TIME-DOMAIN RESPONSE OF DAMPED LINEAR STRUCTURES USING FIRST-ORDER GHM FINITE ELEMENTS
Bibliographic record
Abstract
The use of “GHM” finite-elements is a technique that can be used to incorporate general linear viscoelastic behaviour, i.e., general linear material dynamic behaviour including damping, into time-domain structural dynamics models. The original second-order form of the method has been published previously. This paper introduces the use of the first-order form of the GHM method. This first-order form and its second-order predecessor enable and encourage the incorporation of measured material linear viscoelastic properties. The constant coefficient form necessary for state-space methods is retained, while additional coordinates are added to represent the material properties. The use of a selectable number of modulus function terms allows arbitrarily good representation of general viscoelastic behaviour over a given spectrum of known material response. The method is applied to a prototype shock response problem for illustration. This class of problem is significant in that the excitation and therefore the dynamic response is “broadband”. A model that incorporates material damping must be similarly broadband in its representation of material behaviour, otherwise the model will be incapable of producing a consistent prediction of structural response. In the sample problem, the GHM model is applied to actual viscoelastic material whose behaviour is neither simple viscous nor simple hysteretic.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".