Rayleigh-Ritz analyse van vibrafoonstaven

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Rayleigh-Ritz analyse van vibrafoonstaven

Citation for published version (APA):

Kroon, P. J. M. (1987). Rayleigh-Ritz analyse van vibrafoonstaven. (DCT rapporten; Vol. 1987.011). Technische

Universiteit Eindhoven.

Document status and date:

Gepubliceerd: 01/01/1987

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1.2

b P = \ , 2 ,

. . -

a

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3

1.4

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- .

y”

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u

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r.6

l L

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4

L

-i -,

STAAF @

300 2650

STAAF

1 S T A A F 2

300

4

B

*

S T A A F

5

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Y= ia24 N= 15 I =

-

.30EE O E= .ASOEE -1 D0= .i467E -1 D I = .aamE E LA= .OEEEE 0 R= .O0EEE 0 I= 1 W.I=.OEEEE 0 J= 2 W.J=.EBEEE 0 7= 1024 U= 15 _= .380E 0 3= .49EEE -1 IO=

.

I 4 6 7 ~ -i 11= .EE08E O -A= .0808E E i= .BBBEE 0 I= 3 d.?=.EE0EE 0 I= 4 d.Js0BEEE E BASF I 2 .a4 I BASF J z a a 1.681, I .za . t 0

\

I .za. .ea. -.aa. -.ea. I .a. I .a 3.aa m BASF J 2. 1. i . I . I . 2 . 1= IE24 N= 15 L= .30EE B B= .490EE -1 DE= .1467E -1 Dl=.BEEBE O LA=.aE00E E R = .!380EE 0 I= 5 W.I=.OBBEE E J= 6 W.J=.OBEEE 0 BASF J

I

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BASF I BASF J q= i a 2 4 i= . 3 a a ~ E B= .+aaE - I DI= .aaaaE 0 i ~ = . a a a a ~ a R= .aaaaE a w.:=.~aaa~ a J= i a w.~=.aaaa~ a N= 15 Ei=

.

I 467E -1 I= 9 II= i a 2 4 L= . 3 a a ~ a N= 15 B= .d90aE -1 DB= .1467E -1 D I = . a a m a LA= .aaaaE 0 R= .aaaaE a w.I=.aaaaE a w.~=.aaaa~ a I= 11 J= 12 BASF I 2.00 I

.,I

BASF J 2.51 2.,,1 1.58 I .OO .a0 -.SB -1 .a0 -1 .SE BASF I BASF J

3

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n=

1824 L= . 3 a a ~ a N= 15 B= .49aOE - 1 D0=

.

i 467E - 1 D I = .aa0a~ 0 L A = . ~ ~ B ~ E 0 R= aam^ a W . I = . B ~ ~ E a w.J=.aaaaE 0 I= 13 J = 14 1 .za .8a .48 -.2E -.a0 -1 .za -1.60 SASF J 2 .m, i .sa I .za .ea -.ea -1 .a -1 .60 - 2 . d

BASISFUNCTIES

1 WFW

Y = ia24 L= . 3 a 0 ~ E B= .~SEIBE - 1 D I = .aaaBE a LA= . a ~ a 0 ~ E R= .aaaa~ E w.~=.aam~ a W . J = . B ~ O ~ E 0 N = 15 D0=

.

i467E -1 I= 15 J = 15 -2.ml SASF J

1

2.m

I

W F W

BASISFUNCTIES

~~

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Y= i a 2 4 L= . 3 a a ~ a B= .=wm - I Da=

.

i 4 6 7 ~ - 1 D I = .aaaaE a LA= .aaaaE a R= .aaaaE a w.!=.aaaaE a W.J=.B~OOE a N= i 3 I= 1 J= 2 i .a@. .sa. .SE. ..a. .za. -.m. -.z. -.‘O. -.60. - sa. i .ae_

a .ia .sa .& 1.20 1.50 -.sa 2.,a 2.aa 2’.7a 3l.m

xia-1

m

BASF J

.ZO.

.SO 1.m 2.1a 2’.-a 2’.m 3 a8

xia-1 -.aa. m

LEGENDRE-POLYNOMEN

Y= I a24 i= . 3 a a ~ a E= .dsaaE -I cia= .i467E -i D I = .aaaaE a LA= aam^ a R= .aam€ a w.:=.aaaa~ a w.~=.aaaa~ 0 N= 13 I= 3 J= 4 Y= ia24 L= . 3 a a ~ a B= . w a a E -i m=

.

