Iniversal Relation for beams (transverce natural frequences)
Iniversal Relation for beams with rectangular cross section (transverce natural frequences) with free-free boundary conditions
The example is for Al-alloys ( Poisson's ratio ni=0.33)
Fit E modulus and Density values to experimental results (epsilon- %error)
f(s),
where s=nc. L/r (r=h/(12)^0.5-radii of gyration)- beam dimentionless ratio;
nc_1=1.505619 nc_2= 2.499753; nc_3= 3.50001; nc_4=4.5.
f- natural frequency [Hz]
For comparison f(s)- ASTM calculated from ASTM 1876-09
more info: https://www.researchgate.net/publication/282437414_Universal_experimental_relation_for_natural_frequencies_of_transversal_vibration_of_stubby_free-free_beams