Flexural-Torsional Vibration of Thin-Walled Beams Subjected to Combined Initial Axial Load and End Bending Moment: Application to the Design of Saw Tooth Blades

Table 1

Natural frequency f of the beam with the simply supported ends by Approach 1 and Approach 2.

E	0			h			2h
F0	App. 1 equation (13)	App. 2 equation (29)	Dev. (%)	App. 1 equation (13)	App. 2 equation (29)	Dev. (%)	App. 1 equation (13)	App. 2 equation (29)	Dev. (%)
−200	7.73	7.73	0.00	7.67	7.67	0.00	7.49	7.49	0.00
0	10.73	10.73	0.00	10.73	10.73	0.00	10.73	10.73	0.00
200	13.05	13.05	0.00	13.02	13.02	0.00	12.91	12.91	0.00
400	15.02	15.02	0.00	14.90	14.90	0.00	14.51	14.51	0.00
600	16.76	16.76	0.00	16.51	16.51	0.00	15.71	15.71	0.00
800	18.34	18.34	0.00	17.92	17.92	0.00	16.60	16.60	0.00
1000	19.79	19.79	0.00	19.18	19.18	0.00	17.22	17.22	0.00
1200	21.14	21.14	0.00	20.31	20.31	0.00	17.60	17.60	0.00
1400	22.41	22.41	0.00	21.34	21.34	0.00	17.77	17.77	0.00
1600	23.61	23.61	0.00	22.28	22.28	0.00	17.72	17.72	0.00