#
Non uniform damping (esas.25)

esas.25

This module allows users to add damping characteristics to each structural member in the project. The total composite damping is calculated from user input values or default material damping values. Non uniform damping can be applied for accurate dynamic calculation of mixed steel-concrete constructions, constructions on foundations, etc.

The module a solution to take into account the natural damping of the different kinds of materials in the structure. The logarithmic decrement of steel differs for example from that of concrete caused by another value of the damping ratio.

On top of this, the user is able to attribute manually dampers (by means of damping ratios) to the different elements of the system.

When no damping ratio is inputted on an element, a default value will be used. As default material damping or a global default for damping will be taken into account, dependent on the setting chosen by the user.

InSCIA Engineer, damping can be specified on 1D elements, 2D elements and supports. The damping of each of these elements (or substructures) will be used to calculate a modal damping ratio for the whole structure for each Eigenmode. In the literature this is described as Composite Damping. Composite damping is used in partly bolted, partly welded steel constructions, mixed steel-concrete structures, constructions on subsoil, ...

For structural systems that consist of substructures with different damping properties, the composite
damping matrix *C* can be obtained by an appropriate superposition of damping matrices *C _{i}*
for the
individual substructures:

Where:

*C*is the damping matrix for the i-th substructure in the global coordinate system._{i}- n is the number of substructures being assembled.

Highlights |
---|

Damping values can be input by user on each member (beam or surface) and defined as relative damping, logarithmic decrement or Rayleigh damping. |

Default material damping can be used from the material library. |

Dampers can be added on nodal flexible supports in X, Y and Z direction. |

Total damping of the structure is calculated for each eigenmode. |

Non-uniform damping can be taken into account with harmonic or seismic calculation. |

### Proportional Damping (Rayleigh Damping)

A way of describing the damping is assuming that the damping matrix is formed by a linear combination of the mass and stiffness matrices.

Where:

- a
_{i}and b_{i}are proportional damping coefficients for the i-th part of the structure. - M
_{i}is Mass matrix for the i-th part of the structure in the global coordinate system. - K
_{i}is Stiffness matrix for the i-th part of the structure in the global coordinate system.

### Stiffness-Weighted Damping

For structures or structural systems that consist of major substructures or components with different damping characteristics, composite modal damping values can be calculated using the elastic energy of the structure:

Where:

- is damping ratio of the considered eigenmode.
- E is elastic energy of the structure, associated with the modal displacement of the considered eigenmode.
- n is the number of all substructures.
- is damping ratio for the i-th substructure.
- E
_{i}is elastic energy for the i-th substructure, associated with the modal displacement of the considered eigenmode.

Note: This formula may be used as long as the resulting damping values are less then 20% of critical. If values in excess of 20% are computed, further justification is required.

As specified, in SCIA on each element a damping ratio can be inputted. For this ratio, also the damping of the material can be used from which the element is manufactured.

When no damping ratio is inputted on an element, a default value will be used since all elements need a damping ratio before the above formulas can be applied.

Analogous to the input of other objects in SCIA, Damping on elements will be grouped in a Damping Group. In turn, this Group can be assigned to a Combination of Mass Groups.

### Support Damping

Additional to the damping of 1D and 2D elements, SCIA allows the input of a damper on a flexible nodal support. The modal damping ratio i is calculated by the following formula:

Where:

is the circular frequency of mode j

is the modal displacement in support node s for mode j

C_{s} is the damping constant for the support

Alpha is A user defined parameter (> 0)

As specified, on all 1D and 2D elements a damping ratio has to be defined. This is not the case with supports, not every support needs to have a damping value.

28/07/2014