A Normalized Transfer Matrix Method for the Free Vibration of Stepped Beams: Comparison with Experimental and FE(3D) Methods

Table 8

Percentage error between the computational and experimental results for two-step samples (Group S3). Lowest four nonzero free-free modes.

	Method	Modal frequencies in Hz
		1	2	3	4
S3-80/250
	(A) EXP	403.148	2126.460	4139.830	5153.500
	(B) NTM	420.212	2203.984	4334.192	5605.556
	(C) FE(3D)	404.180	2126.900	4153.700	5169.800
	(D) % error (A, B)	−3.966	3.517	4.484	−8.428
	(E) % error (A, C)	−0.255	−0.020	−0.333	−0.315
S3-80/200
	(A) EXP (Figure 12)	354.790	1727.900	2291.490	4531.380
	(B) NTM	367.381	1788.472	2551.555	4660.983
	(C) FE(3D)	355.230	1728.300	2318.400	4532.200
	(D) % error (A, B)	−3.549	3.386	10.192	−2.860
	(E) % error (A, C)	0.124	0.023	1.160	0.018
S3-80/150
	(A) EXP	335.859	1360.050	1545.130	3778.200
	(B) NTM	346.243	1434.113	1638.174	3889.033
	(C) FE(3D)	336.440	1364.200	1548.500	3781.900
	(D) % error (A, B)	−3.091	−5.445	−6.021	−2.933
	(E) % error (A, C)	0.172	0.305	0.218	0.097
S3-80/100
	(A) EXP	337.400	1018.240	1371.070	3221.200
	(B) NTM	345.942	1074.574	1424.992	3303.837
	(C) FE(3D)	337.480	1024	1372.900	3215
	(D) % error (A, B)	−2.531	−5.532	−3.932	−2.565
	(E) % error (A, C)	0.023	0.565	0.133	−0.192