Chapter 18
General Approach to Damping Design
Michael L. Drake University of Dayton Research Institute, Dayton, OH 45469
The following chapter covers several important steps in the design of a damping system. Designer must 1) verify that there is a problem which is indeed the result of resonant vibration, 2) define the dynamic characteristics of the structure under consideration and 3) define the environmental conditions in which the structure operates. These parameters are required because damping material properties are dependent on both the frequency and the temperature at which the problem occurs. At this point, the problem is completely defined, i.e., the dynamics which cause the problem are known, the dynamic characteristics of the component are known, and the operational environment is established. With this data, the designer can make logical choices of damping polymers and damping configurations to develop the final design(1-3).
There a r e s e v e r a l important steps t o c o n s i d e r a damping system. They a r e a s f o l l o w s :
i n the
Hesign o f
1.
Verify
t h a t t h e problem i s r e s o n a n t v i b r a t i o n i n d u c e d .
2.
Dynamic A n a l y s i s o f t h e system t o d e t e r m i n e r e s o n a n t f r e q u e n c i e s , mode shapes, and damping.
3.
D e f i n e t h e e n v i r o n m e n t a l c o n d i t i o n s i n which t h e system operates.
4.
D e f i n e t h e system damping r e q u i r e d t o e l i m i n a t e t h e problem. 0097-6156/90/0424-0346$06.00/0 © 1990 American Chemical Society
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5.
Select the appropriate configuration.
damping m a t e r i a l s
6.
Develop t h e r e q u i r e d d e s i g n from t h e d a t a
andb a s i c
damping
collected.
Dynamic P r o b l e m I d e n t i f i c a t i o n The p r o p e r i n i t i a l s t e p i n s o l v i n g a n y p r o b l e m i s t o c o m p l e t e l y define that problem. T h i s i s v e r y t r u e when s o l v i n g a v i b r a t i o n i n d u c e d p r o b l e m u s i n g damping t e c h n o l o g y . Therefore, the f i r s t s t e p i n a damping d e s i g n i s t o v e r i f y t h a t t h e problem i s i n d e e d r e s u l t i n g from a s t r u c t u r a l resonance. I n c a s e o f a new d e s i g n , t h e d e s i g n e r m u s t o b t a i n t h e a n t i c i p a t e d force input, i . e . , e x c i t a t i o n environment, f o r the s t r u c t u r a l system and c o r r e l a t e the frequency content o f t h i s information w i t h the r e s u l t s o f a n a t u r a l frequency a n a l y s i s o f the structure. I f n a t u r a l frequencies occur i n the frequency band o f e x c i t a t i o n , t h e p o t e n t i a l o f dynamic problems e x i s t s and s h o u l d be addressed. I f a problem develops i n an e x i s t i n g p a r t , the designer might choose one o f t h e f o l l o w i n g approaches t o i d e n t i f y t h e cause o f t h e problem. I n t h e c a s e o f a c r a c k e d component a c r a c k a n a l y s i s s h o u l d be run to v e r i f y that the crack i s a high cycle fatigue f a i l u r e . An i n s t r u m e n t e d o p e r a t i o n a l t e s t o f t h e component w i l l i d e n t i f y t h e frequencies o f high v i b r a t i o n l e v e l s causing the problem. I f t h e problem under c