Insights Blog
-- Browse All Articles --
Physics Articles
Physics Tutorials
Physics Guides
Physics FAQ
Math Articles
Math Tutorials
Math Guides
Math FAQ
Education Articles
Education Guides
Bio/Chem Articles
Technology Guides
Computer Science Tutorials
Forums
General Engineering
Mechanical Engineering
Electrical Engineering
Aerospace Engineering
Nuclear Engineering
Materials Engineering
Trending
Featured Threads
Log in
Register
What's new
Search
Search
Search titles only
By:
General Engineering
Mechanical Engineering
Electrical Engineering
Aerospace Engineering
Nuclear Engineering
Materials Engineering
Menu
Log in
Register
Navigation
More options
Contact us
Close Menu
JavaScript is disabled. For a better experience, please enable JavaScript in your browser before proceeding.
You are using an out of date browser. It may not display this or other websites correctly.
You should upgrade or use an
alternative browser
.
Forums
Engineering
Mechanical Engineering
Modal mass and kinetic energy in FEM modal analysis
Reply to thread
Message
[QUOTE="Arjan82, post: 6808544, member: 177647"] [B]TL;DR Summary:[/B] What is the formula for modal mass and kinetic energy of a modal analysis FEM computation? I do *not* mean effective modal mass. So, I use Ansys (well known FEM software) and get the next output for a modal analysis toy problem (If you happen to know Ansys that's a pre, but I promise it shouldn't matter). The problem is a simple beam, clamped at one end. I used 160 20-node brick elements to solve it (so no Timoshenko beams or something like that). [CODE title="Ansys output"] The modes requested are mass normalized (Nrmkey on MODOPT). However, the modal masses and kinetic energies below are calculated with unit normalized modes. ***** MODAL MASSES, KINETIC ENERGIES, AND TRANSLATIONAL EFFECTIVE MASSES SUMMARY ***** EFFECTIVE MASS MODE FREQUENCY MODAL MASS KENE | X-DIR RATIO% Y-DIR RATIO% Z-DIR RATIO% 1 81.73 39.42 0.5199E+07 | 0.000 0.00 95.85 61.05 0.000 0.00 2 159.3 40.53 0.2030E+08 | 0.000 0.00 0.000 0.00 96.07 61.19 3 490.2 41.77 0.1981E+09 | 0.000 0.00 30.22 19.25 0.000 0.00 4 593.4 31.73 0.2206E+09 | 0.000 0.00 0.000 0.00 0.000 0.00 5 859.8 48.92 0.7138E+09 | 0.000 0.00 0.000 0.00 31.92 20.33 6 1268. 77.93 0.2472E+10 | 126.6 80.61 0.000 0.00 0.000 0.00 [/CODE] So I know exactly how to get the effective mass, which is dependent on direction. And by exactly I mean exactly. I extract the mass and stiffness matrix from Ansys, compute the eigenvectors of this problem (with Matlab): $$ \left[ K \right] \left\{ d \right\} = w \left[ M \right] \left\{ d \right\} $$ with ##\left[ K \right] ## the stiffness matrix, ##\left[ M \right]## the mass matrix, ##\left\{ d \right\}## an eigenvector and ##w = \omega^2## the eigenvalue. All is 'mass normalized' such that ##\left\{ d \right\}^T \left[ M \right] \left\{ d \right\} = 1##. And now we can compute the participation factor for the x-direction (assuming mass normalization): $$ L_x = \left\{ d \right\}^T \left[ M \right] \left\{ r_x \right\} $$ with ##\left\{ r_x \right\}## the influence vector, or just a vector with 1's at all degrees of freedom of the x-direction and 0 everywhere else. And now the effective modal mass in the x-direction is simply ##L_x^2##. If I do this with e.g. Matlab I get exactly the same results as Ansys does (all digits are the same, except maybe the last). So, no problem there. But the modal mass and kinetic energy (KENE) on the left side of this table are a mystery to me. I need the formula for that but cannot seem to find it, not in the documentation of Ansys, not on the internet (for which the results get swamped by explanations of effective mass) and not in any book about the subject I own. Who knows how to compute those numbers? [/QUOTE]
Insert quotes…
Post reply
Forums
Engineering
Mechanical Engineering
Modal mass and kinetic energy in FEM modal analysis
Back
Top