ANANAS: Golden-Angle Phyllotactic (1, 3, 5, 8) Geodesic Lattice Mechanics for Full-Ocean-Depth Submergence Hulls, Porous Tsunami Wave-Breakers, Hypersonic TMF Panels, and WKB Underwater Acoustic Holography
Year: 2026
Type: preprint
Abstract: Orthogonal `(2, 2)` grid stiffeners and composite monocoque cylinders concentrate shear, buckling, and acoustic diffraction energy along periodic rational cleavage planes—leading to catastrophic interlaminar delamination in deep-submergence hulls (`Titan`-class CFRP failure), overturning resonance in coastal seawalls, thermal-mechanical fatigue (`TMF`) in hypersonic skins, and severe grating sidelobes in sparse underwater acoustic arrays. We introduce `ANANAS` (Phyllotactic Geodesic Lattice & Wavefront Engineering), a unified structural and acoustic framework based on the golden angle $\varphi = 2\pi(1 - \Phi^{-1}) \approx 137.507764^\circ$ and quadruple Fibonacci parastichy bracing `(1, 3, 5, 8)`, verified via deterministic 6-DOF 3D Timoshenko beam-frame Finite Element Analysis (`FEA`) and Wentzel–Kramers–Brillouin (`WKB`) stratified ray-tracing in pure Rust (`VERIFY_REPORT_ANANAS_20261017.md`). Across four domain benchmarks, `ANANAS` demonstrates: 1. Full-Ocean-Depth Submergence Hull (`Module::submergence_hull`): At $4,000\text{ m}$ depth ($40.26\text{ MPa}$), a `Ti-6Al-4V` `(1, 3, 5, 8)` phyllotactic hull achieves a `10,730.2 m` collapse depth (`SF = 2.683`, peak Von Mises stress `283.78 MPa`, radial deflection `8.25 mm`, `> 100,000` dive fatigue life), whereas an equivalent-geometry monocoque `CFRP` hull suffers catastrophic buckling at `3,041.3 m` (`SF = 0.760`, delamination index `0.7897`, failure in `4 dives`) and a conventional ring-stiffened `Ti-6Al-4V` cylinder collapses at `6,419.1 m` (`SF = 1.605`). 2. Porous Coastal Tsunami Wave-Breaker (`Module::coastal_breaker`): Under a `67.5 mph` ($30.18\text{ m/s}$) tsunami bore across $N = 100$ Monte Carlo realizations (`seed = 42`), a porous `(3, 5, 8)` phyllotactic seawall reduces mean peak Von Mises stress by `-57.4%` (`3.71 GPa` $\to$ `1.58 GPa`, $p < 10^{-6}$), peak deflection by `-69.8%` (`17.44 m` $\to$ `5.2626 m`), and overturning moment by `-55.0%` via Bragg phase cancellation and Ergun/Forchheimer porous dissipation. 3. Aerospace Hypersonic TMF Panel (`Module::fea`): Under combined $160\text{ dB}$ acoustic loading, $1,200^\circ\text{C}$ thermal shock, and $50\text{ kPa}$ aerodynamic pressure, the `(1, 3, 5, 8)` geodesic panel reduces Von Mises stress by `-94.1%` (`759.0 MPa` $\to$ `44.8 MPa`), deflection by `-93.1%` (`9.07 mm` $\to$ `0.62 mm`), and increases buckling load factor `14.6×` (`0.84` $\to$ `12.28`). 4. WKB Deep-Ocean Acoustic Holography (`Module::acoustic_holography`): Across a $4,000\text{ m}$ Munk thermocline sound-speed profile ($128$ elements, $15\text{ kHz}$), WKB phase conjugation on a Vogel sunflower aperture restores `100.0%` (`1.0000` vs. `0.0834`, `12.0×` gain) 3D focal intensity, suppresses grating lobe energy by `-81.6%` (`46.2%` $\to$ `8.5%`), improves PSLR by `+7.05 dB` (`3.87` $\to$ `10.92 dB`), and achieves `+16.08 dB` (`98.4%`) broadside monostatic sonar echo reduction. Patent Priority & Filing Status: null (Omnibus Provisional Patent Application No. 4A / 4B officially filed October 20, 2026 via USPS Priority Mail Express under 37 CFR § 1.10). Correspondence: [email protected].
Author: Jonnie (AstroDynamiX Research)
Language: English
Subfield: Mechanics of Materials
Field: Engineering
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223047535