Dynamic Characteristics of Welded Structures

8/8/2019 Dynamic Characteristics of Welded Structures

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E L S E V I E R Nuclear Engineering and Design 160 (1996) 379-385

N u c l e a rE n g i n e e r i n ga n d D e s ig n

Dynamic characteris t ics of welded s tructuresShigeru Aoki

Department o f Mechanical Engineering, Tokyo Metropolitan College of Technology, 1-10-40 Higashi-Ohi, Shinagawa-ku,Tokyo 140, JapanReceived 1 Jun e 1995; accepted 1 S eptembe r 1995

A b s t r a c t

W elding is widely used for joints of ma ny st ruc tures. In this paper , the effec t of welding on d ynam ic charac ter ist icsi s examined based on expe r imen t . F i r s t , dynam ic cha rac te r i s ti c s o f s imple spec imens wi th we lding a re measured . Nex t ,the effec t of welding on random vibra t ion and re l iabi l i ty for the f i rst passage problem is examined by a theore t ica lme thod us ing an ana ly t i ca l mode l wi th r e sponse cha rac t e r i s t i c s measured f rom expe r imen t . F ina l ly , t he app l i cab i l i t yof ob ta ined re su l t s t o ac tua l s t ruc tu re s i s examined by an expe r imen t us ing a f r ame mode l . I t i s conc luded tha t t hedamping ra t io increases when welding is used.

1 . I n t r o d u c t i o n

W e l d i n g is w id e l y u s e d f o r c o n s t r u c t i o n o fm a n y s t r u ct u r es . S t u d ie s o n v i b r a t i o n o f w e l d eds t r u c t u r e s s u b j e c t e d t o c y c l ic l o a d h a v e b e e n c a r -r i e d o u t ( E n g e l h a r d t , 1 99 3; Z u r a s k i , 1 9 93 ). T h e s es t u d i e s a r e m a i n l y c o n c e r n e d w i t h f a t i g u e f a i l u r e .O n r e l ia b i l it y o f w e l d e d s t r u c t u r e s s u b j e c t e d t oe x t e r n a l l o a d i n g , s t u d i e s h a v e b e e n c a r r i e d o u t o ns t a t i c s t r e n g t h ( L a B o u b e , 1 9 9 3 ) a n d a n a l y s i sb a s e d o n f r a c t u r e m e c h a n i c s ( R a h m a n , 1 99 2;S m i t h , 1 9 92 ). S t a t i s ti c a l e v a l u a t i o n o f ( C h e v e r t o n ,1 99 2) a n d f a i l u r e m e c h a n i s m s f o r ( B u s h , 1 9 92 )w e l d i n g h a v e a l s o b e e n p r e s e n t e d .

I n m a n y o f t h es e s t u di e s, d y n a m i c c h a r a c t er i s -t ic s a r e n o t c o n s i d e r e d . T h e e f fe c t o f w e l d i n g o nd y n a m i c c h a r a c t e r i s t i c s h a v e n o t b e e n s t u d i e d i nd e t a i l e v e n f o r t h e e l a s t i c r a n g e . T h i s p r o b l e m i s

e x p e c t e d t o b e u s e f u l f o r s t u d y a n d d e s i g n o fw e l d e d s t r u c t u r e s s u b j e c t e d t o o r d i n a r y d y n a m i cl o a d i n g .

C o n s i d e r i n g t h e a b o v e m e n t i o n e d p o i n t s , th ea i m o f t h i s p a p e r i s t o p r e s e n t t h e e f f e c t o f w e l d -i n g o n d y n a m i c c h a r a c t er i s ti c s o f s t ru c t u r e s a n do n r e s p o n s e c h a r a c t e r i s t i c s a n d r e l ia b i l it y o f s t ru c -t u r e s s u b j e c te d t o r a n d o m v i b r a t i o n . F i r s t , b y a ne x p e r i m e n t u s i n g s i m p l e s p e c im e n s , d y n a m i c c h a r -a c t e r is t i c s o f s p e c i m e n s w i t h w e l d i n g a r e c o m -p a r e d w i t h t h o s e o f s p e c i m e n s w i t h o u t w e l di n g .N e x t , u s i n g r e s u l t s o b t a i n e d b y t h e e x p e r i m e n t ,t h e e f f ec t o f w e l d i n g o n r e s p o n s e c h a r a c t e r i s t i c sa n d r e l ia b i l it y o f s t r u c t u r e s s u b j e c t e d t o r a n d o mv i b r a t i o n a r e e x a m i n e d . F i n a ll y , b y a n e x p e r i m e n tu s i n g a m o d e l o f a c t u a l s t r u c t u r e s , t h e a p p l i c a -b i l it y o f o b t a i n e d r e s u l t s to a c t u a l s t r u c t u r e s i se x a m i n e d .

