This document provides some additional information for users about this keyword.

Transcription

1 Page 1 of 5 *DAMPING_FREQUENCY_RANGE This document provides some additional information for users about this keyword. Why is *DAMPING_FREQUENCY_RANGE needed? The commonly-available damping methods for explicit analysis are mass-weighted (e.g. *DAMPING_GLOBAL), and stiffness-weighted (e.g. *DAMPING_PART_STIFFNESS). Neither are very suitable for applications such as seismic analysis in which the damping of more than one critical mode must be controlled. Mass-weighted damping: Force = constant x mass x velocity, computed for each node, independent of element connectivity Damping ratio for a mode of frequency f is proportional to 1/f No stability criterion, no effect on timestep Damps rigid body modes (unrealistic) Stiffness-proportional damping: Damping stress = constant x rate of change of stress Damping ratio for a mode of frequency f is proportional to f Can require reduced timestep for stability. Does not damp rigid body modes. Rayleigh damping: a combination of mass-weighted plus stiffness-proportional damping. If we have several modes in the range 5Hz to 50Hz that require, say, 2% damping, this cannot be achieved using either of the above. Rayleigh damping can achieve the desired damping ratio at two frequencies only. *DAMPING_FREQUENCY_RANGE overcomes this problem.

2 Page 2 of 5 Outline description Two variants of *DAMPING_FREQUENCY_RANGE are available: *DAMPING_FREQUENCY_RANGE A form of mass-weighted damping: the global motion of each node is damped Damping is independent of element connectivity Rigid body modes will be damped No effect on model stability or timestep Frequency of dynamic response reduces (see notes below) *DAMPING_FREQUENCY_RANGE_DEFORM A form of stiffness-proportional damping: the element stresses are damped Effectively, the damping is calculated from the current tangent stiffness, thus avoiding the problem of over-damping the plastic deformations Rigid body modes cannot be damped Timestep is automatically reduced to prevent instability Frequency of dynamic response increases (see notes below) We recommend *DAMPING_FREQUENCY_RANGE_DEFORM (rather than *DAMPING_FREQUENCY_RANGE) because it does not damp rigid body modes. For both variants, the inputs are the same: CDAMP (the desired damping ratio), e.g. input 0.02 for 2% damping FLOW and FHIGH (the lower and upper limits of the frequency range within which the target damping is to be achieved) A set of parts to which this damping is to be applied. Damping ratio (Versions up to R9) The input damping ratio CDAMP is not achieved exactly. The actual damping varies with frequency, as shown in these examples in the graph below. This applies to both *DAMPING_FREQUENCY_RANGE and *DAMPING_FREQUENCY_RANGE_DEFORM. CAMP=0.02, FLOW=5Hz, FHIGH=50Hz (blue curve) CDAMP=0.02, FLOW=5Hz, FHIGH=150Hz (pink curve) The frequency is shown on a log scale.

3 Page 3 of 5 When the ratio FHIGH/FLOW=10, the desired damping is achieved with an error of approximately plus or minus 3%. For FHIGH/FLOW=30, the error in achieved damping is approximately plus or minus 20%. If accuracy of the achieved damping ratio is important, it is recommended to use FHIGH/FLOW no more than 10. This information applies to LS-DYNA versions up to R9. Damping ratio (Versions from R10 onwards) Within the frequency range FLOW to FHIGH, the user-defined damping ratio is achieved with greater accuracy in version R10 onwards, as shown in the graph below. The same input parameters are used: CAMP=0.02, FLOW=5Hz, FHIGH=50Hz (blue curve) CDAMP=0.02, FLOW=5Hz, FHIGH=150Hz (pink curve) Again, this applies to both *DAMPING_FREQUENCY_RANGE and *DAMPING_FREQUENCY_RANGE_DEFORM. For R10 and above, the maximum recommended ratio FHIGH/FLOW is 100. Damping of frequencies below FLOW and above FHIGH As shown in the graphs above, *DAMPING_FREQUENCY_RANGE provides some damping outside the frequency range FLOW to FHIGH, as shown in the rough guide in the table below. The actual figures will vary slightly according to the ratio FHIGH/FLOW. In the table, CDAMP is the user-input damping ratio. Frequency 0.01*FLOW 0.1*FLOW 0.5*FLOW FLOW FHIGH 2*FHIGH 10*FHIGH 100*FHIGH Approximate Damping Ratio 0.018*CDAMP 0.18*CDAMP 0.75*CDAMP CDAMP CDAMP 0.75*CDAMP 0.18*CDAMP 0.018*CDAMP

