Damping is completely optional in LS-DYNA and is invoked using one the *DAMPING commands.
Be aware that energy dissipation can occur through
means other than *DAMPING, e.g., energy due to hourglass forces,
energy due to rigidwall forces, energy due to contact friction forces,
internal energy from discrete dampers, etc.
Sometimes, contact forces can introduce noise into the response.
In such cases, adding viscous damping via the VDC parameter on
Card 2 of *CONTACT may help reduce the noise.
VDC is input as a percentage of critical damping ... a typical value is 10 to 20.
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Overview of *DAMPING commands:
Mass damping in LS-DYNA, which includes *DAMPING_GLOBAL and *DAMPING_PART_MASS, is intended to
damp low frequency structural modes but it has the added effect of damping rigid body modes.
Thus parts that undergo significant rigid body motion should
EITHER be excluded from mass damping
OR the mass damping should be turned off during the time the part undergoes rigid body motion
OR *DAMPING_RELATIVE should instead be used.
By using *DAMPING_RELATIVE, only motion/vibration
that is relative to the motion of a particular rigid body is damped.
Think of *DAMPING_RELATIVE as being like regular mass damping except that only the motion relative
to the RB motion, as opposed to total motion, is damped. Both translational and rotational
motion of the rigid body are taken into account in determining relative motion.
CDAMP and FREQ in *DAMPING_RELATIVE are used to calculate the mass damping constant
damping constant = CDAMP * (2 * omega_min) = CDAMP * (4 * pi * FREQ)
whereas this damping constant is input directly in the case of *DAMPING_GLOBAL and *DAMPING_PART_MASS.
An example that illustrates the benefit of *DAMPING_RELATIVE is the spinning bar model
http://ftp.lstc.com/anonymous/outgoing/support/FAQ_kw/spinup.bar.impl_dr_relative_damping.k.
Run this example with *DAMPING_RELATIVE commented out and then plot a time history of effective
stress in one of the deformable elements. You'll see a noisy response with oscillations that
do not decay with time.
Rerun the example including *DAMPING_RELATIVE and you'll see the oscillations quickly die out.
Rerun the example again, replacing *DAMPING_RELATIVE with *DAMPING_GLOBAL (included in the
original input but commented out) and you'll see that the bar stops spinning since rigid body
rotation is not excluded from damping.
The critical damping constant in the case of mass damping is 4*pi/T
where T is the period of the mode targeted for damping
(usually the lowest frequency (fundamental) mode).
The period can be determined from an eigenvalue
analysis or estimated from results of an undamped dynamic analysis.
If the user elects to use mass damping, a damping value
less than the critical damping coefficient is suggested.
A value of 10% of critical damping, input as 0.4*pi/T, is fairly typical. You can
choose to damp all parts using the same damping coefficient (*DAMPING_GLOBAL)
or, to tailor the damping to the individual response characteristics of each
part, you can assign a different damping coefficient to each part
(*DAMPING_PART_MASS). In either case, the damping coefficient can vary with
time (useful to turn damping off or on in the middle of a simulation).
*DAMPING_PART_STIFFNESS is intended to damp high frequency modes.
The input variable COEF (input as a positive value) appproximately represents
a fraction of critical damping. A typical value of COEF is 0.1, representing
roughly 10% of critical damping for the high frequency modes.
In an explicit analysis, stiffness damping is sometimes used to promote stability by
reducing high frequency oscillation of the response.
If using *DAMPING_PART_STIFFNESS, TSSFAC in *CONTROL_TIMESTEP should generally be reduced accordingly,
(no specific guidelines given) as the damping affects the critical timestep (sh, bug 12599, 10/20/16).
If an instability occurs due to the addition of stiffness damping,
(1) reduce TSSFAC, and/or
(2) reduce COEF
to the point where stability is restored.
http://ftp.lstc.com/anonymous/outgoing/support/FAQ_kw/spinning_shells_effect_of_stiffness_damping.k
offers a case study of stiffness damping vs. mass damping. See the comments therein.
Mass damping and stiffness damping are implemented for implicit dynamic analysis.
Example of stiffness damping (includes comments in the input deck):
http://ftp.lstc.com/anonymous/outgoing/support/FAQ_kw/demo_stiffness_damping_effect_impl.k .
This example shows that stiffness damping in implicit is dependent on time step.
Another example with 2 cases demonstrating correct treatment of mass and stiffness
damping in an implicit dynamic analysys is
http://ftp.lstc.com/anonymous/outgoing/support/FAQ_kw/damping_implicit_dynamic.k (copius comments
are included in the deck, including this mention of free vibration decay...
[Ref: Dynamics of Structures by Clough and Penzien.
