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.