An e f f i c i e n t method i s described f o r f i n i t e element modeling o f ' three-layer laminates cont a i n i n g a v i s c o e l a s t i c layer. Modal damping r a t i o s are estimated from undamped normal mode r e s u l t s by means of the modal s t r a i n energy (MSE) method.Compar l sons are given between resu l t s obtained by the MSE method implemented I n NASTRAN, by var lous exact s o l u t ions f o r approximate governing d i f f e r e n t i a l equations, and by experiment. Results are i n terms o f frequencies, moda l damping ratios,and mechanical admittances f o r simple beams, plates, and rings.Application o f the f i n i t e eiement/MSE method I n design o f i n t e g r a l l y damped structures I s discussed. I. I n t r o d u c t i o n The use of d i s t r i b u t e d v i s c o e l a s t i c material I n aerospace structures has a long and successful h l s t o r y as a means o f c o n t r o l 1 ing resonant v i brat i o n . One of the most weight-effective methods of incorporating a v i s c o e l a s t i c material i n a b u i l tup s t r u c t u r e i s i n t h e form o f a constrained layer.The elastomer i s sandwiched between two m e t a l l i c sheets and i s bonded t o both.Flexural v i b r a t l o n causes shearing s t r a i n i n the core which d i s s i pates energy and thereby reduces v l b r a t ion.Numerous analyses of simple sandwich structures (beams, plates, cyl inders, etc.) have been pub1 ished [I-51.These general ly begin with part i a l d i f f e r e n t i a l equatlons of motion which are derived by conslderation of a thicknesswise element of the sandwich.Shearing i s assumed t o be the only s i g n i f i c a n t energy storage mechanism I n the core and d i s s i p a t i o n under harmonic loading i s introduced by t a k i n g the core shear modulus t o be complex.Even f o r slmple geometries, the algebraic and/or numerical s o l u t i o n o f the equations o f motion tends t o be lengthy. I n real l i f e s i t uations, a designer I s faced with c o n s t r a i n t s which l i m i t t h e usefulness o f purely a n a l y t i c a l solutions. S t r u c t u r a l geometries are usually complicated and the use of a layered damper I s f e a s i b l e i n only c e r t a l n areas o f a built-up assemblage. Design time schedules are t l g h t so a p r a c t i c a l analysis method must not only give damping e s t imates of useful accuracy, k r t must a l s o glve some indlcat'lon of what should be changed I n order t o Improve a candidate design. Since much o f the d i f f i c u l t y o f designing layered dampers stems from complicated geometries, it i s natural t o look t o f i n i t e element methods f o r solutlons, Just as they are used f o r analysts of general undamped structures. In t h i s paper several approaches t o damped s t r u c t u r a l design are reviewed i n the context o f implementation by exl s t i n g general-purpose f l n i t e element codes. One technique i n p a r t i c u l a r , the modal s t r a i n energy method, i s discussed with examples since...

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