0029-5493/96/$15.00 1996 Elsev ier Science S.A . All rights reser vedS S D I 0029-5493(95)01115-3


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380 S . Ao k i / Nu c l ea r En g i n eer i n g a n d D es ig n 1 6 0 (1 9 9 6 ) 3 7 9 - 3 8 5

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2;2 I I l l i l l l I

Fig. t. Shape of specimen.

2. Estimation o f dynam ic characteristics byexperiment

B y a n e x p e r i m e n t u s i n g s i m p l e s p e c i m e n s , t h ee f fe c t o f w e l d i n g o n d y n a m i c c h a r a c t e r i s t i c s i se x a m i n e d . M e t h o d s a n d r e s u lt s o f t h e e x p e r i m e n ta r e s h o w n .

t i o n a l m o d e a r e e s t i m a t e d , f , i s o b t a i n e d b y t h ef r e q u e n c y s w e e p m e t h o d . ( is o b t a i n e d b y t h ef o l l o w i n g t h r e e m e t h o d s .

( I ) A l o g a r i t h m i c d e c r em en t C~ i s o b t a i n ed b yt h e f r e e v i b r a t i o n , t h e n t h e f o r m u l a ( = 6 /2re is used.( I I) T h e h a l f p o w e r m e t h o d , t h a t i s f r e q u e n -c i es f~ a n d f 2 , w h e r e t h e a m p l i t u d e o n t h er e s o n a n c e c u r v e is 1 / ~ / 2 t i m e s t h e p e a ka m p l i t u d e , a r e o b t a i n e d , t h e n t h e f o r m u l a( = ( f 2 - J l ) / 2 f , i s used .( I II ) T h e r e l a t i o n 1 / 2 ( b e t w e e n t h e r a t i o o f t h er e s p o n s e a m p l i t u d e t o t h e i n p u t a m p l i t u d ea t f , i s u s ed .

I n th e f r e q u e n c y s w e e p m e t h o d , t h e i n p u t a m -p l i t u d e i s f i x ed a s 1 .0 m m p p . A n am p l i t u d e o f2 .0 m m p p i s a l s o u s ed w h en i t is n eed ed .2.2. Results o f experiment

2. I . M etho d o f experimentA s s p e c i m e n s , t h e c a n t i l e v e r m o d e l s s h o w n i n

F i g . 1 a r e u s e d . F o u r t y p e s o f s p e c i m e n s i z e,s h o w n i n T a b l e 1 , a r e s e l e c t e d . T h e s p e c i m e nm at e r i a l i s r o l l ed s t ee l f o r g en e r a l s t r u c t u r e s ( J I SS S 4 0 0 ) . T h e l e n g t h L f o f t h e f i x e d p a r t o f t h es h a k e r i s 1 00 m m . T h i s p a r t i s f i x ed b y t h r ee b o l t s .T h e l e n g t h L w f r o m t h e w e l d l in e t o t h e c e n t e r o ft h e l e f t h o l e i s 2 5 0 m m . T h e f o l l o w i n g t h r e e t y p e so f s p e c i m e n a r e u s e d .

( I ) S p e c i m e n w i t h o u t w e l d i n g .( 2) S p e c i m e n w e l d e d b y m a n u a l o p e r a t i o n .( 3) S p e c i m e n w e l d e d b y t h e a u t o m a t i c C O 2 g a s

s h i e l d e d a r c w e l d i n g m a c h i n e .T h e g r o o v e s h a p e i s V t y p e . S p e c i m e n s a r e b u t tw e l d e d .

