On the Flexural-Torsional Vibration and Stability of Beams Subjected to Axial Load and End Moment

Table 1

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

Boundary condition	Natural frequencies (Hz) at P = 0 and M = 0
	Mode 1		Mode 2		Mode 3
	Exact [38]	FEM (40 elements)	Exact [38]	FEM (40 elements)	Exact [38]	FEM (40 elements)
C-F	2.556	2.556	15.995	15.995	44.858	44.858
C-C	16.266	16.266	44.858	44.858	87.970	87.970
P-P	7.175	7.175	28.718	28.718	64.633	64.633
P-C	11.209	11.209	36.351	36.351	75.611	75.611