Missile control surfaces often contain nonlinearities which affect their performance characteristics and flutter boundaries. Analysis techniques accounting for these nonlinearities and an understanding of their potential influence on the flutter mechanism greatly increase the efficiency of the control surface design process. This paper presents such analysis procedures and discusses their application to the investigation of the dynamics of missile control surfaces containing structural freeplay-type nonlinearities. The problem discussed deals with a missile control surface exposed to subsonic flow. Nonlinearities are associated with freeplay in the root support stiffness. Definition of the loads acting on the control surface uses a simplified aerodynamic representation. The basic assumption of this approach is that the lift force is proportional to and in phase with the torsional, or pitch, motion. Both rigid and flexible control surface configurations have been examined with nonlinearities in either one or both of the root pitch or roll degrees-of-freedom.
Nomenclature
A= amplitude of motion A r ,A rd ,A er ,A e = rigid, rigid-elastic, and elastic aerodynamic loading matrices, see Eq.(2) 70,7 0 ,7^ = rigid control surface inertia properties, see Eq.(2) K = linear spring rate, see Fig. 2 K = effective stiffness L ( t) -load developed in nonlinear spring m n = generalized masses of control surface modes, see Eq. (2) F p = inertia coupling matrix between rigid and elastic body motion, see Eq. (2) = dynamic pressure = generalized coordinates of control surface modes, see Eq. (2) = deadspace, see Fig. 2 =time = describing function -root roll = root pitch = uncoupled frequency = effective frequency q q n 5 t d 0 co co Subscripts 6parameter associated with root roll parameter associated with root pitch
M i s s i l e c o n t r o l s u r f a c e s o f t e n c o n t a i n n o n l i n e a r i & i e s which a f f e c t t h e i r performance c h a r a c t e r i s t i c s and f l u t t e r boundaries. Analysis techniques accounting f o r these nonl i n e a r i t ies and an understanding o f t h e i r potential influence on t h e f l u t t e r mechanism greatly increase the e f f ic i e n c y o f t h e c o n t r o l s u r f a c e d e s i g n process. This paper p r e s e n t s such analysis procedures and discusses t h e i r appl i c a t i o n t o the investigation of the dynamics of m i s s i l e control surfaces cont a i ning s t r u c t u r a l freevlay type nonl inearities. The problem discussed deal s w i t h a missile c o n t r o l s u r f a c e exposed t o subsonic flow. Nonl i n e a r i t i e s a r e a s s o c i a~~d w i t h freeplay i n the r o o t support s t i f f n e s s . D e f i n i t i o n of the loads a c t i n g on t h e c o n t r o l surface uses a simplified aerodynamic representation. The basic assumption o f t h i s approach i s that the l i f t force i s proport i o n a l t o and i n phase w i t h t h e t o r s i o n a l , o r p i t c h , motion. Both r i g i d and f l e x i b l e control surface c o n f i g u r a t i o n s have been examined with n o n l i n e a r i t i e s i n e i t h e r one o r both o f the root p i t c h o r 1-01 1 degrees of freedom. Nomencl aturc? A Amp1 itude of motion. A , , A d ,Aer.A, Rigid, r i g i d -e l a s t i c , and e l a s t i c aerodynamic loading matrices -Equation (2). Rigid control surface i n e r t i a Igg properties -Equation (2). K Linear spring r a t e -Figure 2.
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