A s d y n a m i c c h a r a c te r i st i c s, t h e d a m p i n g r a t io (a n d t h e n a t u r a l f r e q u e n c y f n f o r t h e f i rs t v i b r a -Table 1Size o f specimen (mm)Specimen L B LA 530 65 9B 530 65 6C 460 65 9D 460 65 6

I n T a b l e 2 , v a l u e s o f ( a n d J~ e s t i m a t e d b y t h ee x p e r i m e n t a r e s h o w n . T h e r e s u l ts o f s p e c i m e n B 'a r e t h o s e o b t a i n e d f o r s p e c i m e n B s h a k e n b y2 . 0 m m p p i n p u t a m p l i t u d e . O t h e r c a se s a r eo b t a i n e d f o r a n i n p u t a m p l i t u d e o f 1 .0 m m p p .I n t h i s t ab l e , ( w an d ~ b ' fnw and Jnb are th ed a m p i n g r a t io a n d t h e n a t u r a l f r e q u e n c y f o r t h es p e c i m e n w i t h w e l d i n g a n d w i t h o u t w e l d i n g r e -s p ec t i v e l y . V a l u es o f ( w / ( b an d f ,w / fn b a r e s h o w ni n th e r i g h t - h a n d c o l u m n o f t h e r e s u l ts f o r t h es p e c i m e n w i t h w e l d i n g .

F o r t h e d a m p i n g r a t i o ( , v a r i a t i o n d u e t o t h em e a s u r i n g m e t h o d i s s e e n . I n m o s t s p e c i m e n s , ( wis g r e a t e r t h a n ( b ; (w is a b o u t 1 0 % g r e a t e r t h a n( b . D i f f e r e n c e s d u e t o w e l d i n g m e t h o d s a r e n o tc l e a r l y s e e n. C o m p a r i n g r e s u lt s f o r s p e c i m e n Bw i t h t h o s e f o r s p e c i m e n B ' , ( f o r s p e c i m e n B ' i sa b o u t 5 % g r e a t e r t h a n t h a t f o r s p e c i m e n B . ( w / f hf o r s p e c i m e n B ' i s l e s s t h a n t h a t f o r s p e c i m e n B .

F o r t h e n a t u r a l f r e q u e n c y f , , i n t he g r e a t e stcas e o f f l w / J n b , fnw i s 4 % g r e a t e r t h a n fnb" H o w -ev e r , f ~,~ i s a l m o s t t h e s am e a s f n b in m o s t ca s e s .

I n T a b l e 3 , t h e m e a n v a l u e a n d c o e f f i c ie n t o fv a r i a t i o n ( C O V ) o f ( w /( b andfnw/ f ,b f o r t h e s p ec -i m e n w e l d e d b y m a n u a l o p e r a t i o n a n d t h a t w e l d edb y t h e a u t o m a t i c C O 2 g a s s h i e l d e d a r c w e l d i n gm a c h i n e a r e s h o w n . I n m o s t c a s e s , t h e C O V o f~ ,, ./ (b is le s s t h a n 1 0%. T h e r e f o r e , v a r i a t i o n o f


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S. Aoki / Nuclear Engineering and Design 160 (1996) 379-385 381Table 2Damping ratio and natural frequency of specimenSpecimen Method

(I) (II) (III)( ( X 1 0 - 3 ) ( w /~ 'b ( ( X 1 0 2 ) ( w /~ b ( ( X 1 0 - 2 ) ( w /~ b Jn ( H z ) fnw/fnb

(1) A 7.01 1.68 2.03 20.8B 7.56 5.20 0.97 15.4B' 8.15 5.06 1.21 15.8C 5.72 1.84 1.62 27.2D 7.34 1.70 1.51 20.6(2) A 8.20 1.17 2.10 1.25 2.17 1.07 21.4B 8.88 1.17 5.06 0.97 1.07 1.10 15.8B' 9.38 1.15 5.31 1.05 1.27 1.05 16.0C 6.94 1.21 2.02 1.10 1.72 1.06 27.2D 7.60 1.04 1.94 1.14 1.53 1.01 20.6(3) A 7.50 1.07 2.14 1.27 2.12 1.04 21.0B 9.06 1.20 5.31 1.02 1.10 1.13 16.0B' 9.28 1.14 5.00 0.99 1.29 1.07 16.0C 7.85 1.37 1.83 0.99 1.77 1.09 27.4D 9.20 1.25 1.68 0.99 1.59 1.05 20.9

