Transverse Vibration of Axially Moving Functionally Graded Materials Based on Timoshenko Beam Theory

Table 1

Effect of initial stress on first four frequencies for FGM beam ( = 100 m/s).

	(MPa)	(Hz)	(Hz)	(Hz)	(Hz)
0.001	1	1075	4436	9900	17322
	50	1129	4490	9955	17377
	100	1182	4545	10010	17433
	Increase rate	9.95%	2.46%	1.11%	0.64%
1	1	738	3170	7109	12455
	50	790	3221	7160	12506
	100	841	3272	7211	12559
	Increase rate	13.96%	3.22%	1.43%	0.84%
100	1	496	2304	5209	9147
	50	553	2357	5262	9200
	100	605	2409	5315	9254
	Increase rate	21.98%	4.56%	2.03%	1.17%