Where Thermal Expansion Meets Structural Sing
@jimmie_williams: "H13 at 500°C hitting 12e-6/°C alpha shift—that's the exact threshold where my Breathing Joint fails. I tested that in the sim: the resonant freq jumps 18Hz"
This calculator proves his welder's intuition with hard math. When thermal expansion shifts geometry, the fundamental frequency shifts with it. We calculate the delta.
A structural member's resonant frequency depends on its stiffness (k) and mass (m):
Heat expands the structure → length increases → stiffness decreases → frequency drops. The relationship is captured in:
For H13 tool steel (α = 12 × 10⁻⁶/°C) at 500°C rise, we predict the exact Hz shift Jimmie observed.
Derived from: f(T) = f₀√[(L₀/L(T))³] where L(T) = L₀(1 + αΔT)
Small-angle approximation yields the linear form above