+WE - I D I =

. m a m

a LA= .aaaaE a R= .aaaaE

a

w.~=.aaaa~ a w.J=.aaaaE a N= 13 ~ I= 5

’

J= 6 ~- BhSF I -.2a -.-a. - .60. -1

-7

.a8 5ASF J 1 .aa

LEGENDRE-POLYNOMEN

I

I .an .sa), .SE

I

SASF J

I

.?E. .ze. -.m. -.za:” -.-a.

LEGENDRE-POLYNOMEN

1 W F W

c

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Y= ia24 i= .xm a E= .AgaaE - I ~ i = . a a a ~ 0 ~ ~ = . a a a a ~ a R= .aaaa~ a x.~=.aaaa~ a ul.~=.aaaa~ a N= i3 D0=

.

i"67E -; I= 7 J= 8 - .&a. -.ga. -.LE. -.-a. -.sa. -.sa. i .a@, 54Sc J 1 2 0 - .ea. .GL

38 .sa .sa .za i'.sa i'ga z'.ia 2.+a 2 70 3'.aa x a-' 7;

::::I

I .aa &a. .LB. - , aa. -.a. -.&a.

LEGENDRE-POLYNOMEN

1 W F W

3a .sa .& 1.20 .50 1 .sa

.a. / ,341 .Ga .ia 1.20 1 z . i a 2.+0 2.70 -..a: x10- 9ACF J ?.m

::::y

1 .a0 ~~~

LEGENDRE-POLYNOMEN

~~

Í W F W

Y = ia24 N= ;3 L= . 3 B E a B= .AsaaE - i ga=

.

, 6 6 7 ~ -i D I = .saam a LA= . a a a a ~ a R= .aaaaE a w . I = . ~ ~ o E a vl.~=.aaaa~ a I= i i J = i2 ~~~ BASF I j a0 sa 60

.

-a 20 - as - &a -.*a - Ga -.sa I aa

:::I

I .a0

c

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Y= 182-1 _ - . B ~ E a B= .dsaaE - 1 na=

.

, & W E - 1 D i = .aam€ a LA= . a m a ~ a R= .aaaaE a r l . i = . a a a ~ ~ a ~ . J = . a a a a ~ a N= '3 I -I= 13 i= 13 .LB. -.aE. - .La: -.LE. SASF I \ . 3 a .sa i . 1.58 1.88 z. E 2 LE 2.78 ' a8 X1E-l n

LEGENDRE-POLYNOMEN

I

'WFV

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N

1 - )

2.

3 gi

5 F

2 I I

o

8

o

8\13,?

o

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i

4

0 0

3

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I cf! I CF.

I

n t u

z

T

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I

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A f

(Yz'

I

0

/ I

Pu

O

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L

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8,s

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3 2 2

2 0,6

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S T A A T

p

[,

o

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ie

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I / / I #

7

62 \?

\ \

9222

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I

--mmm

-

d m '\, \ \ \, --mwm 't 4 61'

I

--mmm 6 6 mi I I

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I- 1024

..:. 0

.I- 15

3:: .&300E - 1

I@= .i 467E -.i

) I =

.

i000E - - I .A= ./60BE -1 ?- .W08F -1 [:: 1 r'.!=.5302E 3 J:: 2 ii..r=.i61fiF: 4 .I 1= 1024 4- 15 -= .d00E 0 3 - .4900E -1 IO= .1467E - 1 31= .I000E - I .A=

.

J600E -i ?= .'008E - 1 I - 3 #.1=.3456F 4 I. J=.F074E 4 J- L/ 1 . s s ! / EIGF ,i 1.43 I

.+A

EIGENFIE

MBV

ANAL-FIE

FIGF I 1 .CG EIGF J 1 .G6,

EIGENFIE

MBV

ANAL.FIE

___ F I C T I 1 /Y

/'

x i 0 1 \, ,

,/'

.sa i .LB I .pa I .ea z.ia 2.40 I ' . I B 2.aa

'\ / ' \..\

./'

-._. _,

..

"\

EIGENFIE

MBV

LEGENDRE

I

' W F W

FIGF I .-. a0. \ / \ ,

/

. 0 ..U3 .GM .sa 1.20 1.50 1.Bd 2 . i Q 2.'0 . I 0 3',&3

x10-1 -.,l. - . 1 2 . \

/

7:

.

'i4

I

1 W F W

EIGENFIE

MBV

LEGENDRE

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1- 1024 \I= 15 _= .30@E @ 3:: .?9@0E - i IQ=

.

