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## Modal Mass calculation

Posted Aug 14, 2012, 10:06 AM EDT MEMS & Nanotechnology, MEMS & Nanotechnology, Structural Mechanics & Thermal Stresses Version 4.2a, Version 4.3, Version 4.3a 9 Replies

Is it possible to calculate the modal mass for a particular mode shape? Can someone please explain how to do it.

in the eigenfrequency solver sequence (quite deep down in the solver tree), you have the option for the normalisation of the eigenvectors/frequencies, such as RMS, and model mass, once changed you need to rerun your solver, then your mass participation factors (in kg but units are not mentioned) are the SQUARE of the model participation factors (see the Structural doc)

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Good luck

Ivar

the square of the partcpation factor is the mass, ifyou sum the squares for many modes you will get the total mass per direction

I's described somewhere in the doc too (try a search ;)

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Good luck

Ivar

Thanks for the reply.

Just to clear my head.

For example,

for a particular mode...

MPF in u direction=a

MPF in v direction=b

MPF in w direction=c

so the effective mass for that mode would be= a^2+b^2+c^2

please correct me if I'm wrong.

Thanks

The effective masses are per cartesian orthogonal directions, and each add up to Mass ="total mass" = int1(solid.rho) over all domains.

so when I ask for the mass participation factor I use (MPF_mod1.u)^2/Mass*100 to get the % of total mass per mode

so if you take a canteliever and see 20% in u (or x), at one frequency and 30% in v (or y) at another, you can see that this particular mode has its motion predominantly along x, respective y.

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Good luck

Ivar

I have a total mass of 2.217E-5 kg for clamped edge circular plate.

My MPF for the first mode of vibration are

MPFu= 4.703E-8

MPFv=1.14201E-8

MPFw=0.00343

so the modal mass I get is: (MPFu)^2+(MPFv)^2+(MPFw)^2=1.17649E-5 kg

Now the problem is I don't know whether it is correct or not as don't have any analytical results to compare with. Also, as COMSOL scales its variable, are these MPFs scaled?

i believe you should add up the square of the modal masses for the first N modes direction by direction, then it should get to the total mass, if you take enough modes.

What I do is to calculate the total mass by an variable and an integration of material.rho over all domain(s) and then I use the Derived Values - Global Evaluation to give

MPF_mod1.u^2 / TotalMass*100

to have the mass participation factors in % of the total mas (per direction, separately in u,v,w)

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Good luck

Ivar

I would like to add one question to the discussion.

After running my simulation and computing the effective masses for each direction, let's call them m_eff_x, m_eff_y, m_eff_z, I would like to combine them in order to obtain a meaningful effective mass for each mode i (something like sum over all directions instead of sum over all modes -> m_eff_i = function(m_eff_x_i, m_eff_y_i, m_eff_z_i) ).

Does such a combination exist? Which formula defines it?

Thank you very much for your help!

Best regards

luca

normally the effective mass variable are normalised such that the sum of the square of each participative mass value, per direction adds up to the total mass of the object, so what I often do is to normalise mode_mass_x^2 / Total_Mass and check that I select sufficient modes to get 70-80% or more of the total mass per direction

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Good luck

Ivar

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