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Damping is present in all oscillatory systems and is a measure of a vibration structure to dissipate energy.
The dynamic tools of SCIA Engineer take account of damping. Sometimes it is defined directly by the damping ratio, sometimes by a damping spectrum. Please consult the specific chapters for detail. In general we can say that by default a mean value of damping is taken for the complete system for a mode.
With non-uniform damping, the user is allowed to define damping on the members and on the supports. The program computes a mean value for each mode based on energy considerations.
The non-uniform damping is supported for:
Seismic load
SCIA Engineersupports two types of damping:
) Both types of damping are taken into account by an equivalent damping ratio. For each mode, it is computed as following:
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(7.1) |
where
ξj is the damping ratio in node j
kj is the stiffness in node j
Φij is the modal displacement at node j for mode i
ωi is the frequency of mode i
Cs is the damping constant of support s (kg/s)
Φis is the modal displacement at support node s for mode i
α is a user defined parameter (>0, default =0.5)
Not: At supports, damping is defined separately for the 3 global directions X, Y and Z
The equivalent modal damping 
is obtained by ponderation of the potential energies 
used by the mode in part j of the structure where the damping is 
.
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where [K] and [M] are, respectively, the stiffness matrix and the mass matrix.
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With mjthe mass at node j
We assume that
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In case of the modal displacement is normed by the mass
then the mean internal modal damping of mode I is given by:
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For practical use, we take the same value of damping for all the elements,
We obtain 
For a simple oscillator, the damping is defined by:
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where c is the coefficient of damping
By analogy with material damping, we can state:
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We obtain in total:
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The SEPTEM recommends the value β=0.5 (hence α=1)
Sometimes the user want one value assigned to the whole structure
Sometimes the user have mixed structures
The user is able to overrule easily the damping for some members
The user is able to easily define and correct the damping for the whole structure
Flexible nodal support
Support orientated in global direction XYZ only
The user defines damping groups (similar to mass groups). In order to activate non-uniform damping:
The functionality “Non-proportional damping” is enabled in Project settings
A damping group is defined and linked to a mass combination
A mass combination is defined and linked to a dynamic load case (harmonic or seismic)
Two types of default damping data are available for members (1D/2D). The user is allowed to select the proper default for each damping group:
One value for the whole structure, the “Global default”
One value per material used in the project, the “Material default”
Default damping settings are stored in the set-up of the damping service.
In case of global damping, one value is displayed {default 5%}
In case of material defaults:
The damping is defined in the properties of materials in the material library of SCIA Engineer.
The set-up of the damping service also contains
Max modal damping: one value {used to limit the calculated damping per mode; default 30% }
Alfa {factor for supports; >0; default 1}
In each damping group, the user can assign damping on the elements (similar to additional mass on members in mass groups). Damping can be added on:
a 1D member
a 2D member
a nodal support
Following data is available:
In case of 1D and 2D members, there are 3 possibilities:
Logarithmic decrement: one value {default = 0.001}
Relative damping: one value {default =0.001}
Rayleigh damping: two values { Alfa and beta; default both = 0}
In case of nodal support: 3 values, one value per global direction X, Y and Z {C value; default = 0}
Note that it is not possible to add support dampers
In this case, a message is displayed and input is cancelled
In case the user adds damping in a specific group, then the default is overruled for that member in that group.