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[Xansys] Ansys generalized mass calculation
 
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christopher.wright
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Joined: 17 Jun 2009
Posts: 927

PostPosted: Fri Apr 27, 2012 8:36 am  Reply with quote

On Apr 27, 2012, at 6:51 AM, Kazantzis wrote:

Quote:
I want to calculate the generalized mass of one mode after
performing a modal analysis of a bridge. The definition of
generalized mass is: ΦT M Φ where M is mass matrix and Φ is the
eigenvector. I choose MODOPT, , , , , ,ON in order to normalize
modes shapes to unity and not to the mass matrix (otherwise the
generalized mass is equal to 1).

You need to RTFM a little more carefully. What you're calling
'generalized mass' is properly termed 'Effective Mass' and it's
listed in the ANSYS Classic output file with all the modal data
summary. You can use a *GET to retrieve it from the results file.
It's also equal to the square of the participation factor. You don't
need to make a special effort to normalize the eigenvectors to unity
to get it.

Of course this is for Classic. I haven't any idea how (ho-hum) WB
does it, but I suspect it's the same.

Christopher Wright P.E. |"They couldn't hit an elephant at
chrisw@skypoint.com | this distance" (last words of Gen.
.......................................| John Sedgwick, Spotsylvania
1864)
http://www.skypoint.com/members/chrisw/

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panagiotis.kazantzis
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Joined: 29 Jun 2009
Posts: 7

PostPosted: Mon Apr 30, 2012 12:57 am  Reply with quote

Dear Christopher

Thank you for your response to my question.

The effective mass is not equal to the generalized mass.

The effective mass is: Mei = γi 2 / ΦT M Φ (where γi = ΦiT M D,
participation factor).

The generalized mass is: ΦT M Φ (that’s why you shouldn’t normalize
eigenvectors to the mass matrix).

The effective mass is the mass which is mobilized in a specific direction X,
Y or Z (matrix D in the definition of effective mass), while the generalized
mass is a more “generalized” term which is the mobilized mass not depended
of the direction.

It seems to me that there is no way of getting this mass using ANSYS.

Thank you
--------------------------------------------------
From: "Christopher Wright" <chrisw@skypoint.com>
Sent: Friday, April 27, 2012 6:36 PM
To: "ANSYS User Discussion List" <xansys@xansys.org>
Subject: Re: [Xansys] Ansys generalized mass calculation

Quote:

On Apr 27, 2012, at 6:51 AM, Kazantzis wrote:

Quote:
I want to calculate the generalized mass of one mode after
performing a modal analysis of a bridge. The definition of
generalized mass is: ΦT M Φ where M is mass matrix and Φ is the
eigenvector. I choose MODOPT, , , , , ,ON in order to normalize
modes shapes to unity and not to the mass matrix (otherwise the
generalized mass is equal to 1).

You need to RTFM a little more carefully. What you're calling
'generalized mass' is properly termed 'Effective Mass' and it's
listed in the ANSYS Classic output file with all the modal data
summary. You can use a *GET to retrieve it from the results file.
It's also equal to the square of the participation factor. You don't
need to make a special effort to normalize the eigenvectors to unity
to get it.

Of course this is for Classic. I haven't any idea how (ho-hum) WB
does it, but I suspect it's the same.

Christopher Wright P.E. |"They couldn't hit an elephant at
chrisw@skypoint.com | this distance" (last words of Gen.
.......................................| John Sedgwick, Spotsylvania
1864)
http://www.skypoint.com/members/chrisw/



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akbey.kalkan
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Joined: 21 Oct 2008
Posts: 6

PostPosted: Mon Apr 30, 2012 6:24 am  Reply with quote

Panagiotis

It should be possible to calculate generalised mass using APDL Math by
reading the mass matrix with *smat and by using *dmat to access the mode
shapes.

You need version 13 (?) or later for APDL Math.

