Shock and Vibration

Research Article

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

Table 2

Comparison of the first five natural frequencies, in rad/sec, using the present NTM results with those obtained in [19] for the example shown in Figure 4.
   
(rad/sec)		MethodBernoulli-Euler
Timoshenko
Pinned-pinned
(P-P)		NAT [19]319.4341316.5288
NTM319.4340316.4855
NAT [19]1853.38641789.4207
NTM1853.38641784.8723
NAT [19]4110.13413825.8438
NTM4110.13413836.5347
NAT [19]7709.57146642.9094
NTM7709.57126639.2170
NAT [19]11621.76999886.6243
NTM11621.76989918.8328
Free-clamped
(F-C)		NAT [19]371.5354367.9440
NTM371.5354367.1487
NAT [19]1243.90631216.6220
NTM1243.90651211.5531
NAT [19]3082.08462827.0352
NTM3082.08452849.1465
NAT [19]5541.14104957.9240
NTM5541.14095003.7433
NAT [19]9599.38107673.7578
NTM9599.38107751.3336
Clamped-free
(C-F)		NTM55.125755.0130
NTM616.6018598.5917
NTM2702.32382532.1483
NTM5483.23794969.1659
NTM9570.95867956.5299
Clamped-pinned
(C-P)		NTM480.8915469.8444
NTM2098.05561991.9611
NTM5007.33154589.5676
NTM8366.80737049.5393
NTM13678.711211215.0349
Clamped-clamped
(C-C)		NTM836.3527807.0997
NTM3019.58862772.2732
NTM5583.64694980.5538
NTM9625.89437734.8319
NTM14403.316311538.1581