1.031.031.011.001.001.011.041.011.011.01

(w/(b due to specimen size and input amplitude isrelatively Small. However, variation of fnw/fnb isvery small since the COV O f f n w / f n b is about 1%.

3 . E f f e c t o f w e l d i n g o n r a n d o m v i b r a t i o nc h a r a c t e r i s t i c s

It is assumed that specimens are simulated by asingle-degree-of-freedom system with ( and fn ob-tained by the experiment. T he effect of welding onresponse characteristics of specimens subjected torandom accelerat ion input is examined.Table 3Mean value and coefficient of variation of (w/fb and J'nw/fnbSpecimen Method

(1) (II) (III)~w/b ~/ (b (w/(b Lw/fnb

(2) Mean 1.15 1.10 1.06 1.01COV 0.050 0.085 0.028 0.013(3) Mean 1.20 1.05 1.08 1.02COV 0.084 0.104 0.031 0.012

The equa tion of moti on with respect to thedisplacement of mass relative to the input point zis expressed as follows:

- 5 2 ( ~ n Z - 4 - 0 ) 2 z = - - ) 7 ( I )

where f is the i np ut acc ele rat ion an d (an( = 2ZCfn) isthe natural circular frequency; z, which is relatedto the deflection of specimens, is obtained.

In this paper, the sta ndard deviati on of z isexamined when y is the stationary white noise.The ratio of the standard deviation ~zw for thespecimen with welding to that, azb, for the speci-men without welding is expressed as follows:

= V w A w ) (2 )In Table 4, the obtained results are shown. The

standard deviat ion is re la ted to the maximumresponse (Tajimi, 1960). ~zw is about 7% less thanGzb.

4 . E f f e c t o f w e l d i n g o n r e l i a b i l it yThe effect of welding on reliability when the

structure is subjected to stationary white noise


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38 2 S . Aok i /Nuclear Engineering and Design 160 (1996) 379 385T a b l e 4Ra t io of s ta nd ard de via t ion Cr~w,/O'~b

T a b l e 5R a t i o o f t o l e r a n c e l e ve l BDw /BDb (H ~ I )

S p e c i m e n M e t h o d S p e c i m e n M e t h o d( l ) ( l l ) ( l I D ( l ) ( I I ) ( l I l )

