Table 1: FEM results versus exact data for the first three natural frequencies at = 0 and = 0.

Boundary conditionNatural frequencies (Hz) at P = 0 and M = 0
Mode 1Mode 2Mode 3
Exact [38]FEM (40 elements)Exact [38]FEM (40 elements)Exact [38]FEM (40 elements)

C-F2.5562.55615.99515.99544.85844.858
C-C16.26616.26644.85844.85887.97087.970
P-P7.1757.17528.71828.71864.63364.633
P-C11.20911.20936.35136.35175.61175.611