ï46'iE - 1 11- .7000E -2 -A= .'760EE -1 i= .4008E - 1 1:. 3 t/.I=.L434E 4 J= 4 W.J=.?46iE 4 FIGF I I wl I 5 4 I ."8. EIGF

J

_.

.. .0a

. i a .ha .90 1'.20 1 . 0 I'S 21.ia z'.+a z'.m 3*.m

x10-' m i .a7 .. .-,

1 W F W

~-

EIGENFIE

MBV

ANAL.FIE

EIGF I 1 ./E, \

\

' \ / EIGF J i .79- I .43. i ' . ~ z':0 2'.4a 2' 10 3'.aa xia-1 rn ~. .1 33. -1 .'/SId

EIGENFIE

MBV

ANAL-FIE

I

W F W

F I C T I

/

EIGENFIE

MBV

LEGENDRE

I

WFW

. .. EIGF J Yl0'1 4 . 1 8 3 . 8 2 . 2 . W l . 1

.A

-2.81. ',\\./ --.pa. '\ j, - ,18. .96. 10 +0 .GB . i a i'.m \, I .91. \ 3.82. .t .'/E

FIGENFIE

MBV

LEGENDRE

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B

(a

G

O

B

7 1- 1024 .I- 15 .= .300E 0 3: : .4980E -1 1 0 ~ . i 469F - 1 11- .5080E .-2 .A= .1600E -.l <: .4888E -1 1.1 1 J.IILL779F: 3 I=

2

I . .J=:. I 1 3 Z E 3 '1- 1024 N= 15 L= .300E 0 E- .4900E -1 D0= .1469F -1 D i = .5000E -2 LA- .1680E -1 R = .do085 -1 I- 3 W.I=.1723E 4 J= 4 W.J=..3241E 4 FIGF I I 9 / FIGF J

FIGENFIE

MBV

ANAL.FIE

1 WRW

EIGF I I .8G I .*SI

EIGENFIE

MBV

ANAL .FIE

I

W F W

N- 13 L- .300E 0 B- .d988t 1 DO-

.

i469F 1 D I = .5mw -2 L A = .1600E -1 R= .4088F -1 I 3 J 4 W . I . i 7 9 5 F 4 W.J-.4205F 4 ' , L>R,

:::

/'

'6 48

EIGENFIf

MBV

LEGENDRE

I

W F W

- .G1

*ai

,,,.,FICF J 4.93-

-

EIGENFIE

MBV

LEGENDRE

1 V F W

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K

_e

P

n

G'

F

I

4-

F;

I= I- 1024 1s _ =

.xm

3= ."S0BE 10=:

.

I467E 31 =

.

.30@0E -A= ./60@E ?= . 4 0 a ~ I . 1::. I a i 7~ I -

1

J-2 2 i . .J=. 3776E I= ia24 d= 1s ..300E 0 3= , 4 9 0 0 ~ - 1 10= ,1467E -1 l i = .3@0@E -2 -A= ./6@0E - 1 I = 3 #.1=.1010E 4 I= 4 l.J=. ISS2E 4 ?= . w a E - 1 FICF I 1 I .v.

.s7i

1 .a3.

/'--

FIGF J 1 .'I2 1

.

.r/. .OS. .34.

-. .a0.

\

~- 1.20 .?a :.na 2 . # a 2.4a 2':/w 3'.aa

I .a3. .za - . A t " x10-1 ... OS. m I ,:r1. 1 ,/z-

EIGENFIE

MBV

ANAL-FIE

EIGF I I 95. I 56. I 17. 18. 39. a0. 30 $0 .Ga i a 1 2 0 1 7 0 1.8 z . i e 2 - 0 2'. 3'aa x10 3.3. - /B. m 1 1 7 . 1 56. I 95. EIGF J

\

2.00, I .ca. 1 .20. * 2 . a 2 . ~ 0 ' . i 0 3'00 x10-1 -.ea. m 1 .za. 1 .GO. 2.08..

EIGENFIE

MBV

ANAL.FIE

1 WFU

Y:= ia24 t.- ..im 8 N- 1 9 R:: .4.900E -.1 00::

.

, 46'E --i 01 = .3800E - - 2 LA- ./600E ..i

R= .4008E - 1 I= I W..J=.i271E 3 J- L W.JsAS88F 3 1- 1024 N= 13 L=

.-mac

a oa=

.

i WE

-

i B- .4S0@E - 1 DI= .300@E 2 LA- ./6@0F - 1 I: 3 W.1-. i985E 4 J= I., W.!=.363RF 4 FICF I EIGF