Damping_nodal_data

Data Structure: Damping_nodal_data

Description

"Damping data" data structure for the geomechanical field

Usage

Damping_nodal_data     NUM=ival   where ival  is the data structure number

Description

Overview

The Damping_nodal_data structure defines percentage damping on geometry entities based on an estimated value of the lowest vibration frequency computed using the Rayleigh quotient. It may be applied to the complete problem domain or in specific regions e.g. specific boundaries in a wave propagation problem.

The prescribed percentage of damping is a mass proportional damping defined in the form:

C =α*M

Or in given the diagonal form of the mass matrix:

The lowest frequency ( Ωmin) of the current deformation mode can be estimated by the Raleigh quotient defined as:

The upper bound of the oscilation frequencies is defined by the critical time step as:

The frequency used in the evaluation of mass proportional damping is the minimum frequency evaluated by the two methods above. This constraint is applied to prevent inappropriate frequencies that may result if the approximation fort Kij is poor (e.g. due to local instabilities). The proportionality constant ( α) is evaluated every time step so that the fluctuating effective stiffness of the system is accounted for. Higher frequencies are damped more strongly than lower frequencies and so diminish first and consequently α tends to a constant value as the quasi-static solution is approached.

Notes

•Only one Damping_nodal_data data structure may be specified and re-specification will overwrite the existing data structure

•Percentage damping is specified in the range 0 < damp < 1, where 0.1 corresponds to 10% damping of the lowest eigenvalue

•Generally percentage damping is specified in the range 0.01 - 0.03 (recommended value 0.02). If larger values of damping are specified they can result in significant over-damping of higher frequencies

Examples

demonstrating the usage of Damping_nodal_data include:

•damp_2d4n_001a

•damp_2d4n_001b

•damp_2d4n_001c