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...

C 10 F F

F,

:

(tG 2:

(t

F , , , . H,

F F

D.E..:

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F F

. I

D.E..,

, ..,

.

, , DF.

. F

, . .det [ ]

D :

A

;

F F

1 2

1 2

21

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F , :

F :

.82 / 2.618 /

F F

A:

.82 / 2.618 /

< < = ,

.

= .

E

.

F F

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, .

A . .

.

, .

F F

1

1.618

1

0.618

1 2

./ ./

. =

1 DF

F F

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.H (5),

.I

.

F F

.

1 1.618

. =3.62 1 1.618

.

1 .618

. 1 .618

. =0.382

, . H,

= =

:

F F

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F F

j mass number row n mode number column

D:

1 (1)

D: A (1), 1

F :

: .

.

F F

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F F

Therefore,

This means that the natural modes are not only orthogonal but are

normalized with respect to m. They are then called a mass orthonormal set.

When the modes are normalized, we will have

:

G 11.26 11.6 ;

16 66

1

16 1 661.26 1

241 .644

1.2616 1 661.261.26

241 .81

1

16 1 661.6 1

11 .567

1.6

16 1 661.61.6

11 .924

.644 .567.81 .924

F F

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F F

A

( ).

, I ( 3 ):

F F

, u, it is possible to

evaluate the qs :

nTm

B ,

;

,

8/10/2019 Part 11 - Ch 10 Mdof - Free Vibration

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F F

I , , .

F 2 DF:

I ,

( ).

8/10/2019 Part 11 - Ch 10 Mdof - Free Vibration

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: ?

. ,

2 DF :

1 2

. 1 2

.

E:

1

2

/2 /2

12

12 11

2

2

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D 3 .

D: 1 = 1 1 = 600

2 = 1.5 2 = 1200

3 = 2 3 = 1800

A , 3 :

14.5 1.

.65.

1.2 1.

.61.68

46.1 1.2.62.5

1

1

3 2

3 2

2 = 1000

H, , ,

1 1 1.65 .61 2.6. .68 2.5

F ,

1 1.5 2

1

1,2,

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D ,

1 .65 .1 .61 .681 2.6 2.5

1 1 . 5 2

1 1 1.65 .61 2.6. .68 2.5

1.812

2.466 29.2

H 1.812; 2.466; 29.2

1 .65 .1 .61 .681 2.6 2.5

1

656126

H 65; 61; 26

3 :

1:

14.5 . (1)

2:

1.2 . (2)

3:

46.1 . (3)

(1), (2), (3) 3 DF

.

1

2.47 1 14.5

.254 1 1.2

.5 1 46.7

1*

1* 1

*

2*

2* 2

*

3*

3* 3

*

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3 DF , ,

.

, ,

I :

.

1:

1 2.47 1 14.5 1 .254 1 1.2 1.51 46.7

( )

1:

1 2.47 1 14.5 1 .254 1 1.2 1.51 46.7

2:

.65 2.47 1 14.5 .61 .254 1 1.2 2.6 .5 1 46.7

3:

. 2.47 114.5 .68 .254 11.2 2.5.5146.7

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,

D.E..:

,

I :

D IIIA CDII.

,

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G: 12

1:

2:

D :

[

[

1 2

,

E.

1 1.618 1 1

12

1 1.618 1 1 11.618

1.17

1 .618 1 1

12

1 .618 1

1

1

.618

.16

,

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? ( )

G:

11.618

1 1.618 1 1

11.618

1 1.618 1 1 11.618

1 .618 1 1 11.618

1 .618 1 1 1.618

,

H:

: I

,

.

: ICIE F EII AIE