Modal Scaling

Modal scaling is a simple technique to predict the response of the model/structure without damping effects and not even performing complicated and time consuming frequency response analysis.

Method:

Let's assume that response for the cantilever beam shown below need to predicted under external vibration.

Where δ is measured modal displacement from FEA 

Acceleration (a_test) need to be measured on the actual vehicle at max displacement location (In this case tip of cantilever).

Acceleration (a_mod) is calicluated as per the formula

                          a_mod= ω²_* δ

Where  ω=2 π f

 the modal displacement measured at the same location in FEA model

 

   Modal Scaling Factor=a_test/a_mod         

The stresses from FEA are measured, as there are not actual stress values , they will be multiplied by the modal scaling factor  to get the actual stress values

                    

                                                       σ_act=Modal scaling factor * σ

Once the actual stress values are obtained they can be compared against acceptable limit or fatigue evaluation can be performed.

Refer to the excel sheet for an example

https://docs.google.com/spreadsheets/d/e/2PACX-1vQE0ZoY8OB63NsBemDxmEBZfRNeThccRV_u8zY9Hqt3oZD3bMoP9L56L4dw3PwMDBlr3e7k-1VAUKSi/pubhtml

 Advantages of the Modal scaling:

This method is very effective in the first pass of the design where predicting the natural frequencies are very important.

 Disadvantages of the Modal scaling:

1. The  problem with this method is measured displacement should be relevant and the value should not be measured close to the the node of the mode. 

2.100% energy assumed to be participating in the mode which is very conservative approach.

3. The damping effects are ignored.