o n s i d e r a t i o n i s h i g h n o i s e r a d i a t i o n , an o p e r a t i o n a l e v a l u a t i o n s h o u l d b e made t o d e t e r m i n e b o t h t h e frequencies andmagnitudes o f the n o i s e b e i n g r a d i a t e d and t h e source o f r a d i a t i o n . An unacceptable v i b r a t i o n l e v e l environment p r o b l e m s h o u l d b e a t t a c k e d i n t h e same b a s i c m a n n e r a s t h e n o i s e p r o b l e m u s i n g v i b r a t i o n measurements i n s t e a d o f a c o u s t i c measurements. As a r e s u l t o f t h e above i n v e s t i g a t i o n s , t h e d e s i g n e r h a s determined t h e o p e r a t i o n a l dynamic cause o f t h e p r o b l e m , v e r i f i e d t h a t t h e cause i s resonant v i b r a t i o n , and d e f i n e d the resonant f r e q u e n c i e s w i t h t h e h i g h dynamic response. Dynamic
Characteristics
A s u c c e s s f u l damping d e s i g n c a n o n l y be d e v e l o p e d from a complete u n d e r s t a n d i n g o f t h e dynamic b e h a v i o r o f t h e s t r u c t u r a l system t o be damped. G e n e r a l l y , a frequency range over which t h i s dynamic t h i s i n f o r m a t i o n i s needed i s d e f i n e d from t h e a n a l y s i s c o m p l e t e d d u r i n g the f i r s t s t e p . The dynamic range c a n be d e f i n e d from o p e r a t i o n a l t e s t i n g o r c a n be d e t e r m i n e d from knowledge o f t h e p a r t under c o n s i d e r a t i o n , i . e . , a p r o b l e m i n a component where t h e e x c i t a t i o n f o r c e s a r e known t o be e n g i n e - o r d e r r e l a t e d ; l o w f r e q u e n c y e x c i t a t i o n from road roughness t o t h e s u s p e n s i o n ; or acoustic e x c i t a t i o n t o a i r c r a f t f u s e l a g e components due t o j e t e n g i n e exhaust. Once a f r e q u e n c y r a n g e i s c h o s e n , a c o m p l e t e d y n a m i c i n v e s t i g a t i o n must be c o n d u c t e d . One m u s t a c c u r a t e l y d e t e r m i n e a l l
American Chemical Society Library 1155 16th St. N. W.
Washington, D. C. 20036
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the r e s o n a n t f r e q u e n c i e s , c o r r e s p o n d i n g s t r u c t u r a l mode shapes, and i n h e r e n t modal damping v a l u e s i n the r e q u i r e d f r e q u e n c y range. Ifa tuned a b s o r b e r i s t o be p r o p e r l y a p p l i e d , t h e modal mass and s t i f f n e s s a r e a l s o needed. T h i s d a t a c a n be o b t a i n e d a n a l y t i c a l l y or e x p e r i m e n t a l l y . I n t h e e a r l y d e s i g n s t a g e s where a p r o t o t y p e i s a v a i l a b l e , t h e optimum s o l u t i o n f o r d a t a a c q u i s i t i o n i s t o use e x p e r i m e n t a l a n a l y s i s on t h e p r o t o t y p e s t r u c t u r e t o r e f i n e an a n a l y t i c a l model which c a n t h e n be used f o r damping d e s i g n ( 4 ) . O f t e n , when a damping a p p l i c a t i o n i s u s e d as a r e d e s i g n approach, t h e n e c e s s a r y dynamic c h a r a c t e r i z a t i o n c a n be a c q u i r e d e f f i c i e n t l y t h r o u g h t h e use o f modern e x p e r i m e n t a l methods. E x p e r i m e n t a l methods c a n q u i c k l y determine t h e d a t a needed f o r h i g h