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Section 5
5-141
3.
Alternatively enter d1, d2, d3, etc. as the damping
ratios for each mode. With the Explicit option each value
can be preceded by a repetition factor (rf*damp) without
spaces. For example:
EXPLICIT 0.03 7*0.05 0.04 <= mode 1 damping is
.03, modes 2 to 8 are .05, mode 9 is .04.
If there are fewer entries than modes, then the last damping
entered will apply to the remaining modes. This input may be
continued to 10 more input lines with word EXPLICIT only on line
1; end all but last line with a space then a hyphen. There may be
additional sets of EXPLICIT lines before the END.
Damping ratios must be in the range 0.0 through 1.0.
______________________________________________________
The formula used for CALCULATE (to calculate the damping per
modal frequency based on mass and/or stiffness proportional
damping) is:
D(i) = (
α / 2ω
i
) + ( ω
i
β / 2 ) = damping ratio for modes i =
1 to N. If the resulting damping is greater than MAX, then MAX
will be used (MAX=1 by default). If the resulting damping is less
than MIN, then MIN will be used (MIN=1.E-9 by default). This is
the same damping as D = (
α Μ + β Κ).
Example: To get 4% damping ratio at 4 Hz and 6% damping ratio
at 12 Hz
Mode Hz Rad/sec Damp Ratio
1 4.0 25.133 0.04
3 12.0 75.398 0.06
D(i) = (
α / 2ω
i
) + ( ω
i
β / 2 )
.04 =
α / 50.266 + 12.567 β
.06 =
α / 150.796 + 37.699 β
α = 1.13097
β
= .0013926