On the Finite Element Model of Rotating Functionally Graded Graphene Beams Resting on Elastic Foundation

Table 1

First three nondimensional fundamental frequencies of the beam subjected to the axial load .

Boundary condition	Vibration mode	Exact [45]	Exact [46]	FEM with 8 elements [47]	This work
					4 elements	6 elements	8 elements	10 elements	12 elements
S-S	1	6.24	—	6.24	6.247	6.243	6.242	6.242	6.241
	2	36.40	—	36.41	36.505	36.402	36.383	36.377	36.375
	3	85.81	—	85.93	61.891	85.924	85.768	85.721	85.703
S-C	1	—	13.01	13.01	13.018	13.006	13.003	13.003	13.003
	2	—	47.35	47.38	47.493	47.356	47.323	47.313	47.309
	3	—	101.54	101.73	101.053	101.630	101.450	101.384	101.358