(2) A 0 .885 0 .856 0 .924B 0 .885 0 .969 0 .913B' 0 .918 0 .962 0 .961C 0.908 0 .953 0 .971D 0 .982 0 .935 0 .996

(3) A 0 .953 0 .873 0 .964B 0.861 0.93 2 I) .888B' 0 .923 0 .991 0 .955C 0.841 0 .989 0 .941D 0 .880 0 .992 0 .963

(2) A 0.91 0 (I .881 0.951B 0 .910 0 .997 0 .939B' 0.927 0.961 0.971C 0.908 0 .953 0 .971D 0 .982 0 .935 0 .996

(3) A 0 .962 0 .882 0 .974B 0.894 0 .968 0 .923B' 0 .933 1 .000 0 .965C 0.850 0 .998 0 .95 ID 0.888 1 .000 0 .972

e x c i t a t i o n s i s e x a m i n e d . S o m e t y p e s o f fa i l u r e a r ea s s u m e d i n t h e s t u d y o n r e l i a b il i ty o f s t r u c t u r e ss u b j e c t e d t o r a n d o m v i b r a t i o n . F a i l u r e d u e t o f i r s tp a s s a g e is o n e o f t h e m o s t i m p o r t a n t t y p e s o ff a i l u r e ( C r a n d a l l , 1 9 63 ; L i n , 1 9 6 7) . I n t h i s p a p e r ,t h e f i r s t p a s s a g e p r o b l e m i s d e a l t w i t h w h e r ef a i l u r e o c c u r s a t t h e i n s t a n t w h e n t h e a b s o l u t ev a l u e t z (t ) [ o f t h e r e s p o n s e f i rs t c r o s s e s t h e t o l e r -a n c e l e v e l B D . I n t h i s c a s e , t h e f i r s t p a s s a g e p r o b -a b i l i t y i s o b t a i n e d b y t h e f o l l o w i n g e q u a t i o n :P r ( t) = 1 - e x p ( - 2 v t ) ( 3)w h e r e1 (v = - - ~ o n e x p - (4 )27r 2o~]T h e t o l e r a n c e l e v e l B D b f o r t h e s p e c i m e n w i t h o u tw e l d i n g i s d e t e r m i n e d b y u s i n g c rz b a s f o l l o w s :B D b = n O -z b ( 5 )

F i r s t , t h e e f f e c t o f w e l d i n g o n r e l i a b i l it y i se x a m i n e d b y o b t a i n i n g t h e r a t i o B Dw o f t h e t o le r -a n c e l e v e l f o r t h e s p e c i m e n w i t h w e l d i n g t o B D bf o r t h e c a s e w h e r e P r f o r th e s p e c i m e n w i t h w e l d -i n g is e q u a l t o t h a t f o r th e s p e c i m e n w i t h o u tw e l d i n g . B D w / B D b i s o b t a i n e d b y t h e f o l l o w i n ge q u a t i o n :B D w [ 2 ( l: a f3 n b l o g J C n w ~ > 1 . '2B D b- - n 2 (w .f~ ,~ . f , b + (6)I n T a b l e 5 , t h e r e s u l t s f o r n = 1 a r e s h o w n . B Dw i sa b o u t 5 % l e s s t h a n B D b . T h i s m e a n s t h a t Pr f o r

t h e s p e c i m e n w i t h w e l d i n g i s l o w e r t h a n t h a t f o rt h e s p e c i m e n w i t h o u t w e l d i n g f o r t h e s a m e v a l u eo f t o l e r a n c e l e v e l .

I n o r d e r t o e x a m i n e t h e e f f e ct o f n, th e m e a nv a l u e o f B D w / B D b i s s h o w n i n F i g . 2. W h e n n isl es s t h a n a b o u t 2 , /Dw/BDb d e c r e a s e s a s n i n -c r e a s e s . W h e n n i s g r e a t e r t h a n a b o u t 2 , B D w / B D bi s a b o u t 0 . 93 5 . W h e n n is l e ss th a n a b o u t 0 .3 ,B D w / B D b i s g r e a t e r t h a n 1 . T h e r e f o r e , w h e n n i sg r e a t e r t h a n a b o u t 0 . 3, P .. f o r t h e s p e c i m e n w i t hw e l d i n g i s l es s t h a n t h a t f o r t h e s p e c i m e n w i t h o u tw e l d i n g .

N e x t , t h e e f f e c t o f w e l d i n g o n r e l i a b i l i t y ise x a m i n e d b y c o m p a r i n g t h e f ir st p a ss a g e p r o b a b i l -i t y P f ,, . f o r t h e s p e c i m e n w i t h w e l d i n g w i t h t h a t ,P n ,, f o r t h e s p e c i m e n w i t h o u t w e l d i n g f o r t h es a m e v a l u e o f t o l e r a n c e l ev e l. B o t h p r o b a b i l i ti e sa r e o b t a i n e d b y t h e f o l l o w i n g e q u a t i o n s :P ~ ( r ) = l - e x p - e x p - (7)

1 - 0 00 .9

" ~ 0 . 9 (r n0 . 9 ,0 9 2 0 i 2 4 5n

F ig . 2 . Ra t i o o f t o l e r a nce l eve l . B l) ~ /BDb


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S . A o k i I Nu c lea r En g in eer ing a n d Des ig n 1 6 0 (1 9 9 6) 3 7 9 -3 8 5 383Table 6First excu rsion probability (n = l , r = 5)Specimen Method

