Introduction to DampingIntroduction to Damping Impact, Mechanisms, and Measurements

Presented ByMichael L. Drake for

Brush Beryllium & Composites

Structural Damping

= “Energy Dissipation”R l f E f= Removal of Energy from

Vibration of Interest

Effects of Damping onSystems Motions

Steady State : Limits Motions controlled by energy balance

Resonance Broad Band Broad - Band Spatial Resonance (Trace Matching)Free Vibrations : Increase Rate of Decay

With Time With Time With DistanceOnset of Vibration : Decreases Rate of Build - UpSelf - Excited Vibration : Limits Amplitude

Flutter Stick Slip

Practical Consequencesof Damping

• Increased Fatigue Life• Increased Impedance (for Improved

Vib i I l i )Vibration Isolation)• Reduced Sound Transmission• Reduced Noise from Repetitive Impacts• Reduced Transmission of Vibrations and

Structure - Borne Sound

Single Degree of Freedom Examplep

10Q

X =F

ko

2m F s i no t

11

2

2

2 2

n n

m

k c

0.1

X 1 Fo

X FoX Fo

0.01

/n<<1 /n>>1

Xk

X o

2M

Xk

n 1

0 1 2 3 4 5 6

Simple System:Steady State

x = X s in t

F = F s ino t

mx W = 1 2 mv kx2 2 1 2 1 2 m Xn2 2At

Resonance

D = cv. c Xcycle

2dx

D2 c c c

m

k c

2W

cm

ckm

ccn c

2F kxk

F cvc

n2 k

m

c km Critical Damping Coefficient" 2 "c km Critical Damping Coefficientc 2

Ranges of Material Loss Factor Near Room Temperature 0.010.1

110

10

ers

cous

Liq

uids

0.1

1d A

lloys

Dam

ped

posi

tes

rdC

ork

Dry an

d

icle

Boa

rd

e se Asp

halt

tics

& R

ubbe

Gel

s &

Vis

c

0.01

oppe

r, Tin

Lead

h -D

ampi

ng

rick

/ Blo

ck

aphi

te E

poxy

ompo

site

s

Inte

gral

ly D

G /

E C

omp

Gyp

sum

Boa

rD Sa

k, F

ir Ti

mbe

r

lyw

ood,

Par

ti

Con

cret

eLi

ght,

Den

Plas

t

0.0001

0.001

Aluminum,

Brass, Bronze,Steel, Iron

Co T

Hig

GlassB

r

Gra C G

Oak Pl

Magnesium

System Damping

D DTOT i 5

432

1

D = 2 Wi ii

W WTOT i

D W6 7

8

system

TOT

TOT

i

i

DW

WW

2

i

If only 1 0 :

system1

TOT

WW

1

If only 1 0 :W

W needs to be > 01

TOT1 needs to be > 0

How Different Levels of Damping Capacity Affect Vibration Decay

0 8

1.0

Free Vibration Decay at 1 0 H z, Lo ss F acto r = 1.0E-4

Free Vibration Decay at 1 0 H z, Lo ss F acto r = 1.5E-3

0.2

0.4

0.6

0.8

lace

men

t

-0 .4

-0.2

0.0

0.2

Nor

ma

lized

Tip

Dis

pl

-1 .0

-0.8

-0.6

N

0 10 20 30 4 0 50 6 0Time (sec)

How Elastic Modulus Affects Vibration Decay if Materials Have Same Damping Capacity

For Equal Initial Load

0.8

1.0

Aluminum , Loss Factor = 1.0E-3, Natural F requency = 40 HzAl-62wt% Be, Loss Factor = 1.0E-3, Na tu ra l Frequency = 75 HzBerylium , Loss Factor = 1.0E-3, Natural F requency = 100 Hz

0 2

0.4

0.6

cem

ent

-0.2

0.0

0.2

Nor

mal

ized

Tip

Dis

plac

-0.8

-0.6

-0.4N

-1.00 1 2 3 4 5 6 7 8 9 10

Tim e (sec)

How Elastic Modulus Affects Vibration Decay if

Aluminum , Loss Factor = 1.0E-3, Natural Frequency = 40 HzE l I iti l Ti Di l t

How Elastic Modulus Affects Vibration Decay if

Materials Have Same Damping Capacity

0.8

1.0

Aluminum , Loss Factor 1.0E 3, Natural Frequency 40 HzAl-62wt% Be, Loss Factor = 1.0E-3, Natura l Frequency = 75 HzBerylium , Loss Factor = 1.0E-3, Natural Frequency = 100 Hz

Equal Initial Tip Displacement

0.2

0.4

0.6

acem

ent

0 4

-0.2

0.0

Nor

mal

ized

Tip

Dis

pla

-0.8

-0.6

-0.4N

-1.00 1 2 3 4 5 6 7 8 9 10

Tim e (sec)