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Parametric Measurement of 3D Monolithic Spatial Resonators Across 22 cm, 44 cm, and 66 cm Scales

By Denis founder of Triaural

1. Executive Summary & Intent The objective of this four-month pilot study is to experimentally verify the acoustic, modal, and cymatic behavior of the three-armed spatial resonator TRIAURAL-TETRAMID, defined by a 120° rotational symmetry and a 109.47° tetrahedral vector core fabricated from a single continuous metal monolith.Phase 1 focuses on a tightly controlled 3 × 3 matrix (9 specimens) using a uniform arm cross-section derived from the existing reference prototype. This scope makes it possible to measure material-associated differences and frequency-scaling relationships across three isotropic scales. All resulting datasets, CAD files, protocols, and documentation will be released into the public domain under a CC0 license.

2. Experimental Specimen Matrix (3 × 3 = 9 Monoliths) The study evaluates three engineering metals across three isotropic scales.Materials Aluminum 6061-T6: nominal density 2,700 kg/m³; E = 69 GPa. Baseline reference material. Phosphor bronze: nominal density 8,800 kg/m³; E = 115 GPa. Titanium Ti-6Al-4V Grade 5: nominal density 4,430 kg/m³; E = 114 GPa.Isotropic Scales (Overall Monolith Height) 22 cm: reference scale; preliminary fundamental frequency of the aluminum prototype approximately 310 Hz. 44 cm: 2× linear scale. 66 cm: 3× linear scale.The 22 cm Aluminum 6061-T6 specimen has already been fabricated as a reference prototype; this budget covers fabrication of the remaining eight monoliths.

3. Deliverables (4-Month Output) Eight newly fabricated precision monoliths: continuous 5-axis CNC machined specimens accompanied by foundry material certificates and dimensional inspection reports. Complete acoustic and modal dataset: measured natural frequencies, decay times, Q-factors, and inter-arm phase relationships across all nine resonators under both fixed-anchor and free-resonator boundary conditions. FEM versus measurement validation: direct comparison between finite-element modal predictions and physical measurements, establishing empirical scaling relationships across 22 cm, 44 cm, and 66 cm. Standardized cymatic archive: high-resolution photographic and video documentation of fluid surface interference patterns under strictly controlled liquid volume, vessel, and lighting conditions across all three metals and sizes. Open-science CC0 repository: full public release of parametric CAD models, raw measurement datasets, analysis scripts, and the Phase 1 technical monograph.

4. Estimated Fabrication Costs (5-Axis CNC Machining) Isotropic scaling increases the required raw metal billet volume cubically: a 66 cm specimen requires 27 times the billet volume of a geometrically similar 22 cm specimen. Raw alloy requirements and multi-axis machining time contribute to fabrication costs.22 cm Series Aluminum 6061-T6: already fabricated; reference cost approximately €350. Phosphor bronze: approximately €750. Titanium Grade 5: approximately €1,050.44 cm Series Aluminum 6061-T6: approximately €1,350. Phosphor bronze: approximately €2,800. Titanium Grade 5: approximately €3,800.66 cm Series Aluminum 6061-T6: approximately €3,800. Phosphor bronze: approximately €8,000, including the heavy solid bronze billet. Titanium Grade 5: approximately €10,500, including the high-grade titanium billet and extended 5-axis milling time.Subtotal for eight new specimens: €32,050. International DDP freight, customs and VAT, including heavy crating for the 66 cm units: €5,450. Total fabrication and logistics: €37,500.

5. Phase 1 Pilot Budget (4 Months, 2 Researchers) Core Research Team — €38,400 Two researchers × 160 hours per month × 4 months = 1,280 hours at €30 per hour. The all-inclusive contractor rate covers taxes, social contributions, and dedicated full-time research.Fabrication of Eight Monoliths and DDP Shipping — €37,500 5-axis CNC milling of the 22 cm, 44 cm, and 66 cm specimens in aluminum, bronze, and titanium, with certified alloys (€32,050), plus air/rail DDP freight, customs, and VAT (€5,450).In-House Measurement and Cymatic Setup — €3,500 Calibrated measurement microphone and interface, precision laboratory scale with 0.01 g resolution, heavy-duty clamping/suspension rigs for the 44 cm and 66 cm units, optical lighting, and standardized cymatic vessels.External Validation Access (SLDV / Chamber) — €2,500 Two days of paid facility access for non-contact scanning laser Doppler vibrometry (SLDV) or anechoic verification of primary mode shapes.FEM Modeling and CC0 Open Release — €1,100 Computational setup, data curation, technical monograph layout, and public CC0 repository deployment.Technical Contingency — €4,000 Reserve for raw titanium/bronze price fluctuations, freight adjustments, or repeat validation trials; approximately 4.6% of the total request.Total Phase 1 request: €87,000 for the complete nine-specimen study across 22 cm, 44 cm, and 66 cm scales.

6. Timeline and Milestone-Based Disbursement (4 Months) Month 1 — Design Freeze and Machining Kickoff Finalize parametric CAD across all three scales, initiate 5-axis CNC production of all eight specimens in Week 1 to accommodate lead times on the 66 cm units, run baseline FEM modal simulations, and build test fixtures.Month 2 — Metrological Inspection and Calibration Receive all eight new monoliths, log physical dimensions, angular deviations, and masses alongside the existing prototype, and calibrate the acoustic and cymatic measurement rigs.Month 3 — Primary Measurements and Cymatics Execute systematic frequency, decay, phase, and cymatic recordings across all nine specimens, including external SLDV validation.Month 4 — Data Analysis and CC0 Publication Perform statistical comparison between FEM predictions and experimental results, curate raw datasets, and publish the Phase 1 monograph under CC0

7. Conclusion and Funding Case TRIAURAL-TETRAMID Phase 1 will establish an experimental reference dataset for a three-armed monolithic spatial resonator across three materials and three isotropic scales. The four-month study combines documented fabrication, acoustic and modal measurements, finite-element comparison, and standardized cymatic imaging to quantify how material, scale, and support conditions relate to measured resonance behavior.The €87,000 request supports eight new monoliths, measurement of the complete nine-specimen matrix, two researchers, measurement infrastructure, and external validation access. The existing 22 cm aluminum prototype provides the reference geometry for this focused pilot.The lasting output will be a publicly reusable research resource: parametric CAD, raw and processed measurements, analysis scripts, measurement protocols, a cymatic archive, and a technical monograph released under CC0. These outputs will support independent replication and evidence-based decisions about subsequent research.