(1) (II) (11I)(l) 0.619(2) A 0.579 0.563 0.599B 0.579 0.619 0.593B' 0.589 0.608 0.608C 0.581 0.601 0.608D 0.612 0.593 0.617(3) A 0.604 0.566 0.610B 0.570 0.596 0.584B 0.591 0.619 0.604C 0.548 0.619 0.600D 0.570 0.619 0.608

P r w ( r ) = 1 - e x p - - T f ~ b e x p (8 )w h e r e r = ~O n bt. I n T a b l e 6 , t h e r e s u l t s f o r n = 1a n d ~ = 5 a r e s h o w n . P rw is a b o u t 5 % l e s s t h a nP r o. T h i s m e a n s t h a t P r f o r t h e s p e c i m e n w i t hw e l d i n g i s l o w e r t h a n t h a t f o r t h e s p e c i m e n w i t h -o u t w e l d i n g f o r t h e s a m e v a l u e o f th e t o l e r a n c eleve l .

I n o r d e r t o e x a m i n e t h e e ff e ct o f n a n d r , m e a nv a l u e s o f th e f ir s t p a s s a g e p r o b a b i l i t y a r e s h o w ni n F i g . 3 . C o n s i d e r i n g t h e r e s u l t s o f F i g . 2 , v a l u e so f n g r e a t e r t h a n 0 . 3 a r e s e l e c t e d . P r w i s l e ss t h a nP rb f o r a ll v a l u es o f n a n d r . T h e m a x i m u md i f f e r e n c e b e t w e e n P~w a n d P a , is a b o u t 1 0 % .T h e r e f o r e , P r f o r th e s p e c i m e n w i t h w e l d i n g i s le sst h a n t h a t f o r t he s p e c i m e n w i t h o u t w e l d i n g f o rt h e s a m e v a l u e o f t o l e r a n c e l e ve l.

8 0 i 2 ~ . ' - - "

= ! , : : - - -

1 0 0 3 0 4 0 5 0Fig. 3. F irs t passage probability.

0 0

! ! ] ; -IiIi

J t ~ ,

Fig. 4. Frame model.

118

5 . A p p l i c a t i o n t o a c t u a l s tr u c t u r e sT h e a p p l i c a b i li t y o f th e r e s u lt s o b t a i n e d i n S ec -

t i o n 2 t o a c t u a l s t r u c t u r e s is e x a m i n e d b y e x p e r i-m e n t . A f r a m e m o d e l s h o w n i n F i g . 4 is u s e d .T w o c o l u m n s a r e c o n n e c t e d u s i n g H - s t e e l a t t h et o p . T h e c o l u m n m a t e r i a l i s r o l l e d st ee l f o r g en -e r a l s t ru c t u r e s , t h e s a m e a s t h a t o f t h e s p e c i m e n ss h o w n i n S e c t i o n 2 . T h i s m o d e l i s f i x e d a t t h eb o t t o m o n t o t h e s h a k i n g t a b le a n d s h a k e n i n t h eh o r i z o n t a l d i r e c t i o n . T h e i n p u t , a m p l i t u d e is0 .5 m m p - p . F r o m t hi s e x p e r im e n t , t h e d a m p i n gr a t i o a n d n a t u r a l f r e q u e n c y f o r t h e fi rs t v i b r a -t i o na l m o d e a r e m e a s u r e d b y th e m e t h o d s h o w ni n S e c t i o n 2 . W e l d i n g i s d o n e b y t h e a u t o m a t i cC O 2 g a s s h ie l d e d a r c w e l d i n g m a c h i n e . T h r e et y p e s o f m o d e l a r e u s e d.

( a ) M o d e l w i t h o u t w e l d i n g .( b ) M o d e l o f w h i c h o n e c o l u m n i s w e l d ed .( c) M o d e l o f w h i c h t w o c o l u m n s a r e w e l d ed .

