Out-of-Plane Vibration of Curved Uniform and Tapered Beams with Additional Mass

Table 10

Nondimensional out-of-plane natural frequencies of half circled uniform and symmetrical tapered beams (θ = 180°).

Type	Mode	Amount of the additional mass
		Bare	25 kg	50 kg	75 kg	100 kg
Uniform	1	1.825	1.112	0.870	0.739	0.653
	2	5.265	5.265	5.265	5.265	5.265
	3	11.038	9.082	8.758	8.626	8.554
	4	18.910	18.910	18.910	18.910	18.910
Tapered	1	2.370	1.449	1.135	0.963	0.851
	2	6.353	6.353	6.353	6.353	6.353
	3	12.860	10.457	10.066	9.908	9.822
	4	21.880	21.880	21.880	21.880	21.880