Submersible Mixer Noise & Vibration Analysis
Project: Seastead Design | Date: 2025 | Configuration: 3 × NACA 0035 Foil Legs (21.5 ft × 8.5 ft chord)
Design Note: Your description mentions "4 legs/floats" in the mixer section, but the main design specifies 3 legs (trimaran configuration). This analysis assumes 3 mixers (one per leg). If you intend 4 mixers, increase total acoustic power by ~1.25 dB and review structural loading on the 4th attachment point.
⚠ Engineering Estimate Disclaimer: These are
first-principles estimates based on typical submersible mixer data (e.g., ABS/ICEAS standards, Landia/INVENT/FLYGT specs) and scaling laws. Actual values depend critically on:
- Specific mixer model (propeller diameter, blade count, RPM, motor type)
- Mounting geometry (cantilever length, bracket stiffness)
- Rubber isolator dynamic stiffness & damping ratio (at operating frequency)
- Leg internal damping (compartments, ballast, battery mass)
- Structural resonance frequencies of the leg & triangle frame
Prototype testing (OMA/EMA) is strongly recommended before finalizing isolation specs.
Key Design Parameters Used
| Parameter | Value | Basis / Note |
|---|
| Number of Mixers | 3 (one per leg) | Per trimaran leg configuration |
| Mixer Type | Slow-speed submersible (direct drive, ~30–120 RPM) | Typical for wastewater/bioreactors; assumed 0.5–1.5 kW per unit |
| Propeller Diameter (est.) | 0.8 – 1.2 m (2.6 – 4 ft) | Scaled to 8.5 ft chord leg; fits near bottom |
| Mounting | Cantilevered bracket off leg trailing edge | Near bottom (~0.5 m above keel) |
| Isolation Layer | 1 inch (25 mm) tire-derived rubber | Assumed static deflection 3–5 mm; dynamic stiffness ratio ~1.5–2.5 |
| Leg Mass (per leg, est.) | 15,000 – 25,000 lbs (wet, with batteries) | Provides inertial mass for isolation |
| Water Depth at Mixer | ~7.25 ft (half of 14.5 ft draft) | Hydrodynamic added mass significant |
Estimated Noise & Vibration by Vessel Speed
The dominant excitation is Blade Passing Frequency (BPF) and its harmonics. Flow noise increases with speed. Isolation effectiveness depends on frequency ratio (forcing freq / isolator natural freq).
Mixer RPM (typical)
40 – 60 RPM (0.67 – 1.0 Hz shaft)
Blade Passing Freq (3-blade)
2.0 – 3.0 Hz (Fundamental)
Isolator Nat. Freq (est.)
8 – 12 Hz (1" rubber on 20k lb leg)
Frequency Ratio (r)
0.17 – 0.38 (r < 0.5 = amplification zone)
Predicted Levels at Mixer Mount (Source)
| Metric | Estimated Range | Assessment |
|---|
| Underwater Radiated Noise (URN) @ 1m | 115 – 125 dB re 1 µPa (1/3 oct, BPF) | Low Typical for slow mixers |
| Structure-Borne Vibration (Bracket) | 1.5 – 4 mm/s RMS (10–1000 Hz) | Moderate Amplified by isolation (r<0.5) |
| Airborne Noise in Leg (1m from hull) | 45 – 55 dB(A) | Very Low Well below speech interference |
| Transmitted Accel. to Triangle Frame | < 0.005 g RMS | Negligible Mass law + isolation |
Key Insight: At very low speed, flow noise is minimal. The main risk is isolation amplification because BPF (2–3 Hz) is below the isolator natural frequency (8–12 Hz). The 1" rubber acts as a soft spring, potentially amplifying displacement by 1.1–1.5×. Ensure bracket stiffness pushes system resonance >15 Hz if possible.
Mixer RPM (typical)
60 – 90 RPM (1.0 – 1.5 Hz shaft)
Blade Passing Freq (3-blade)
3.0 – 4.5 Hz (Fundamental)
Flow-Induced Vibration (Vortex Shedding)
St ≈ 0.2 → 1–2 Hz (On mixer body/strut)
Frequency Ratio (r)
0.25 – 0.55 (Approaching isolation region)
Predicted Levels at Mixer Mount (Source)
| Metric | Estimated Range | Assessment |
|---|
| Underwater Radiated Noise (URN) @ 1m | 122 – 132 dB re 1 µPa (1/3 oct, BPF) | Moderate +5–7 dB vs 0.5 mph |
| Structure-Borne Vibration (Bracket) | 2.5 – 6 mm/s RMS | Moderate-High Flow + BPF combined |
| Airborne Noise in Leg (1m from hull) | 50 – 60 dB(A) | Noticeable In quiet cabin |
| Transmitted Accel. to Triangle Frame | 0.005 – 0.015 g RMS | Low Perceptible if resonant |
Key Insight: Flow noise becomes significant. Vortex shedding on the mixer housing/strut (1–2 Hz) may coincide with BPF harmonics. Isolation begins to transition toward attenuation (r → 0.5). Critical check: Ensure no structural resonance of the cantilever bracket at 3–5 Hz.