T h e l e n g t h f r o m t h e w e l d l in e t o t h e b o t t o m o ft h e c o l u m n i s 2 1 0 m m .T a b l e 7 s h o w s t h e r e su l ts . T h e d a m p i n g r a t i o o f

t h e m o d e l w i t h w e l d i n g is a b o u t 1 0 % g r e a t e r t h a nt h a t o f th e m o d e l w i t h o u t w e l d in g . T h e d a m p i n gr a t i o o f m o d e l c i s g r e a t e r t h a n t h a t o f m o d e l b ,b u t t h e d i f f e r e n c e i s v e r y s m a l l . T h e n a t u r a l f r e -q u e n c i e s o f th e s e m o d e l s a r e a l m o s t t h e s a m e .


6/7

38 4 S . Ao k i / Nu c l ea r En g i n eer i n g a n d D es ig n 1 6 0 (1 9 9 6 ) 3 7 9 3 8 5T a b l e 7D a m p i n g r a t i o a n d n a t u r a l f r e q u e n c y o f f r a m e m o d e lS p e c i m e n M e t h o d

( l ) ( l l ) ( I l l )( ( x l 0 3 ) ( w / ( b ( ( x l 0 2 ) ( w / ( b ( ( x l 0 2 ) ( w / ( b J ~ ( H z ) Jn ,~ "~ nb

(a) 7.47 1.48 2.84 22.0(b) 8.46 1.13 1.55 1.05 3.36 1.18 22.6 1.03(c) 8.88 1.19 1.59 1.07 3.25 1.14 22.0 1.00

T h e r e f o r e , t h e r e s u l t s o b t a i n e d i n S e c t i o n 2 a r ee x p e c t e d t o a p p l y t o a c t u a l s t r u c t u r e s .

6. ConclusionsB y a n e x p e r i m e n t u s i n g s i m p l e s p e c i m e n s , d y -

n a m i c c h a r a c t e r i s t i c s o f s p e ci m e n s w i t h w e l d i n ga r e c o m p a r e d w i t h t h o se o f s p e c im e n s w i t h o u tw e l d i n g . T h e e f f ec t o f w e l d i n g o n r e s p o n s e c h a r a c -t e r i s t i c s a n d r e l i a b i l i t y a r e t h e n e x a m i n e d . T h eo b t a i n e d r e s u l t s a r e s u m m a r i z e d a s f o l l o w s .

( 1) T h e d a m p i n g r a t io o f t he s p e c i m e n w i thw e l d i n g i s a l m o s t 1 0 % g r e a t e r t h a n t h a t o f t h es p e c i m e n w i t h o u t w e l d i n g .

( 2) T h e n a t u r a l f r e q u e n c y o f th e s p e c i m e n w i t hw e l d i n g is a l m o s t t h e s a m e a s t h a t o f t h e s p e c i m e nw i t h o u t w e l d in g .

( 3 ) W h e n t h e s p e c i m e n i s s u b j e c t e d t o s t a t i o n -a r y w h i t e n o i s e e x c i t a t i o n , t h e s t a n d a r d d e v i a t i o no f t h e s p e c i m e n w i t h w e l d i n g is s m a l l e r t h a n t h a to f t h e s p e c i m e n w i t h o u t w e l d in g .

( 4 ) W h e n t h e s p e c i m e n i s s u b j e c t e d t o s t a t i o n -a r y w h i t e n o i s e e x c i t a t i o n , t h e f ir s t p a s s a g e p r o b a -b i l i t y f o r t h e s p e c i m e n w i t h w e l d i n g i s l o w e r t h a nt h a t f o r t h e s p e c i m e n w i t h o u t w e l d i n g .

( 5) B y a n e x p e r i m e n t u s in g a f ra m e m o d e l , t h ed a m p i n g r a t i o b e c o m e s g r e a t e r w h e n t h e c o l u m no f t h e m o d e l i s w e l d e d . S o t h e o b t a i n e d r e s u lt s a r ee x p e c t e d t o a p p l y t o a c t u a l s t r u c t u r e s .