l y complex s t r u c t u r a l system; however, measurements on o p e r a t i o n a l systems c a n be e x t r e m e l y d i f f i c u l t and c o s t l y . The F o u r i e r a n a l y z e r i s t h e most p o w e r f u l e x p e r i m e n t a l t o o l c u r r e n t l y a v a i l a b l e t o do t h e e x p e r i m e n t a l work; however, h o l o g r a p h i c methods f o r d e t e r m i n i n g mode shapes and s t a n d a r d s i n e sweep methods f o r r e s o n a n t f r e q u e n c i e s and modal damping v a l u e s a r e e x t r e m e l y useful(5-7). The D e s i g n e r must choose t h e most e x p e d i e n t method t o develop the r e q u i r e d data. Environmental
Definition
Important d a t a s t i l l r e q u i r e d t o d e s i g n a damping a p p l i c a t i o n a r e the o p e r a t i o n a l environment i n which t h e d e s i g n must o p e r a t e . T h i s , a t f i r s t thought, might seem t o be a r a t h e r s i m p l e t a s k b u t t h e importance o f a c c u r a t e e n v i r o n m e n t a l d a t a cannot be o v e r s t r e s s e d . A b r o a d b r u s h approach t o temperature such as t h e s t a n d a r d temperature range f o r o p e r a t i o n o f many a i r c r a f t components o f 65°F t o 250°F i s n o t t h e answer. T h i s may be t h e maximum range seen by t h e component; however, i t w i l l n o t g e n e r a l l y be n e c e s s a r y t o p r o v i d e h i g h damping over t h i s e n t i r e range. The e n g i n e e r must determine o v e r what s p e c i f i c temperature range t h e damage i s o c c u r r i n g and d e s i g n h i s a p p l i c a t i o n f o r t h a t range w h i l e m a i n t a i n i n g an awareness o f t h e r e q u i r e d s u r v i v a b i l i t y temperature range. Time r e l a t e d r e c o r d i n g s o f v i b r a t i o n and temperature d a t a from o p e r a t i o n a l t e s t s c a n be used t o determine t h e temperature range o v e r which damaging v i b r a t i o n s o c c u r . Operational tests can a l s o s u p p l y t h e n e c e s s a r y maximum temperature l i m i t s t o be u s e d i n the d e s i g n . I f temperature d a t a from a l a r g e number o f d i f f e r e n t o p e r a t i o n a l t e s t s are a v a i l a b l e , a s t a t i s t i c a l study o f the data w i l l r e v e a l t h e temperature range i n which t h e m a j o r i t y o f o p e r a t i o n a l time i s s p e n t ( 8 ) . An example o f t h i s type o f d a t a f o r an a i r c r a f t i s shown i n F i g u r e 1 where minimum and maximum t e m p e r a t u r e s a r e shown a l o n g w i t h p e r c e n t o f t o t a l o p e r a t i o n a l time s p e n t i n each temperature range. I t i s easy t o see t h e v a l u e o f t h i s type o f d a t a , p a r t i c u l a r l y i f v i b r a t i o n l e v e l and temperature d a t a cannot be s i m u l t a n e o u s l y o b t a i n e d f o r o p e r a t i o n a l c o n d i t i o n s . I n t h e e a r l y s t a g e s o f s t r u c t u r a l system d e s i g n , complete o p e r a t i o n a l temperature d a t a may n o t be a v a i l a b l e . I n such a c a s e , d a t a from s i m i l a r systems s h o u l d be r e v i e w e d and t h e b e s t e s t i m a t e s o f temperature s h o u l d be d e v e l o p e d and used i n t h e damping d e s i g n procedure.
