Nonlinear Vibrations of Beams With Bilinear Hysteresis at Supports: Interpretation of Experimental Results
Bibliographic record
Abstract
Abstract Several structures of important industrial relevance feature large-amplitude vibration, which can have an initially hardening or a softening behavior. Models with quadratic and cubic nonlinear stiffness terms are often used to predict the nonlinear dynamics of such structures. If boundary conditions constitute an important cause of nonlinearity, however, it may not be possible to describe the nonlinear behavior of these systems by means of these nonlinear terms. The bundles of fuel rods immersed in the coolant flow of pressurized water reactors constitute an important example of extreme softening behavior, which is not described accurately by the simple adoption of nonlinear stiffness terms proportional to the square and to the cube of displacement in the equation of motion. In fact, the spacer grids, which support the nuclear fuel rods inside the reactors, constitute nonlinear boundary conditions, and are responsible of the peculiar softening behavior. Dedicated experiments on the rotational constraint applied by the spacer grids were performed, revealing a softening stiffness, which conforms extremely well with a bilinear model with hysteresis, such as the one formulated by Caughey. Therefore, a single degree-of-freedom equation with bilinear stiffness terms was employed to model the large-amplitude vibrations of single and bundled fuel rods immersed in quiescent water, which were detailed by previous stepped-sine experiments. A viscous dissipative term was initially retained for modelling damping, since several sources of dissipation are present for fuel rods immersed in water, besides hysteresis at the spacer grid supports. A satisfying fit of the experimental frequency- and time-domain curves was achieved through the use of an optimization algorithm for the tuning of stiffness and damping terms. Viscous damping, however, is not constant during large-amplitude vibrations, but is amplitude-dependent. Therefore, the value of the relevant parameter had to be changed at each forcing level. The model was then refined by introducing four additional switch points for stiffness, besides the initial one. Moreover, a nonlinear damping term of the quadratic type, suitable for softening structures immersed in fluids, was included. The resulting equation of motion with a five-switch piecewise linear stiffness describes with improved accuracy the experimental results. Also, one set of damping parameters is capable of describing the experimental results in the entire forcing (vibration amplitude) range. All this clarifies that a simple multilinear stiffness model, with the inclusion of quadratic damping, can be successfully employed to describe the behavior of rods immersed in fluid, in presence of nonlinear boundary conditions introduced by spacer grids.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| 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 | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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 teacher head, 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".