Regarding "Free-Vibration Decay",
Damping ratio can be determined from the ratio of two displacement amplitudes measured at an interval of m cycles.
Damping ratio = ln(dn/d(n+m))/(2*pi*m*(omega/omega_damped))
For damping ratios less than 0.2, the change in frequency omega due to damping can be neglected with little (<2 percent) error.
"log decrement" mentioned above is ln(dn/d(n+m)), where dn is the amplitude of displacement at cycle n and
d(n+m) is the amplitude of displacement at cycle(n+m).]
Note that for implicit dynamic analyses, some numerical damping can be introduced via
the GAMMA and BETA values: gamma=0.6 and beta=0.4 have been used to good effect,
but I've also used double the default values (1.0 and 0.5) to eliminate high amplitude dynamic oscillation.
Mass damping affects type 1 and type 2 beams in implicit IF direct integration is used but
has NO affect if modal superposition is used.
http://ftp.lstc.com/anonymous/outgoing/support/FAQ_kw/damping_beams_impl.k
http://ftp.lstc.com/anonymous/outgoing/support/FAQ_kw/hlbeam_damp_directimpl.k
Another damping alternative is a frequency-independent damping
option which targets a range of frequencies
and a set of parts (*DAMPING_FREQUENCY_RANGE).
Damping_frequency_range was developed by Arup and its theoretical details
are confidential, however there are some helpful notes on
*DAMPING_FREQUENCY_RANGE and *DAMPING_FREQUENCY_RANGE_DEFORM provided in
http://ftp.lstc.com/anonymous/outgoing/support/PAPERS/DAMPING_FREQUENCY_RANGE_support_note_May2021.pdf
It was developed with the intent of helping LS-DYNA to handle damping
in vibration prediction problems properly - including vehicle NVH time-history analysis
as well as certain classes of seismic problems and civil/structural vibration problems.
The key points of *DAMPING_FREQUENCY_RANGE are:
- Use for low amounts of damping only, e.g. up to 1% or 2%
- The damping treatment slightly reduces the stiffness of the response -
that's because the applied damping force lags slightly behind the
"theoretically correct" damping force, due to the need to evaluate frequency content.
- The frequency range specified by the user should ideally be no more than
a factor of 30 between highest and lowest. Damping is still achieved outside
the frequency range but the amount of damping reduces.
This damping is based on the nodal
velocities; these might oscillate due to structure modes or due to rigid
body rotation.
In the example http://ftp.lstc.com/anonymous/outgoing/support/FAQ_kw/spinup.bar.expl_dr.dampfreqrange.k, damping is
applied to a spinning bar. The damping
works much better with the two frequencies spaced
far apart. With FHIGH/FLOW = 3,
the internally-calculated parameters are very poorly
chosen - this might be considered a flaw in the original implementation.
However, when FHIGH/FLOW is raised to 30,
response is much better - damping reduces at low frequency. For rigid body motion,
the rigid body velocity drops a little at first (while the frequency
content gets sorted out initially) but thereafter it remains constant.
There is still some gradual decline in velocity after the relatively large
initial drop thus a sustained but small damping effect on the RB
(spinning) motion is unavoidable with this type of damping.
In version R7.0.0, *DAMPING_FREQUENCY_RANGE is also implemented for
implicit dynamic solutions.
Example: http://ftp.lstc.com/anonymous/outgoing/support/FAQ_kw/damp_fr_imp.key.gz
jpd
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Additional commentary on damping ...
In Rayleigh damping, the damping matrix is expressed as a linear combination
of the mass and stiffness matricies:
C = alpha*M + beta*K
The LS-DYNA implementation of Rayleigh damping for
explicit analysis is done at the element level.
This is done for numerical convenience, since in the explicit
method we don't form the stiffness matrix K.
Instead, we compute internal forces by simply integrating
stresses over the element area. The Rayleigh damping
terms are implemented as corrections to these stresses.
When COEF>0, stiffness damping provides an APPROXIMATE fraction of critical damping in the high
frequency domain. For example, COEF=0.1 approximately corresponds to 10% of critical damping.
When COEF<0, an old, alternative formulation of stiffness damping is invoked whereby
-COEF is approximately equal to the Rayleigh beta value.
In other words, critical stiffness damping would be represented by
-COEF = beta = 2/omega = T/pi = 1/(pi*f)
where
omega = circular frequency (radians/time) targeted for damping,
pi = 3.1416
T = period (time)
f = cyclic frequency (cycles/time)
This old formulation is particularly prone to instability if the time step > -COEF,
which would often be the case in explicit analysis.
NOTE: Setting IRATE=1 in *CONTROL_IMPLICIT_DYNAMICS not only turns off material rate effects
in implicit analysis but also shuts off stiffness damping.