Computerized Viscoelastic Master Plots for Vibration Damping

22 Computerized Viscoelastic Master Plots for Vibration Damping Applications

Downloaded by UNIV OF IOWA on September 3, 2016 | http://pubs.acs.org Publication Date: September 24, 1982 | doi: 10.1021/bk-1982-0197.ch022

RICHARD P. CHARTOFF and JOHN L. GRAHAM University of Dayton, The Center for Basic and Applied Polymer Research, Dayton, OH 45469 Using a computerized data reduction scheme that incorporates a generalized WLF equation, dynamic mechanical data for two different polymers were correlated on master curves. The data then were related to the vibration damping behavior of each material over a broad range of frequencies and temperatures. The master curves are represented on a novel reduced temperature nomograph which presents the storage modulus and loss tangent plots simultaneously as functions of frequency and temperature. The data reduction procedure cited is particularly useful in treating resonant vibration measurements where frequency varies during a scan over a range of temperatures. Normally to obtain a master curve using such instruments, data must be obtained for several samples having different shapes and sizes. However, using the procedure discussed only a single scan over a range of temperatures is required in order to obtain a master curve. Viscoelastic data for polymethylmethacrylate obtained independently with a resonant vibration instrument and a constant frequency instrument are shown to be equivalent. V i b r a t i o n Damping C o n s i d e r a t i o n s . The n e c e s s i t y f o r a b s o r b i n g v i b r a t i o n a l energy o c c u r s whenever a s t r u c t u r a l u n i t h a s t h e p o s s i b i l i t y o f being excited mechanically o r acoustically t o v i b r a t i o n modes h a v i n g v e r y h i g h a m p l i t u d e s . I n t h e most c r i t i c a l s i t u a t i o n s such as i n a i r c r a f t systems t h i s can l e a d t o s t r u c t u r a l f a t i g u e and f a i l u r e . P r a c t i c a l s o l u t i o n s t o damping

0097-6156/82/0197-0367$06.00/0 © 1982 American Chemical Society

Provder; Computer Applications in Applied Polymer Science ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

368

C O M P U T E R APPLICATIONS I N APPLIED P O L Y M E R SCIENCE

these

vibrations

materials

to

usually

selected

involve

areas.

application

Frequently

of high

these

damping

materials

are

polymers. The as

part

ability of

a

properties. A

polymer

in

These

Figure


change

t o be

energy

i s

dissipated.

strate

i n

film

constrained i n a

the

layers

the

material

need

of

temperature

to

perature

or a

layer

that

its

of

modulus

the

of

oblique

be

The

T

curve read

shown

by

6)

from

a metal

a

sub-

i t s

surface

The dominant

while

give

transition

the

dominant

layer(4^)

maximum

region,

i n the

over

damping

while

high

con-

temperature

using

lines

i n this

over

is

data

range

range

we

of

to

tem-

other

master

curves

a

i n a

i n terms to

presented

limited shift also

data

frequency

an a u x i l i a r y

plot

number

be

right-

paragraph.

reduced must

given

a

r

on the

frequency,

use because It

range

a^

contains

scale

as

represent

values,

subsequent of

i n

are displayed

frequency

directly.

using

a broad

utility.

The diagram

way

a

time-temperature-

temperature and a

whether

application

instances

extended

curves

cumbersome

the p l o t

limited

The s i m u l a t e d

explained

rather

temperature

i t s

tangent

temperatures

be

over

viscoelastic

master

frequency. the

a the

form

evaluate

damping

i n most

are then

and extend

using

to

properties

to

typical

will is

to

frequency

determined

(or table)

for

of

values.

Reduced

Temperature

Construction modulus

region

as

sufficient

plate.

