How to calculate the modal mass and modal stiffness?
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In ANSYS Release 10.0, you can use the kinetic energy to extract the modal mass. ANSYS normalizes the mass, so the modal mass matrix is an identity matrix and the modal stiffness matrix is a diagonal matrix of the 1/omega^2 values, where omega is the natural frequency of each mode in radians/sec. If you want the modal mass with the modes normalized to unity, the modal mass is {phi}T[M]{phi}, where phi is the mode shapes. With the mode normalized to unity, the kinetic energy is equal to ½ * modal mass * omega^2. Thus, the modal mass can be extracted from the kinetic energy. In addition, the modal stiffness is omega^2 * modal mass, so the modal stiffness can be calculated from the modal mass and omega. /prep7 et,1,182,2 mp,ex,1,10e6 mp,prxy,1,.3 mp,dens,1,1e-4 rect,0,100,0,1 esize,2 amesh,all nsel,s,loc,x,-.01,.01 d,all,all,0 alls /solu antype,modal modopt,lanb,1,,,,1 ! normalized to unity mxpand,,,,yes solve /post1 set,first ! use first mode etable,kene_,kene ! find kinetic energy per element ssum ! sum the element kinetic energies *get,ke1,ssum,,item,kene_ ! get the total kinetic energy for first mode *get,f1,mode,1,freq ! get the frequency for the first mode omega = 2*acos(-1)*f1 ! convert frequency to radians (omega) modemass = 2*ke1/omega**2 ! KE = 1/modalmass*omega^2 modestiff = omega**2*modemass ! omega = sqrt(modal stiffness/modal mass) |
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