T h e a u t h o r p l a n s t h e f o l l o w i n g f u t u r e i n v e s t i g a -t i o n s .A l t h o u g h t h e r a n g e o f n a t u r a l f r e q u e n c ie s o fs p ec i m en s u s ed i n t h is p ap e r i s r e l a t i v e l y w i d e ,w e l d i n g i s u s e d f o r m a n y s t r u c t u r e s w i t h a w i d e rr a n g e o f n a t u r a l f r e q u e n c i e s a n d e x c i t a t i o n fr e -

q u e n c i e s. T h e n a t u r a l f r e q u e n c i e s o f s o m e s t r u c -t u r e s a r e l o w e r t h a n t h o s e o f t h e s p e c i m e n s u s e di n th i s s t u d y . F o r s u ch s t r u c t u r e s , t h e e f f ec t o fw e l d i n g o n d y n a m i c c h a r a c t e r i s t ic s o f h i g h e r v i-b r a t i o n a l m o d e s i s a l s o i m p o r t a n t .

I n t h i s p a p e r , s p e c i m e n s w i t h o n e w e l d a r ea d o p t e d . I n s o m e s t r u c t u r e s t h e r e a r e m o r e w e l d s .I n s u ch a ca s e , t h e e f f ec t o f t h e p o s i t i o n s o f w e l d st o s i g n i f i c a n t d e p e n d i n g o n m o d e s h a p e s .

T h e a u t h o r i n t e n d s t o i n v e s t i g a te t h e e f fe c t o fw e l d i n g o n d y n a m i c c h a r a c t e r i s t ic s o f h i g h e r v i-b r a t i o n a l m o d e s , a n d t h e e f f e c t o f s o m e w e l d s a n dp o s i t i o n s o f w e l d s o n d y n a m i c c h a r a c t e r is t i c s .

AcknowledgementsT h e a u t h o r w i s h e s t o t h a n k P r o f e s s o r S .F u k u d a , a n d P r o f e s so r Y . A m a n o o f T o k y o

M e t r o p o l i t a n C o l l eg e o f T e c h n o l o g y f o r h is k i n d -n e s s i n a l lo w i n g u s e o f t h e a u t o m a t i c a c i d c a r b o nw e l d i n g m a c h i n e . H e a l s o w i sh e s to t h a n k M r . A .Y u t a , M a n a g i n g D i r e c t o r o f E m i c C o r p ., f o r hi sa i d w i t h p r e p a r i n g t h e s h a k e r . H e t h a n k s M r . K .S a i t o o f H i t a c h i B u i l d i n g S y s t e m S e r v ic e C o . , L t d .a n d M r . M . K o s u g i o f F u j i E l e c t ri c C o . , L t d . , a n dt h e f o r m e r s tu d e n t s o f T o k y o M e t r o p o l i t a n C o l -l e ge o f T e c h n o l o g y f o r t h e i r h e l p i n t h e e x p e r i -m e n t .

ReferencesS.H . Bush , ASME J . P ressure Vesse l Technol . , 114(4) (1992)

389.R .D . Chever ton and D .L . Se lby , ASME J . P ressure Vesse lTechnol. , 114(4) (1992) 396.


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S. A oki / Nuclear Engineering and Design 160 (1996) 379-3 85 38 5S . H . C r a n d a l l a n d W . D . M a r k , R a n d o m V i b r a t i o n i n M e -

chan ica l Sys tem s , Academ ic Press , 1963 .M . D . E n g e l h a r d t a n d A . S . H u s a i n , A S C E J . S t r u c t. E n g . ,

119(2) (1993) 3357.R , A . L a B o u b e a n d W . W . Y u , A S C E J . S t r u c t . E n g . , 1 1 9 ( 7 )

(1993) 2187.Y . K . L i n , P r o b a b i l i s t ic T h e o r y o f S t r u c t u r a l D y n a m i c s , M c -Graw-Hi l l , 1967 .

S . R a h m a n a n d F . B r u s t , A S M E J . P r e s s u r e V e s s e l T e c h n o l . ,114(4) (1992) 410.

E . Sm ith , ASME J . P ressure Vesse l Technol . , 114(4) (1992)405.

H . T a j i m i , P r o c . 2 n d W o r l d C o n f . o n E a r t h q u a k e E n g i n e e r i n g ,Vol. II , 1960, p. 781.

P .D . Zurask i , ASCE J . S t ruc t . Eng . , 119(10) (1993) 3056 .

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