Table 1.

ln values used in the theoretical model to predict resonant frequencies for the fixed-free conical beam

(At/Ab)½ Mode 1 Mode 2 Mode 3
1.00 3.516 22.034 61.701
0.500 4.625 19.55 48.50
0.333 5.289 18.76 43.78
0.250 5.850 18.51 41.34
0.100 7.201 18.71 37.10
0 8.718 21.146 38.45
  • Values are from Table 1 by Georgian (1965). Our values were interpolated from this table to adjust for measured tip and base diameter. At is the area of the tip of the conical cantilever beam, and Ab is the area of the base.