Regards

Akbey Kalkan
Jacobs

-----Original Message-----
From: xansys-bounces@xansys.org [mailto:xansys-bounces@xansys.org] On Behalf
Of Kazantzis
Sent: 30 April 2012 08:57
To: ANSYS User Discussion List
Subject: Re: [Xansys] Ansys generalized mass calculation


Dear Christopher

Thank you for your response to my question.

The effective mass is not equal to the generalized mass.

The effective mass is: Mei = i 2 / T M (where i = iT M D, participation
factor).

The generalized mass is: T M (that's why you shouldn't normalize
eigenvectors to the mass matrix).

The effective mass is the mass which is mobilized in a specific direction X,
Y or Z (matrix D in the definition of effective mass), while the generalized
mass is a more "generalized" term which is the mobilized mass not depended of
the direction.

It seems to me that there is no way of getting this mass using ANSYS.

Thank you
--------------------------------------------------
From: "Christopher Wright" <chrisw@skypoint.com>
Sent: Friday, April 27, 2012 6:36 PM
To: "ANSYS User Discussion List" <xansys@xansys.org>
Subject: Re: [Xansys] Ansys generalized mass calculation

Quote:

On Apr 27, 2012, at 6:51 AM, Kazantzis wrote:

Quote:
I want to calculate the generalized mass of one mode after performing
a modal analysis of a bridge. The definition of generalized mass is:
T M where M is mass matrix and is the eigenvector. I choose
MODOPT, , , , , ,ON in order to normalize modes shapes to unity and
not to the mass matrix (otherwise the generalized mass is equal to
1).

You need to RTFM a little more carefully. What you're calling
'generalized mass' is properly termed 'Effective Mass' and it's listed
in the ANSYS Classic output file with all the modal data summary. You
can use a *GET to retrieve it from the results file.
It's also equal to the square of the participation factor. You don't
need to make a special effort to normalize the eigenvectors to unity
to get it.

Of course this is for Classic. I haven't any idea how (ho-hum) WB does
it, but I suspect it's the same.

Christopher Wright P.E. |"They couldn't hit an elephant at
chrisw@skypoint.com | this distance" (last words of Gen.
.......................................| John Sedgwick, Spotsylvania
1864)
http://www.skypoint.com/members/chrisw/




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christopher.wright
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Joined: 17 Jun 2009
Posts: 927

PostPosted: Mon Apr 30, 2012 10:24 am  Reply with quote

On Apr 30, 2012, at 2:56 AM, Kazantzis wrote:

Quote:
The effective mass is not equal to the generalized mass.
Apologies. I read through your post too fast. A long time ago ANSYS
used to report something they called the 'equivalent' mass which was
independent of excitation direction. Maybe that's what you're after.
I couldn't see much use for that particular quantity, but out of
curiosity I once reproduced the calculation using the mass matrix of
an example problem. Unfortunately I have no record of the work,
although I did the matrix arithmetic in Excel. You might have to
extract your problem's mass and modal matrix, but I don't think
that's difficult, nor is the matrix arithmetic

One thing you might try (I'd use a fairly simple example problem) is
to have ANSYS report the eigenvectors normalized to unity, and see if
it might provide you with the quantity you're after. You might also
check through a good text like Timoshenko's _Vibration Problems…_ to
see if you can back calculate your generalized mass from the
information you have. Timoshenko shows how to figure the mass-
normalized eigenvectors, so maybe you can reverse the process.

Quote:
The generalized mass is: ΦT M Φ (that’s why you shouldn’t
normalize
eigenvectors to the mass matrix)

As to this, in experience the effective mass is invaluable in
assessing the significance of a particular vibration mode and whether
I've considered enough modes in my solution. So I figure I absolutely
*should* normalize to the mass matrix.



Christopher Wright P.E. |"They couldn't hit an elephant at
chrisw@skypoint.com | this distance" (last words of Gen.
.......................................| John Sedgwick, Spotsylvania
1864)
http://www.skypoint.com/members/chrisw/

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