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SOUND AND VIBRATION DAMPING WITH POLYMERS
Temperature i s not the o n l y e n v i r o n m e n t a l f a c t o r which must be considered. The e n g i n e e r must know i f the a p p l i c a t i o n w i l l come i n c o n t a c t w i t h contaminates such as s a l t water, g a s o l i n e , j e t e n g i n e f u e l , h y d r a u l i c f l u i d , or any o t h e r s u b s t a n c e which might a f f e c t the p e r f o r m a n c e o r l o n g e v i t y o f the c a n d i d a t e damping m a t e r i a l s ( 2 . 4 . 9 ) . Required
Damping
Increase
The r e m a i n i n g q u e s t i o n to be answered b e f o r e a damping d e s i g n c a n be s t a r t e d i s "How much damping i s needed t o e l i m i n a t e the problem?" In the " f i x - i t " damping b u s i n e s s , the g e n e r a l a p p r o a c h found i n the l i t e r a t u r e i s t o d e s i g n a damping system w i t h a h i g h damping l e v e l and t e s t i t i n s e r v i c e . I f the f a i l u r e s a r e e l i m i n a t e d the p r o b l e m is solved. I n r e a l i t y , the d e s i g n e r s h o u l d use the minimum v a l u e o f system damping which w i l l e l i m i n a t e the v i b r a t i o n problem. I f the damped d e s i g n a c c o m p l i s h e s j u s t the minimum r e q u i r e d damping u s i n g an optimum damping system, the d e s i g n s h o u l d a l s o be o p t i m i z e d from a weight, s i z e , and c o s t s t a n d p o i n t . The method f o r d e t e r m i n i n g the minimum r e q u i r e d system damping w i l l depend on the problem t o be s o l v e d . From the dynamic c h a r a c t e r i z a t i o n , the i n h e r e n t system damping has been d e t e r m i n e d . The c o r r e s p o n d i n g v i b r a t i o n problem ( h i g h dynamic s t r e s s , n o i s e l e v e l r a d i a t e d , h i g h dynamic a m p l i t u d e response, e t c . ) i s d i r e c t l y r e l a t e d t o the i n h e r e n t damping. Quick c a l c u l a t i o n s can be made t o determine the r e q u i r e d i n c r e a s e i n system damping t o e l i m i n a t e the v i b r a t i o n problem. B a s i c a l l y , i f a 20 p e r c e n t d e c r e a s e o f system r e s p o n s e i s needed, then the system damping needs t o be i n c r e a s e d 20 percent. I f an a n a l y t i c a l model has been d e v e l o p e d , an a n a l y s i s c a n be c o n d u c t e d t o v e r i f y the v a l u e o f system damping needed t o e l i m i n a t e the v i b r a t i o n problem. In the l i t e r a t u r e , most o f the s u c c e s s f u l damping systems c u r r e n t l y i n use were d e s i g n e d t o a c h i e v e n e a r maximum damping from a g i v e n c o n f i g u r a t i o n w i t h o u t r e g a r d t o e l i m i n a t i n g the problem w i t h the l e a s t r e q u i r e d amount o f damping. Damping M a t e r i a l S e l e c t i o n and A p p l i c a t i o n
Design
To t h i s p o i n t the p r i m a r y f u n c t i o n o f the d e s i g n e r has been t o d e v e l o p an a c c u r a t e and complete d e f i n i t i o n o f the r e s o n a n t v i b r a t i o n problem. The f r e q u e n c i e s o f the component a t which the p r o b l e m e x i s t s d u r i n g o p e r a t i o n a r e d e f i n e d a l o n g w i t h the a s s o c i a t e d dynamic c h a r a c t e r i s t i c s . I t now becomes a s i m p l e m a t t e r to determine which r e s o n a n t modes o f the component a r e c r e a t i n g the v i b r a t i o n problem which i n t u r n d e f i n e s the f r e q u e n c i e s a t which damping i s needed and the c o r r e s p o n d i n g r e s o n a n t mode shapes, the undamped modal l o s s f a c t o r s , and the r e q u i r e d damped modal l o s s factor. T h i s complete s e t o f dynamic d a t a combined w i t h the e n v i r o n m e n t a l c o n d i t i o n s p r o v i d e the d e s i g n e r w i t h a l l the d a t a n e c e s s a r y t o b e g i n a n a l y s i s and e v a l u a t i o n o f damping m a t e r i a l s and damping d e s i g n c o n f i g u r a t i o n s . The d e s i g n e r must f i r s t l o o k a t the temperature range f o r which damping i s needed and the s u r v i v a b i l i t y temperature l i m i t s t o see i f e i t h e r o f t h e s e temperature ranges e l i m i n a t e s a p a r t i c u l a r method o f damping a p p r o a c h because no a v a i l a b l e m a t e r i a l s meet the temperature
