By France) International Colloquium on Gasdynamics of Explosions and Reactive Systems (9th : 1983 : Poitiers, N. Manson, A. K. Oppenheim, J. R. Bowen, R. I. Soloukhin
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Extra resources for Dynamics of Shock Waves, Explosions, and Detonations (Progress in Astronautics and Aeronautics)
T h e arbitrary constants Aj, Β ι, C , and D can be e v a l u a t e d a c c o r d i n g to the appropriate root b o u n d a r y condition. 39c) l l w h e r e m e t h o d s for d e t e r m i n i n g the nonrotating natural frequencies c o are p r e s e n t e d in the s u c c e e d i n g s e c t i o n s . A l t h o u g h closed forms for the m o d a l integrals defined in E q . ( 3 . 3 2 ) are not directly a v a i l a b l e , explicit definitions of the i n t e g r a n d s are thus available from E q s .
Blades that have no pitch, twist, or p r e c o n i n g . Such simplified blade configurations p r o d u c e what w e will refer to as uncoupled mode characteristics. T h e u n c o u p l e d modal responses are characterized as h a v i n g , for any one m o d e , cui of the motion in either the i n - p l a n e , out-of-plane, or torsional degrees of freedom. In reality, rotor blades d o h a v e all of these c o m p l i c a t i n g characteristics (pitch, twist, and p r e c o n e ) , and material is therefore presented explaining h o w the basic u n c o u p l e d characteristics for the simplified blade are modified or " c o u p l e d " by these additional c o n s i d e r a t i o n s .
7 . H o w e v e r , the veracity of the orthogonality principle is not limited to this simple p r o b l e m , but can easily be generalized to other m o r e c o m p l i c a t e d , but linear, d y n a m i c s y s t e m s . / = 1 // ω; Σ 2 // ιη,-xy''x'r = Σ // Σ / = ! / = ! 82b) 24 ROTARY WING STRUCTURAL DYNAMICS Since for conservative s y s t e m s , Κ· = K the sums on the right-hand sides of these t w o equations are e q u a l . 83) 0 S i n c e , for/? Φ r , the first term is clearly n o n z e r o , the second term must be zero.
Dynamics of Shock Waves, Explosions, and Detonations (Progress in Astronautics and Aeronautics) by France) International Colloquium on Gasdynamics of Explosions and Reactive Systems (9th : 1983 : Poitiers, N. Manson, A. K. Oppenheim, J. R. Bowen, R. I. Soloukhin