In order

only

on the diagram.

presented

master

vs.

five

to

tensile

However,

and loss

temperature

particular

arp

at

These

When

a

reduced

insert

side.

cannot

some

superposed

in

the

the

applied

and constrained

3)

the

The d a t a

data

2 where taken

metal

is

be that

or with

for a particular

p r o c e d u r e (_5,

of

layer

treatments

Curves.

and frequencies

drawing

hand

behavior

must

assure

efficiently

quantities

the

2_,

viscoelastic

A

function

of

and frequency.

correlate

then

i n

transition

shear.

layer

suitable

Figure

and

analysis.

zone.

or frequency.

superposition

points

the

applied

second layer

is

side

i s

free

layer(_1, free

Master

is

these

temperatures

a

energy

viscoelastic

vibrations

rubbery

w i l l

i t a

free

p e r f o r m most

know

measure

that

foil i n a

transition

we can

as

for free

Viscoelastic given

to

linear

mechanical

by

the polymer

Usually

low temperature

of

dynamic

covered

that

either

constrained

indicate

strained end

form

by metal

Theories in

configuration

deformation

damping

dissipate

i t s

f o r damping

glassy

effective

i n a

mode

to

1.

order

of

by

range

from

effectively

related

are measured

structure

mode

to

c a n be

and frequency

properties In

a polymer

h a s maximum p o t e n t i a l

temperature where

of

structure

and loss

Nomograph

and Use o f tangent

the Nomograph.

values

as

a

function

The c a l c u l a t i o n of

frequency


at

of a


22.

CHARTOFF AND GRAHAM

Viscoelastic

Master Plots

369

TEMPERATURE Figure 1. Typical dynamic mechanical modulus and loss tangent data as a junction oj temperature. Key: a, glassy region; b, transition region; and c, rubbery region.


Provder; Computer Applications in Applied Polymer Science ACS Symposium Series; American Chemical Society: Washington, DC, 1982. T

Figure 2. Viscoelastic master curves represented on reduced temperature nomograph. Key: solid symbols, modulus values and open symbols, loss tangent values. Insert at upper left shows the shift factor function, a , used for data reduction.

TEMPERATURE


22.

constant

temperature,

T-^, c a n b e

defining

an a u x i l i a r y

function,

of

temperature

aT a t

Jones(7) the

reading

of

nomograph abscissa

of

right

for the plots

along

the

lines,

value

at

6

at

curves

values E '

10

to

find

(point

f

= constant,

of

Figure line

at

( f ,T»2.) / p o i n t

fa-p

i t

follows B,

from

and tan 6

Data to for

computerized TQ

This The

lines

= 1.2,

is

done

by

derived

by

ceramics

about

experiment

to

set

fre-

points

a^

itself.

f=10.0 Hz of

the

E ' and

master

assume

T - i of

we frequency

the horizontal

EX, defines Hz.

2

that

a n d some

From

and tan 6

a

this

that

The nomograph

data If

and i s

line

value

of

value

of

E ' = 10

3

N/m ,

the test

on an e x t e n s i v e

the generalized

data

assumed

T used

i t s e l f

2

position

etc., i n

values

readily

convenient

the proper

and T i , T2/

TQ

faT with

ax v s .

lends

particularly

one s e l e c t s

to place

of

a

A.

AT between

calculating

and f i t

4*10

of E '

point

used

Thus of

values

using

at

line

T

procedures.

values

scale

on

form

the reduced f j .

a

same

v s . fa-p.

fjaTj_

values

this,

to

the

the ordinate

of

the nomograph,

Procedure.

can be

appropriate

From

determined

fja _]_,

D, o f

and the interval

of

frequency

converted using

tangent

frequency

The i n t e r s e c t i o n

of viscoelastic

for grid

2.

fj

defines

and tan 6

the plots

Reduction

reduction

E '

CX, with

fa-p

point

of

onto

the

fa«p.

the use o f

the value

to

a»p, e t c .

by

directly

facilitate

as

Hz r e p r e s e n t

T i can be

i t

i s

of

The values

on the

vs.

curve

and loss

o f which

f=1.0

upward

and tan 6

illustrate C)

point

to

constructed

f i g u r e (7) .

where of

To f

o f modulus is

value

frequencies.

function

T-j_ c o r r e s p o n d i n g

temperature

of

a

by

the

was d e v e l o p e d

i n order

a master

as

scale

each

one decade

represents

wish

of

the abscissa

shift

tan

frequency

side

oblique

quency A

as

f j a ^

a-p^ i s

by p l o t t i n g

for selected

procedure,

by p l o t t i n g

auxiliary

the

data

this

considerably

where

procedure

curve

371

Plots

simplified

function

master

Master

f jaip. ,

A novel

this

frequency

Following

An

Tj_.

for applying

reduced

direct


Viscoelastic

CHARTOFF AND GRAHAM

then

of

a

Computerized Viscoelastic Master Plots for Vibration Damping

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