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Download Examination 1 Practice Problems on Vibration Analysis | MAE 415 and more Exams Mechanical Engineering in PDF only on Docsity!
MAE 415. Vibrations. Exam #1. October 1, 2004. Please show all work. Each problem is worth the same amount, so plan your time accordingly. 1. An aircraft wing with a tip fuel tank of mass m = 250 kg is tested in.a fixture that supports the wing at the root. It is harmonically forced at various frequencies by shaking the support at a known amplitude, and the displacement of the tip is recorded. The wing has inherent structural damping and an effective spring constant, but the test engineers must determine how to characterize those properties. {a) Find the general equation of motion for the displacement of the tip tank (x(t)) in terms of its mass, the wing equivalent damping and spring constants, and the harmonic shaking, y(t) = ymax cos(wt). (b) The figure shows the maximum displacement amplitude relative to the the shaking amplitude (2max/Ymax) 48 a function of shaker frequency. Estimate the damped natural frequency of the wing. Estimate the effective spring constant, k.,and the effective damping constant, c.. (&). Fes fs ae Bt vaste — ., ie Wee + 696 koe = wi (- Cytah SIMD & Ir + eos wrt) Max tip displacement/Support displacement , L As bong. ag, oltompeerg., ms wnat, too bowypt, pean. webttd OdChte RAMA G) = ull x f(i-U-s? yy 4 4p°U-s) Solving fpr Spee Se OIE . N Wn 2 MYTH 2 GABF kyr wale re prmerenp , MS: Coe bgdmk = 933 Fr 
