What does a complex eigenvector output from QRDAMP mean, and can you provide an example?


At 9.0, the complex eigenvector can be requested with MODOPT,QRDAMP,,,,,ON using the QR Damped eigenvalue extraction method. This type of output was already available in the past with DAMP or UNSYM methods.

Essentially, complex eigenvector output implies that there is phase difference, analogous to harmonic analysis output. Combining the real and imaginary results with a user-defined macro (use ANHARM.MAC in the "apdl" subdirectory as a starting point, for example) will aid the user in visualizing the time-varying response.

For proportional damping (such as with alpha and/or beta damping), since there is no phase difference, the imaginary eigenvector will essentially be zero. For non-proportional damping, however, the imaginary eigenvector will be non-zero.

An example of a simple beam is shown below:
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finish
/clear

NO_ELEM = 20

/prep7
et,1,3
r,1,1,1/12,1
mp,ex ,1,10e6
mp,dens,1,0.1/386.1

n,1,0,0,0
n,2,100,0,0
fill,1,2,NO_ELEM,3,1

type,1$real,1$mat,1
e,1,3
e,NO_ELEM+2,2
e,3,4
*repeat,NO_ELEM-1,1,1

et,2,14
keyopt,2,2,2
r,2,,1e-1

nsel,s,node,,node(33,0,0)
cm,TEMPNODE,node
ngen,2,100,all
type,2$real,2
eintf
cmsel,u,TEMPNODE
d,all,all

et,3,14
keyopt,3,2,2
r,3,,5e-1

nsel,all
nsel,s,node,,node(66,0,0)
cm,TEMPNODE,node
ngen,2,101,all
type,3$real,3
eintf
cmsel,u,TEMPNODE
d,all,all

allsel,all
finish

/solu
antype,modal
modopt,qrdamp,10,,,yes
mxpand,10

d,1,all

allsel,all
solve
finish

/post1
set,1,2
pldisp,2

*afun,deg
*get,MY_DSCALE,graph,1,dscale,dmult
/user,all
/dscale,all,MY_DSCALE
/seg,dele
/seg,multi
lcdef,1,1,2,0
lcdef,2,1,2,1
*do,MY_ANGLEINCR,0,330,30
/com, angle: %MY_ANGLEINCR%
REAL_COMP=cos(MY_ANGLEINCR)
IMAG_COMP=-(sin(MY_ANGLEINCR))
lcfact,1,REAL_COMP
lcfact,2,IMAG_COMP
*if,REAL_COMP,eq,0,then
lcfact,1,1e-10
*endif
*if,IMAG_COMP,eq,0,then
lcfact,2,1e-10
*endif
lcase,1
lcoper,add,2

/replot
*enddo
/com, loop finished

/seg,off
anim,12,1,0.2
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