4 Page 4 of 5 Effect on dynamic stiffness The main disadvantage of *DAMPING_FREQUENCY_RANGE (including the _DEFORM option) is that it modifies the dynamic stiffness of the structure, resulting in changes of natural frequency. This is a side-effect of the way in which the frequency-dependent damping forces or stresses are calculated. The effect is proportional to CDAMP. For this reason, only low values of CDAMP should be used typically up to about 0.02 to The appropriate limit on CDAMP for a particular application depends on whether the accuracy of the natural frequencies of the structure is important. Furthermore, the error becomes greater if the ratio FHIGH/FLOW exceeds 30 (R9 and below) or 100 (R10 and above). *DAMPING_FREQUENCY_RANGE reduces dynamic stiffness, and hence reduces the natural frequency of each mode. The fraction change of frequency can be predicted from CDAMP, FLOW and FHIGH, and is shown in the LS-DYNA User Manual. Typically, with FHIGH/FLOW in the range 3 to 30, the maximum fraction reduction of natural frequency is approximately 3*CDAMP at low frequency, reducing to less than 1*CDAMP at high frequency. For example, with 1% damping, the frequencies are reduced by 0-1% at FHIGH and about 3% at FLOW. The user may wish to compensate this by increasing the input value of elastic stiffness. *DAMPING_FREQUENCY_RANGE_DEFORM increases dynamic stiffness, and hence increases the natural frequency of each mode. The fraction change has the same dependence on CDAMP and FHIGH/FLOW, but the error is greater at high frequency than at low frequency. The user may wish to compensate this by decreasing the input value of elastic stiffness. There is some evidence that real-life materials that exhibit damping also have dynamic stiffness that is slightly greater than static stiffness, so it could be argued that the influence of the _DEFORM option on dynamic stiffness is not unrealistic. However, the real-life increase of stiffness under dynamic conditions may not match the increase caused by this damping card, so this should not be relied on. Example: CDAMP=0.01, FHIGH/FLOW=30: Error in natural frequency *DAMPING_F_R *DAMPING_F_R_DEFORM At FLOW -3% +1% At FHIGH -1% +3% Recommendations and Applicability We recommend to set FHIGH and FLOW such that FHIGH/FLOW is in the range 10 to 30 (10 to 100 in LS- DYNA R10 onwards). We recommend setting CDAMP no higher than 0.02 to 0.05 (the limit depends on how important it is to retain the accuracy of the natural frequencies in the model). *DAMPING_FREQUENCY_RANGE_DEFORM is available only for the following element types and formulations: Solids ELFORM -1, -2, 1, 2, 3, 4, 9, 10, 13, 15, 16, 17, 99 Beams ELFORM 1, 2, 3, 4, 5, 9 (note: not type 6) Shells ELFORM 1-5, 7-17, 20, 21, 23-27, 99 Discrete elements Multiple *DAMPING_FREQUENCY_RANGE cards may be defined. A different Part Set (PSID) should be given for each card. One card may have PSID=0: this defines the default for all nodes not damped by any other *DAMPING_FREQUENCY_RANGE card. In this context, non-zero PSID is processed only for Solid, Beam, Shell and Thick Shell parts, i.e. nodes belonging to these element types will be damped. Note that the Part Set PSID cannot be used to include lumped mass elements the PID input field on *ELEMENT_MASS is ignored.

5 Similarly, multiple *DAMPING_FREQUENCY_RANGE_DEFORM cards may be defined, and PSID=0 defines the default for all supported element types/formulations. Page 5 of 5