# Beam natural-frequency screening
# Scope: First bending mode of a uniform Euler-Bernoulli cantilever.
# Status: illustrative worked example; engineering review pending.
# Inputs are example values. Checks are editable example requirements, not standards.

length = 0.3 m
width = 25 mm
depth = 12 mm
modulus = 69 GPa
density = 2700 kg/m^3

area := width*depth [m^2]
inertia := width*depth^3/12 [m^4]
frequency := 1.875104^2/(2*pi*length^2)*sqrt(modulus*inertia/(density*area)) [Hz]

check first mode target: frequency >= 80 Hz

scenario alternative: length = 0.24 m