Mixer RPM (typical)
80 – 120 RPM (1.3 – 2.0 Hz shaft)
Blade Passing Freq (3-blade)
4.0 – 6.0 Hz (Fundamental)
Flow-Induced Vibration
2 – 4 Hz (Vortex shedding + turbulent buffet)
Frequency Ratio (r)
0.33 – 0.75 (Entering attenuation zone r>√2)
Predicted Levels at Mixer Mount (Source)
| Metric | Estimated Range | Assessment |
|---|
| Underwater Radiated Noise (URN) @ 1m | 128 – 138 dB re 1 µPa (1/3 oct, BPF) | High Significant broadband + tonal |
| Structure-Borne Vibration (Bracket) | 4 – 10 mm/s RMS | High Risk of fatigue at bracket welds |
| Airborne Noise in Leg (1m from hull) | 55 – 68 dB(A) | Intrusive Speech interference possible |
| Transmitted Accel. to Triangle Frame | 0.015 – 0.04 g RMS | Moderate Felt on floor; check resonance |
Key Insight: BPF (4–6 Hz) is now closer to isolator natural frequency. If isolator fn = 8 Hz, r=0.5–0.75 → amplification still possible. If fn = 12 Hz, r=0.33–0.5 → attenuation begins. Broadband flow noise dominates URN. Bracket fatigue life should be verified (DNV-RP-C203 / ABS Guide for Vibration).
Isolation System Design Recommendations
| Aspect | Recommendation | Reasoning |
|---|
| Isolator Natural Frequency |
Target fn ≥ 15 Hz (static deflection ≤ 1.1 mm) |
Moves BPF (2–6 Hz) deep into attenuation zone (r ≤ 0.4). 1" rubber is too soft for 20k+ lb leg. Use engineered mounts (e.g., Barry Controls, Trelleberg, GMT) with 2–4 mm static deflection. |
| Damping Ratio (ζ) |
Target ζ = 0.15 – 0.25 |
Critical to limit amplification at resonance (r≈1). Tire rubber ζ≈0.05–0.1. Specify high-damping compound or add constrained-layer damping. |
| Mount Geometry |
Shear/compression mounts; avoid tension |
Shear provides lower fn for same deflection. Use 4–6 mounts per mixer bracket in a symmetric pattern. |
| Bracket Stiffness |
1st bending mode > 25 Hz |
Prevents bracket resonance amplifying mixer forces. Use box section or triangulated gussets. |
| Electrical Conduit | Flexible conduit with slack loop | Rigid conduit bypasses isolation, transmitting vibration directly to leg. |
| Operational Protocol |
Reduce mixer RPM during transit > 1 kt |
Lowers BPF, reduces hydrodynamic load, cuts noise 5–10 dB. Run mixers only on station. |
Measurement & Validation Plan
- Bench Test: Mount mixer on test frame with candidate isolators. Measure FRF (Frequency Response Function) and transmissibility (base accel → bracket accel) from 1–100 Hz.
- In-Situ OMA (Operational Modal Analysis): Accelerometers on mixer bracket, leg wall (in/out of waterline), triangle frame corner. Run mixers at all RPMs at 0, 0.5, 1, 1.5 kt.
- URN Measurement: Hydrophone at 1m, 5m, 20m per ANSI/ASA S12.64. Compare to DNV Silent class notation thresholds if applicable.
- Fatigue Assessment: Strain gauges on bracket-to-leg welds during 24h sea trial. Check against DNV-RP-C203 Detail Category 71/80.
Summary Table
| Speed |
BPF Range |
URN @ 1m (dB re 1µPa) |
Bracket Vib (mm/s RMS) |
Cabin Noise (dBA) |
Frame Accel (g RMS) |
Primary Concern |
| 0.5 MPH | 2 – 3 Hz | 115 – 125 | 1.5 – 4 | 45 – 55 | < 0.005 | Isolation amplification (r < 0.5) |
| 1.0 MPH | 3 – 4.5 Hz | 122 – 132 | 2.5 – 6 | 50 – 60 | 0.005 – 0.015 | Flow noise + BPF; bracket resonance risk |
| 1.5 MPH | 4 – 6 Hz | 128 – 138 | 4 – 10 | 55 – 68 | 0.015 – 0.04 | High vibration; fatigue; speech interference |