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requirements. An example h e r e would be a damping r e q u i r e m e n t o v e r the temperature range o f 150°F t o 250°F w i t h a s u r v i v a b i l i t y t o 600°F. T h i s would e l i m i n a t e most t y p i c a l p o l y m e r i c damping m a t e r i a l s such as a c r y l a t e s and v i n y l s u s e d i n c o n s t r a i n e d l a y e r o r f r e e l a y e r damping d e s i g n s . I f t h e temperature range c o n d i t i o n s c a n be met, t h e n e x t c o n s i d e r a t i o n i s t h e mode shapes o f t h e r e s o n a n t f r e q u e n c i e s which r e q u i r e damping. Tuned dampers r e q u i r e d i s p l a c e m e n t s o f some magnitude w h i l e c o n s t r a i n e d and f r e e l a y e r a p p l i c a t i o n s r e q u i r e l a r g e a r e a s o f l o c a l i z e d b e n d i n g which c a n deform t h e damping material(10^12). H i g h l y l o c a l i z e d s t r a i n d i s t r i b u t i o n s w i l l negate the e f f e c t i v e n e s s o f a l a y e r e d treatment. From t h e temperature c o n d i t i o n s and t h e dynamic c h a r a c t e r i s t i c s , t h e d e s i g n e r c a n choose t h e a p p r o p r i a t e c l a s s o f damping polymers and the a p p r o p r i a t e type o f damping c o n f i g u r a t i o n f o r the s t a r t i n g p o i n t to design the s p e c i f i c a p p l i c a t i o n f o r the s t r u c t u r e h a v i n g t h e v i b r a t i o n problem. The b a s i c p r i n c i p l e s o f f r e e l a y e r and c o n s t r a i n e d l a y e r damping a p p l i c a t i o n s and tuned dampers and a n a l y s i s t e c h n i q u e s a r e d i s c u s s e d i n R e f e r e n c e s 10, 11 and 12. V a r i o u s d e s i g n a n a l y s i s methods a r e o f t e n a p p r o p r i a t e f o r problems; however, i t i s n e c e s s a r y t o o b t a i n a l l t h e b a s i c i n f o r m a t i o n d i s c u s s e d p r e v i o u s l y t o be s u c c e s s f u l r e g a r d l e s s o f t h e a n a l y s i s p r o c e d u r e used. A d e s i g n f l o w c h a r t a p p r o p r i a t e f o r any o f the d e s i g n a n a l y s i s t e c h n i q u e s i s seen i n F i g u r e 2. The dynamic and temperature d a t a i s the i n p u t and t h e output i s t h e s t r u c t u r a l l o s s factor. The c h a r t l o o p s a r e c o n t i n u e d u n t i l t h e p r o p e r rj i s a c h i e v e d a t which time t h e damping d e s i g n i s complete. Design t e c h n i q u e s a r e d i s c u s s e d i n r e f e r e n c e s 10, 11, and 12. Summary R e s t a t i n g t h e importance o f t h e problem d e f i n i t i o n i s a p p r o p r i a t e a t this point. I n a c c u r a t e temperature range f o r m u l a t i o n w i l l e l i m i n a t e any b e n e f i c i a l e f f e c t s o f t h e damping m a t e r i a l . T h i s c a n be seen i n F i g u r e 3 ( F i g u r e 3 i s dynamic modulus d a t a f o r 3M ISD-112) where a temperature s h i f t o f 100°F causes a s i g n i f i c a n t r e d u c t i o n i n t h e l o s s f a c t o r . I f t h e s u r v i v a b i l i t y temperature l i m i t s a r e i n c o r r e c t , the damping a p p l i c a t i o n may w e l l p r o v i d e t h e n e c e s s a r y r e d u c t i o n i n the v i b r a t i o n l e v e l s b u t w i l l be d e s t r o y e d by an o v e r - t e m p e r a t u r e condition(13). Guesses a t temperature d a t a w i l l i n v a r i a b l y l e a d t o the f a i l u r e o f a damping d e s i g n . The o t h e r major a r e a where a c c u r a t e d a t a a r e n e c e s s a r y i s t h e dynamic c h a r a c t e r i s t i c s o f t h e system under c o n s i d e r a t i o n . The placement o f a l a y e r e d damping d e s i g n on a p o r t i o n o f t h e s t r u c t u r e which w i l l n o t undergo major m o t i o n i n a p a r t i c u l a r mode i s as i n e f f e c t i v e as p l a c i n g a tuned damper on a node l i n e o f t h e mode y o u wish to c o n t r o l . As w i t h any d e s i g n p r o j e c t , s u c c e s s f u l r e s u l t s r e q u i r e a c c u r a t e i n f o r m a t i o n upon which t o base the d e s i g n . Temperature and dynamic c h a r a c t e r i s t i c s a r e t h e two prime f a c t o r s which must be m e t i c u l o u s l y measured t o o b t a i n good damping d e s i g n r e s u l t s . A l l the steps r e q u i r e d i n a damping d e s i g n a r e summarized on page 346.
