Akın Oktav | Searcharxiv

arXiv2026

Boundary-condition identification from a scale-invariant frequency ratio in shear-deformable and nonlocal beams and plates

The ratio of a structure's first two natural frequencies depends on its boundary conditions but not on its size, material density, or absolute stiffness, which multiply every frequency equally and cancel in the quotient. We use this to identify the boundary conditions of a small-scale beam or plate from two ratio measurements, without knowing its exact dimensions or material. The paper first establishes how the ratio $r=ω_2/ω_1$, and the fractional shift $Δr$ it undergoes when a boundary condition changes, respond to the two effects that matter at small scale: transverse shear deformation, through Timoshenko beam and Mindlin plate theory, and small-scale elasticity, through Eringen's nonlocal Timoshenko model. Using a locking-free Rayleigh-Ritz beam solver and a finite-element Mindlin plate solver, each checked against benchmarks, we find an asymmetry. The absolute ratio moves appreciably with thickness, by 12 to 14 per cent over the shear-deformable range, and with orthotropy, by 6 to 9 per cent, but only weakly with nonlocality; the shift $Δr$, by contrast, varies by less than 0.2 per cent over the full nonlocal range and by a few per cent under thickness change. Because $Δr$ is largely independent of these details, a measured shift identifies which boundary-condition transition a deliberate change of support has produced, with a resolution we quantify and verify against molecular-dynamics data. Two spring continua then extend the method to estimating support compliance, with the non-uniqueness of the tip-support case stated explicitly. The method needs no value of the small-scale parameter or the material constants.

physics.app-ph↗

arXiv2026

What does the model actually see? Evaluation protocols and input availability in data-driven prediction of room acoustic parameters

Machine-learnt models are increasingly used to predict ISO 3382-1 room acoustic parameters at unmeasured seats from sparse measurements, with reported coefficients of determination frequently above 0.85. This paper shows that such figures are often determined by the evaluation protocol rather than by the model. Using a multi-condition measurement campaign in a 264-seat conference hall and a 180-seat concert hall, three model families were evaluated under a factorial protocol ablation: validation splits either row-based or grouped by receiver position, and inputs either including measured-at-test quantities (the target position's impulse response, co-located parameter measurements, position identifiers) or restricted to source-receiver geometry and environmental state. Row-based splits with measured-at-test inputs reproduce the high reported accuracies (mean R^2 of 0.81 for the core parameters); grouped splits with deployment-consistent inputs reduce these to 0.09-0.60 and reorder the apparent difficulty of parameter classes. Access to the target's own impulse response at test time reproduces the high accuracy of the row-based folds but provides no benefit under grouped folds. The row-based figure reflects condition interpolation at the measured positions rather than transferable acoustic information. Under the deployment-consistent protocol the spread between Random Forest, the hybrid network, and inverse-distance weighting is several times smaller than the spread between protocols for a fixed model; the learnt models retain a measurable advantage for sound strength and reverberation time, and the high accuracy of the original pipelines re-emerges as condition interpolation at measured positions, a distinct and operationally useful task. A reporting checklist operationalises the findings.

eess.AS↗