Non uniform damping

This type of calculation is a dynamic calculation that takes into account non-uniform damping on members and supports.

There is a possibility to input a damping value on each 1D and 2D member. It can be (i) relative damping, (ii) logarithmic decrement or (iii) Rayleigh damping. Moreover, a damper can be input in direction X, Y, Z of a nodal flexible support.

If a dynamic calculation (seismic + harmonic) is carried out and the load case has "Damping group" defined, then SCIA Engineer takes into account the non-uniform damping of the members and supports. The modal relative damping for each direction (i.e. the damping percentage for each mode and each direction) is calculated automatically for each load case.

All 1D and all 2D members must have the damping value assigned before the calculation starts or the default value is used. The input of damping in supports is possible only in the GCS directions.

Background information

The effect of damping is significant in the vicinity of resonance. The phenomenon resonance appears when the frequency of the source of vibration (=driving frequency) corresponds to the eigenfrequency of the system. In this case, large deformations are expected which can cause damage of the structure. Damping of the system is a solution to prevent this.

The most famous example of resonance was the collapse of the Tacoma Narrows Bridge in Washington state in 1940. Because of high windspeeds, this bridge began to vibrate torsionally firstly. Later, the vibrations entered a natural resonance frequency of the bridge which started to increase their amplitude.

Also the Erasmusbrug in Rotterdam became a danger due to resonance causing by the vibration of the cables. To prevent this in the future, hydraulic dampers were provided as a measure.

In SCIA Engineer, different damping methods are available.

First of all, the user is able to input uniform damping which influences the entire structure. For example, the damping value is taken into account in the harmonic analysis by means of the logarithmic decrement:

with Xi being the damping ratio of the structure.

For the CQC-method in a seismic analysis, it's also possible to define a damping curve:

In the third case, a functionality non proportional damping is provided in SCIA Engineer.

Damping can have different causes. The component that is always present is structural damping. Structural damping is caused by hysteresis in the material: the transfer of small amounts of energy into warmth for each vibration cycle possibly increased by friction between internal parts.

Other causes can be the foundation soil of the building and aerodynamic damping due to the diversion of energy by the air. In many cases, damping is increased by adding artificial dampers to the structure.

Non proportional damping allows the user to input manually dampers into the system and also to calculate the influence of the damping of the material. Structural systems composed of several structural elements with different properties can present high nonproportional damping.

Non proportional damping

The module non proportional damping gives 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.

In SCIA 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  Ci for the individual substructures:

With:

Ci= The damping matrix for the ith substructure in the global coordinate system.

N = The number of substructures being assembled.

Different ways of describing the damping can be assumed:

Rayleigh damping

In this method the damping matrix is formed by a linear combination of the mass and the stiffness matrices

Stiffness-Weighted Damping

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

Support damping

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