Final Exam 2 - Fall Term 2013 MECH 330 — Machine Dynamics...

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Unformatted text preview: Fall Term 2013 MECH 330 — Machine Dynamics Question # 1: [25%] A 10 kg machine has a rotating unbalance of mac =1 kg- m. The machine is supported by a cantilever beam E1 =1-104 N - m2, length 0.8m and negligible mass. It is required that the steady-state displacement of the machine is less than 20 cm. Find the required damping constant C if the Operating range of the machine is 0 - 1000 RPM. . . . . P 9 Hint: The displacement of a cantilever beam With end load P 15 y(z) : 6H ((3: — L) (Table D2) Page 2 of 10 Fall Term 2013 MECH 330 7 Machine Dynamics Page 3 of 10 Fall Term 2013 MECH 330 7 Machine Dynamics Question # 2: [25%] . N N -S . . For the system 111 the figure m =1 kg , (1 =1 m, I: 2.5 m, k. : 4000— , c 2 60— and the exc1tat10n m m force is F(t)= Elsinbrvt). It is required that the steady—state acceleration of the mass is less than 2 m/s2 . Assuming that the beam is rigid and massless, find the maximum allowable value of F0 for each of the following cases: a) The range of w is up to 3 Hz. _ F0 sin(wt) b) The range of w [S up to 5 Hz. Page 4 01°10 Fall Term 2013 MECH 330 — Machine Dynamics Page 5 of IO Fall Term 2013 MECH 330 7 Machine Dynamics Question # 3: [20%] Two identical disks of mass m and radius r are connected by a spring k and damper c, and roll without slipping. Express your answers in terms of m, r; k and c. a) Determine the equations of motion. b) Find the natural frequencies of the system. Page 6 of ID Fail Term 2013 MECH 330 — Machine Dynamics Page 7 OfIO Fall Term 2013 MECll 330 — Machine Dynamics Question #4: [30%] A coupled pendulum is subjected to an external force F (t) = E, sin(wt) . It is known that the natural frequencies and modes of this coupled pendulum are: WIZJE,W)— 2k”;+§,xl= 1 ,X2= I . I ‘ ml' 1 1 e1 . -d ‘ Giventhat m=0.5kg, 121m, (120.5111, k220E, c=6§~§, F022Nand w=5i,t1ndthe m m s steady—state displacement amplitude of the masses. Masslcss rod of length Page 8 of 10 Fall Term 2013 MECH 330 — Machine Dynamics Page 9 of 10 Fall Term 2013 MECH 330 7 Machine Dynamics END Page 10 ONO ...
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