1. Bending-torsional flutter of an airfoil with balance mass
- Author
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S. P. Strelkov, Polina S. Landa, and M. V. Yakovleva
- Subjects
Physics ,Nuclear and High Energy Physics ,Section (category theory) ,Stereochemistry ,Astronomy and Astrophysics ,Statistical and Nonlinear Physics ,Electrical and Electronic Engineering ,Electronic, Optical and Magnetic Materials - Abstract
The critical speed for bending-torsional flutter can be increased by decreasing the unbalance of the airfoil [i], i .e. , by moving the center of mass of each spanwise element closer to the stiffness axis. This can be achieved by adding balance masses ahead of the stiffness axis or even by adding a single concentrated mass at a certain section of the airfoil. The size and situation of the mass have a definite influence on the magnitude of the critical flutter speed. In the usual design calculation for bending-torsional flutter of an airfoil by the Bubnov-Galerkin method [I], an equivalent two-degree-of-freedom system is introduced. The va r i ab l e s in this s y s t e m a r e two "gene r a l i z e d " coord ina tes c o r r e s p o n d i n g to two p r e s c r i b e d modes : bending and to r s ion of the a i r fo i l . The p a r a m e t e r s of the "equiva len t" s y s t e m a r e the values of the fol lowing quant i t ies : the mass of the a i r fo i l , its m o ment of ine r t i a , its bending and to r s iona l s t i f fness , and the s ta t ic m o m e n t d e s c r i b i n g the ine r t i a l coupl ing between bending and to r s ion . Acco rd ing to the Bubnov-Ga le rk in method, the ef fec t of the balance m a s s on the c r i t i c a l f lu t t e r speed is as fol lows. The ins ta l la t ion of a ba lance m a s s changes the p a r a m e t e r s of the "equ iva len t " t w o d e g r e e o f f r e e d o m sys t em, i nc r ea s ing the e f fec t ive m a s s and momen t of iner t ia and d e c r e a s i n g the ef fec t ive coef f ic ien t of i n e r t ia coupling between the " g e n e r a l i z e d " bending and t o r s ional coord ina te s . The d e c r e a s e in coupling leads to a d e c r e a s e in the amount of e n e r g y f r o m the a i r flow, and hence the c r i t i c a l f lu t t e r speed is d e c r e a s e d . A method of de t e rmin ing the c r i t i c a l f lu t t e r speed of an a i r fo i l based on the d i r e c t solut ion of the equations for bend ingto r s iona l v ib ra t ions by means of an analog compute r was d e s c r i b e d in [2]. This method makes no assumpt ions about the types of v ibra t ion . The a c c u r a c y of the solut ion depends only on the extent to which the equat ions d e s c r i b e an actual wing, the a c c u r a c y in spec i fy ing the p a r a m e t e r s and ae rodynamic f o r c e s , and the machine e r r o r s . This method is used below to det e r m i n e the c r i t i c a l f lu t t e r speed, toge the r with the f requency and type of the f lu t t e r modes of an a i r fo i l with ba lance m a s s . The r e s u l t s obtained a r e c o m p a r e d with the c o r r e s p o n d i n g r e s u l t s given by the BubnovGalerk in method. It is shown that for the given example (also c o n s i d e r e d in [2]) of a un i fo rm a i r fo i l t h e r e a r e d i s c r e p a n c i e s be tween the two methods , at l e a s t for ce r t a in b a l a n c e r p a r a m e t e r s . 1. The equat ions for the bend ing to r s iona l v i b r a tion of a long un i fo rm a i r fo i l a r e [1]
- Published
- 1968
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