- Problem 3 Use Table 6 6 To Calculate The First Three Transverse Natural Frequencies Of A 0 5 Meter Long Steel Bar With 1 (31.66 KiB) Viewed 34 times
TABLE 6.6 SAMPLE OF VARIOUS BOUNDARY CONFIGURATIONS OF A SLENDER BEAM IN TRANSVERSE VIBRATION OF LENGTH/ILLUSTRATING WEIGHTED NATURAL FREQUENCIES AND MODE SHAPES Weighted frequencies Bl and characteristic equation Configuration Mode shape σn cosh B,x+cos Bt 0 (rigid-body mode) 4.73004074 7.85320462 0.9825 −ơ, (sinh Byx + sin B,x) 1.0008 10.9956078 0.9999 14.1371655 1.0000 Free-free 17.2787597 0.9999 (2n + 1)m 1 for n> 5 2 cos Bl cosh B/= 1 1.87510407 cosh B - cos B,,x 0.7341 4.69409113 1.0185 7.85475744 =ơ, (sinh Bạt - sin B,x) 0.9992 10.99554073 1.0000 Clamped-free 14.13716839 1.0000 (2n-1) for n> 5 1 for n> 5 2 cos B/ cosh B/= -1 3.92660231 cosh B - cos Bt 1.0008 7.06858275 1 for n > 1 10.21017612 -a (sinh B,x-sin B,,x) 13.35176878 Clamped-pinned 16.49336143 (4n+ 1)m 4 tan Bí = tanh Bí 2.36502037 cosh Bx - cos Bt 0.9825 1 for n>1 5.49780392 8.63937983 —ơ, (sinh Bax – sin B,z) - 11.78097245 14.92256510 Clamped-sliding (4n-1)m for n> 5 4 tan Bí + tanh B = 0 4.73004074 cosh Bx-cos Bx 0.982502 7.85320462 1.00078 10.9956079 mơ, (sinh Bạt → sin B,x) 0.999966 14.1371655 1.0000 17.2787597 1.0000 1 for n > 5 (2n + 1)m Clamped-clamped 2 cos B/ cosh B/- 1 -X FITT none sin 3/-0 Pinned pinned for n> 5 for n> 5 for n> 5 sin Η Π.Χ.