understanding mass participation

[RamiHabchi93]

hi,
I am trying to understand basics of mass participation factor.
My questions are:
1-could someone help me figure out why sum of effective mass of all modes equals the total mass of the system.
2-the higher the mass participation factor the more the mode contribute in total response.why?

 

[KootK]

1-could someone help me figure out why sum of effective mass of all modes equals the total mass of the system.

Because, when all is said and done, the entire mass of the system must be accounted for in order for the technique to be valid. It wouldn't make any sense for a portion of the system mass to simply not participate in the vibratory response, right? We designed the technique to have this aspect of conservation built into it.

2-the higher the mass participation factor the more the mode contribute in total response.why?

It's kind of a chicken and egg thing. We devised the technique specifically so that we would know how much each mode of vibration contributes to total response. And, low and behold, the technique does allow us to know how much each mode of vibration contributes to total response.

Your questions are a bit irrational in the sense that you're effectively asking:

Why does this mathematical technique designed to do [A & B] do [A & B]? The technique does [A & B] because we formulated it to do [A & B]. When you think of it that way, it's self evident. It's a bit like why asking why 2 + 3 = 5 or why 3 > 2. Those things are true because we formulated or system of mathematics such that they would be.

I don't mean for any of this to be condescending. I simply think that you need to see things in this light in order to recognize that these techniques are man made formulations designed to produce exactly the results that you're questioning.

 

[RamiHabchi93]

I only know the formula of mass participation factor.but how defining it in this way makes it sum up to total mass I could not prove it and this is the problem.and same for my second question.I mean modal participation factor is visible in the differential equations but mass participation factor is not.so it makes sense that the higher the modal participation factor is,the larger the amplitude of the mode.but for mass participation i couldnt prove it.

 

[Agent666]

Maybe you are not considering all the modes possible for your structure. You have likely made an error, and you have not given any information regarding what you have done except 'it doesn't work'. Try a simple structure with 2-3 modes to minimise the chance of errors and see if it works.

 

[RamiHabchi93]

I think I found solution correct me if I am wrong.