Impulse Response
E80 Modal VibrationsSpring 2009
The Question
• In the event of a crash landing of your rocket, what will be the effect on the instruments inside the rocket?
(Translation)• What is the velocity of impact? • What is the impulse response of the
rocket structure?
Tap Test
Normal Modes of Three Mass Oscillator
Rossing,T.D. & Fletcher,N.H, “Principles of Vibration and Sound”, Springer, 1994
Bending Waves in a Beam
Radius of Gyration
Bending Waves in a Beam
Transverse Waves
2yt 2
EK 2
4yx4
Complex Displacement y Y (x)e j t
d 4Ydx4
2
EK 4 Y 4
v4Y where v KcL and cL
E
Now write Y (x)Aex where 2
2 2
v2
v
or jv
Bending Waves in a Beam
Transverse Waves
y(x, t)e j t Ae xv Be
xv Ce
j xv De
j xv
Rossing,T.D. & Fletcher,N.H, “Principles of Vibration and Sound”, Springer, 1994
Bending Waves in a Beam
Transverse Waves on Beam with Free Ends
y(x, t)cos t A coshxv
cosxv
B sinh
xv
sinxv
For a beam of length L
coshLv
cosLv
1 roots at
L2v
43.011, 5, 7,....... (2n 1)
2 2 2 22 3.011 , 5 , 7 ,....... (2 1)
84
3.011, 5, 7,....... (2 1)
n
n
K Ef nL
Ln
Bending Waves in a Beam
Rossing,T.D. & Fletcher,N.H, “Principles of Vibration and Sound”, Springer, 1994
Bending Waves in a Beam
Rossing,T.D. & Fletcher,N.H, “Principles of Vibration and Sound”, Springer, 1994
E80 Modal Vibrations Lab1. Compute first three modal frequencies for polycarbonate
hollow cylinder.2. Record hammer “impulse” input3. Record transient vibration data from strain gauges along
the cylinder4. Record transient vibration data from accelerometer on
the cylinder5. Record transient vibration data from your rocket6. Estimate the impulse response of your rocket.