The Damping tab offers various setting options to consider viscous structural damping in the analysis using the linear time history analysis.
Damping
In the Base is the linear implicit Newmark analysis, only the 'Damping type'Rayleigh is available. For the linear modal analysis method, on the other hand, the list provides two options:
- Lehr's damping | Constant
- Rayleigh
When applying the Rayleigh damping to a linear modal analysis, the Rayleigh damping coefficients α and β are converted to Lehr's damping values, Di, (see Parameter). The solution is then unique.
In the case of the Rayleigh damping, it is possible to determine the damping parameters automatically from Lehr's damping. Select the 'Calculation from Lehr's damping' check box. Then, enter the parameters of the two most dominant mode shapes for the 'natural frequencies' f1 and f2 of the model with the corresponding values for the 'Lehr's damping' D1 and D2.
In the lower section, the 'Natural Frequencies - Damping diagram' is displayed for the Rayleigh damping. It represents the ratio that is available between the natural angular frequency and Lehr's damping constant.
Parameters
In this dialog section, you can define the parameters of the damping. They differ, depending on the damping type.
Lehr's Damping
Lehr's damping is defined by the ' Lehr's damping constant' D. It is defined for each individual shape i as a factor between the existing and the critical damping as follows:
| ci | Entries in the diagonal damping matrix |
| mi | Modal masses |
| z | Height above ground |
The damping matrix C must be a diagonal matrix.
Rayleigh
The damping matrix of the Rayleigh damping is defined by means of the two damping parameters α and β as follows:
| cp,mean | Time-averaged pressure coefficient |
| z | Height above ground |
| K | Static stiffness matrix |
The damping matrix C does not necessarily have to be a diagonal matrix for the direct time history analysis. More information about the Rayleigh damping can be found in [1], for example.
The following relation exists between the Rayleigh coefficients and Lehr's damping:
This equation is displayed in the following graphic. Different constellations for the damping parameters α = 0.2 and β = 0.001 are considered.
Different Lehr's damping values result for each pair of Rayleigh coefficients. They depend on the angular frequency.