Engineering resonance-flow diagrams

These diagrams describe conceptual flows you can render as SVG, Mermaid, or other formats.

Diagram 1 – Structural resonance load (Problem 1)#

Nodes:

• Triadic stiffness: $$D_6$$
• Resonant-time: $$τ_r$$
• Load: $$L = D_6 / τ_r$$

Flow:

1. $$D_6$$ enters a division node.
2. $$τ_r$$ enters the denominator.
3. Output is $$L$$.
4. A control arrow from “vibration tuning” adjusts $$τ_r$$.

Diagram 2 – Thermal expansion (Problem 2)#

Nodes:

• Temperature coupling: $$ΛΘ$$
• Frequency elevation: $$T_f$$
• Expansion: $$E = ΛΘ T_f$$

Flow:

1. $$Λ$$ and $$Θ$$ merge to form $$ΛΘ$$.
2. $$T_f$$ enters a multiplier node.
3. Output is $$E$$.
4. A feedback arrow from “thermal control system” adjusts $$Θ$$ or $$T_f$$.

Diagram 3 – Fluid flow resonance (Problem 3)#

Nodes:

• Emitter constant: $$F_3$$
• Resonant-time: $$τ_r$$
• Squaring node: $$τ_r^2$$
• Flow rate: $$Q = F_3 τ_r^2$$

Flow:

1. $$τ_r$$ flows into a squaring node.
2. $$F_3$$ enters a multiplier node.
3. Output is $$Q$$.
4. A control arrow from “flow regulation” adjusts $$τ_r$$.