shapes (a set of vector). Their amplitude can be very low. So the modal masses can also be very low. This is not good.
When modal mass is normalized, something doesn't change : the Eigen frequency .
Because an Eigen frequency is just a ratio between modal stiffness and modal mass.

When you do that, the modal mass matrix is therefore the identity matrix. This is very useful from numerical point of view. Indeed, when you gonna do your SDM (Structural Dynamic Modification), you will have to inverse the modal mass matrix and compute this matrix: (M)-1K.

When mass or stiffness are added in order to do structural modification, you can suppose that the modal mass matrix won't be ill-conditionned.

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