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SOUND AND VIBRATION DAMPING WITH POLYMERS
Literature Cited 1.
Sharp, J.D. and M.L. Drake, "Elimination of Resonant Fatigue Problems for Major Maintenance Benefits," ASME Publication Number 77-DET-135.
2.
Drake, M.L. and J.D. Sharp, "An Example of Additive Damping as a Cost Savings Alternative to Redesign," ASME Publication Number 77-WA/GT-2.
3.
Drake, M.L. and M.P. Bouchard, "On Damping of Large Honeycomb Structure," Journal of Vibration, Acoustics, Stress, and Reliability in Design, Vol. 107, pp. 361-366, October, 1985.
4.
Flora eta, "Dynamic Analysis and Testing of Damped Intermodule Plates for the Sigma Laser Device," ASIAC Report No. 1182.1A, November 1982.
5.
Brown, Dave, Lecture notes - short course, "Modal Analysis Theory and Measurement Techniques," sponsored by the University of Cincinnati and Hewlett Packard.
6.
Ramsey, K.A., "Effective Measurements for Structural Dynamics Testing," Sound and Vibration, November 1975, pp 2435.
7.
Drake, M.L. and J.P. Henderson, "An Investigation of the Response of a Damped Structure Using Digital Techniques," Shock and Vibration Bulletin 45, Part 5, 1975.
8.
L.C. Rogers, and M.L. Parin, "Additive Damping for Vibratory Stress Reduction of Jet Engine Inlet Guide Vanes," presented at the 47th Shock and Vibration Symposium, Albuquerque, NM, 1976, published in the 47th S&V Bulletin.
9.
Henderson, J.P. and M.L. Drake, "Investigation of the Effects of Damping Treatments on the Response of Heated Fuselage Structure," NoisEXPO, National Noise and Vibration Control Conference, New York, New York, March, 1976.
10. Jones, D.I.G., J.P. Henderson, and 1/Lt. G.H. Bruns, "Use of Tuned Viscoelastic Dampers for Reduction of Vibrations in Aerospace Structures," Air Force Materials Laboratory, presented at the 13th Annual Air Force Science and Engineering Symposium at Arnold Air Force Station, Tennessee, September 27-29, 1966. 11. Nashif, Ahid D., David I. G. Jones, and John P. Henderson, "Vibration Damping," John Wiley & Sons, 1985.
18. DRAKE General Approach to Damping Design
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12. Soovere, J., and M. L. Drake, "Aerospace Structures Technology Damping Design Guide, Volume I - Technology Review, Volume II - Design Guide, Volume III - Damping Material Data," Technical Report AFWAL-TR-84-3089, Dec. 1985. 13. Jones, D.I.G. andC.M.Cannon, "Control of Gas Turbine Stator Blade Vibrations by Means of Enamel Coatings," Journal of Aircraft, Vol. 12, No. 4, pp. 226-230, April 1975. RECEIVED January 24, 1990
