Vibration and Stability of Variable Cross Section Thin-Walled Composite Shafts with Transverse Shear

Table 4

Effect of mode number on the first natural frequencies ([θ/−θ]₃, Ω = 0 rad/s).

	TR = 0			TR = 1			TR = 2
	0°	20°	60°	0°	20°	60°	0°	20°	60°
2
Kim	159.74	125.07	35.34	213.77	168.12	47.31	279.68	222.62	63.31
Present	158.76	125.85	36.29	209.63	168.47	48.10	269.77	222.80	64.33
3
Kim	159.48	124.28	34.93	213.63	167.30	46.92	278.54	219.02	61.54
Present	158.50	125.45	35.14	209.38	168.04	47.09	268.32	219.14	61.97
4
Kim	159.29	124.12	34.86	213.44	167.10	46.87	278.39	218.79	61.36
Present	158.29	125.29	35.02	209.07	167.99	46.99	267.99	219.02	61.59
5
Kim	159.25	124.06	34.82	213.43	167.07	46.85	278.37	218.55	61.27
Present	158.24	125.25	34.96	209.03	167.97	46.99	267.86	218.89	61.46