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Produced by the NASA Center for Aerospace Information (CASI)
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Contractors Name and Address

Dr. M. J. Crocker

Department of Mechanical ENgineering

247 Wilmore Labs

Auburn University, AL 36849

Title of Report

"Measurement of Damping of Graphite Epoxy Materials"

Period: April 1-April 30, 1985

Dauw of Publication

May 1, 1985

Type of Report and Contract Number

Monthly Report

Contract No. NAS8-36146

Author

Dr. M. J. Crocker

Prepared for George C. Marshall Space Flight Center, Alabama 35812

(NASA —CR-175793) MEASUREM&tT OF DAMPING OF U85-26925

GRAPHITE EXPDXY MATERIALS Monthly Report, 1

Apr. — 30 Apr. 1965 (Auburn Univ.) 15 p

HC 102/MF A01 CSCL 11D Unclas

G3/24 21290

^rCElV^^.

IPgo "^,:
Progress Report No. 7

1

Project Title: "Measurement of Damping of Graphite Epoxy Material"

Sponsor: NASA George C. Marshall Space Flight Center, Huntsville, AL

35812

Period: April 1, 1985 - April 30, 1985

r: B

During this period damping measurements were made on the cylindrical

graphite epoxy specimen using the forced-vibration test method. Thus the

i

work performed during this period is a continuation of that reported in the

last progress report.

a

The specimen was carefully mounted directly on the shaker through the

supporting ring and the impedance head. This was done to simulate an

idealized free-free boundary condition at the two edges. The damping ratio

value and the natural frequency (first mode) obtained in this experiment

v!;?re 043% and 508.75 Hz respectively. In order to check the damping

induced by the supporting ring, measurements were made with the top half of

the ring removed. The'specimen then was supported only by the bottom half

of the ring (half ring). It was observed that the natural frequency of the

specimen (first mode) increased to a value of 552.5 Hz due to the influence

of the reduced mass of the supporting ring. But the damping ratio value

obtained was the same as that obtained with the full supporting ring,

namely 0.13%. This gave more confidence in the measured value of the

damping ratio of the specimen. The frequency response (velocity/force)

curves of the specimen as obtained with the full supporting ring and with

the top half of the supporting ring removed (half ring) are shown in

Figures (1a) and (1b).
The next set of experiments was conducted on the cylindrical tube specimen using the half ring support in order to study the variation of the

damping ratio values with different modes of vibration. Fig. 2 shows the

frequency response curve of the specimen in the frequency range of 450Hz to

3050Hz. The first six resonance frequencies of the specimen can be

observed from the peaks of the curve. The numerical value of the resonance

frequency of each mode of vibration of this specimen cannot be accurately

estimated from this plot due to its large frequency range and hence poor

frequency resolution. To offset this problem two techniques may be used a)

to reduce the frequency range of analysis or b) to zoom the frequency

response plot at the natural frequency of interest.

Figures 3 and 4 show the effect of reducing the upper limit of frequency of interest to I.SkHz and 700Hz respectively. It is seen that the

first and second resonance frequencies can be clearly identified from Fig.

3 but only the first from Fig. 4, In all these figures the amplitude of

vibration is not the same since random input signal was used for excitation 

which is different for different frequency range of measurement.

The resonance frequency and damping estimated from the plots obtained

through zoom analysis for the first six modes of the specimen are tabulated

in Table I. It is seen from the table that the damping ratio value

increases with the mode number. However further investigation is being

carried out to study this aspect in more detail. 

In all the experiments conducted so far, the cylindrical tube specimen

was excited using random input signal. In order to study the effect of

other types of excitation the cylindrical tube specimen with the half ring

was excited using two other types of excitation namely: (a) pseudo-random
input signal (b) and swept sine input signal. A random input signal is a

non-deterministic signal which can be characterized by a probability density function and a power spectral density function. A pseudo-random input

signal is a deterministic signal which is always periodic within the sample

window. A swept sine input is a non periodic signal where a periodic sine

wave is swept up or down through the frequency range of interest. Figures

5, 6, and 7 show the frequency response curves obtained for the specimen

with these three different types of excitation. It is observed that the

random noise excitation produced the best response curve with a sharp peak,

when compared to the response curves obtained with other two types of

excitation. However, all the three methods, gave the same resonance frequency estimate for the first mode of vibration. The damping ratio values

as estimated from the three curves are as follows.

Random Noise excitation K = 0.13%

Pseudo Random Noise excitation K = 0.27%

Swept Sine Wave excitation K = 0.36%

The discrepancy in the value of the damping ratio can be attributed to the

following reasons. A random input signal gives the best linear approximation for any nonlinearities present in the system. It is by far the best

input signal. One of the main disadvantages of pseudo-random excitation is

that nonlinearities in the system under investigation, will generate

periodic noise signals which cannot be averaged out of the data. Due to

this condition the overall quality of a pseudo-random measurement is

generally lower than that made by any other technique. Regarding the

swept sine input, the sweeping in the present case was performed manually

which is not uniform. A more uniform sweeping can be obtained by using an

excitation control system. The damping ratio values reported using these
three types of excitation were from preliminary experiments. Further

experiments will be conducted to investigate the discrepancy in the

measured value of damping ratio with the above three types of excitation.

Figs. 8 and 9 show the real and imaginary parts of the mobility funcvelocity

tion (

force

) for the tube specimen when it is vibrating in its 1st mode

and excited by random noise. The real part of the mobility function has a

maximum value when the frequency of excitation is at the resonance frequency of the specimen and correspondingly the imaginary part has a zero

value at this frequency. Further work is in progress to develop a curve

fitting algorithm to estimate the real and imaginary parts of the mobility

function. This would then enable us to estimate the values of the damping

ratio and resonance Frequency more accurately.

t
Table I

Mode N

1

2

3

4

5

6

Nat. frequency

(Hz)

552.5

1514

1873

2204.5

2232

2841.75

ef(Hz) Damping ratio (c)%

1.5 0.135

7.5 0.267

12.5 0.336

15.5 0.351

16.0 0.358

20.5 0.360
OF, POOR c. .1, •.

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SETUP 117

11EASUREMEWT- DUAL SPECTRUM AVEPh.14C

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(Random input signal)

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