# Mass participation factor and it's role in modal anlysis

• subha_iit
In summary, it's up to the individual engineer to decide how many modes to check for resonance. For complex geometry or systems with higher frequencies, it's possible that the nodes of vibration may be located on the geometry itself. It is also possible that the amplitude at higher modal frequencies may be higher than that of lower modal frequencies. For continuous systems, there are likely to be at least six fundamental frequencies.

#### subha_iit

When we are doing modal analysis, how many mode should we extract? For complex piping system with thicker wall and less diameter the no of modes to be consider is a difficult task. How can I define upto how many modes should I evaluate for the modal results and check it with external excitation.

I am surprise there is no clear cut answer to this till now, as far as I know and I got. There are very few documents where they have written the mass participation factor, and it's direction, external excitation direction and mode shape determine the no of modes we have to consider. As far as my understanding, I also think like that only and do the same.

But there is a little bit confusion with my friends, who told me only first few modes (for piping four modes) is need to examine for resonance, no need to go for higher modes even though mass participation factor is high enough!

And can anyone tell me for complex 3d geometry, is that the nodes of vibration always lie on the geometry itself??

And is it possible that the amplitude at higher modal frequency can be higher than that of lower modal frequency??

And for continuous systems how many fundamental frequency are there??

As a general rule, you probably want to look at as many modes as it takes to fully explore the frequency excitation range you're expecting. For piping, look at things like pumps and motors, find what frequency they operate at (probably no higher than a couple hundred Hz) and go from there.

Typically for structural excitations I look at 6 modes minimum (obvious) and don't normally look at more than 10 modes or a couple of hundred Hz (say 500 Hz).

For me, my compressor frequency is very low(in the range of 47 to 48) and we always avoid the range from [0-compressor frequency+0.1*compressor frequency]. I don't have any doubt in that. But we are also look for higher frequencies (upto six modes) if that frequency is matching with the harmonics(like 1x, 2x,3x,4x...) of the compressor frequency.

Till now we are not considering the mass participation factor for targeting the modes. But if the first six modes only contribute 60% mass participation, and above 12 th mode also if for 13 mode the mass participation factor is higher should we check with compressor harmonics upto that or not!

## 1. What is the mass participation factor?

The mass participation factor is a dimensionless quantity that represents the amount of modal mass that is participating in a specific mode of vibration. It is usually expressed as a percentage and is used to evaluate the significance of a mode in a modal analysis.

## 2. How is the mass participation factor calculated?

The mass participation factor is calculated by dividing the modal mass of a specific mode by the total mass of the system. This value is then multiplied by 100 to get the percentage of mass participation.

## 3. What is the significance of the mass participation factor in modal analysis?

The mass participation factor is important because it helps in identifying the most significant modes in a system. A higher mass participation factor indicates that a large portion of the system's mass is involved in that mode, making it more critical in the overall dynamic behavior of the system.

## 4. How does the mass participation factor affect the natural frequencies of a system?

The mass participation factor has a direct impact on the natural frequencies of a system. A higher mass participation factor means that more mass is involved in a particular mode, which results in a lower natural frequency for that mode. On the other hand, a lower mass participation factor leads to a higher natural frequency for that mode.

## 5. Can the mass participation factor be used to optimize a system's design?

Yes, the mass participation factor can be used to optimize a system's design by identifying the most significant modes and their corresponding natural frequencies. Engineers can then make design changes to reduce the mass participation factor of unwanted modes, leading to a more efficient and reliable system.