Problem 2 Use Table 6 5 To Calculate The Fixed Inertia Primary Natural Frequency Of A 0 25 Meter Long 0 01 Meters Squar 1 (25.43 KiB) Viewed 41 times
Problem 2: Use Table 6.5 to calculate the fixed-inertia primary natural frequency of a 0.25 meter long 0.01 meters square solid aluminum bar with a polar mass-moment of inertia of 1 kg-m² attached at the end. Use Excel Goal Seek or another numerical method to calculate n.
TABLE 6.5 SAMPLE OF VARIOUS CONFIGURATIONS OF A UNIFORM SHAFT IN TORSIONAL VIBRATION, OF LENGTH I, ILLUSTRATING THE NATURAL FREQUENCIES AND MODE SHAPES Frequency (rad/s) or characteristic equation Configuration Mode shape 0 NTC 1 COS Free-free x (2n-1)mc 21 Fixed-free NTC * J Jimmy Fixed-fixed @k = = A₂C = n = 0, 1, 2,... n=1,2,... n=1,2,... Gy an cot an @n= Fixed-spring (rotational) X cut an Jo sin XnC Fixed-inertia wn "Here c = VGy/pJ. The values of y can be found in Table 6.3. Note that a numerical proce dure is required for the last two cases, as illustrated in Example 6.4.1. The free mode shape is a constant. Jo An ply (2n-1) 21 FTX 1 in A sin sin sin
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