-Q 



CD 



105 



100 





S 295 



i_ 1— c\ 



Q- o 



c O 



§^ 

 </) 



CD 



> 



90 

 85 



-2 80 

 or 



a x o unrestrained rods 

 • o clamped tubes 



am m 



Jl 



ercury -filled tubes /*\&s y \ J s / ' 



I i i /I JLi >^ 



>^P e 0c (J 



2.00 210 



lOOft./sec. 



/sec 



Figure 21. The sound pressure radiated by a cylinder shedding vorticces in air, as a function of 



speed. (From Etkin et al [53].) 



the vortex shedding along its entire length, causing the sound pressure to increase by 

 a factor (L/bD) 1 / 2 . 



Although the sound generated by the vibration itself is neglected by both Etkin 

 and Phillips, it should be noted that in a relatively dense liquid such as water, the 

 amplitude of the sound may be increased by the vibration even in the absence of any 

 modification of the pattern of vortex shedding. To indicate the magnitude of the 

 sound that may result from vibration, consider a rigid cylinder held by compliant sup- 

 ports so that the cylinder vibrates transversely, when immersed in water, in free oscilla- 

 tion at a frequency /,. with logarithmic decrement -n-8- Assume, as a first approximation, 

 that the amplitude of vibration is so small that the gross motion of the fluid is not at 

 all affected. The cylinder vibration will result from a reaction to the force exerted by 

 the cylinder on the fluid. In terms of the force exerted by a fixed cylinder, e.g., the 



force F given by Eq. (26), the reaction force acting on the cylinder is — (F + M a U), 

 with M a being the added mass due to the water. If the force and vibration are sinus- 

 oidal with frequency /., equal to the shedding frequency, so that F — F°e 2 ~ if 1 t and 



U — U°e 2 ' !rif 1 t , the amplitudes F° and U° are related by 



77° = [F°/(M a + Me)] • [(fr/fi) 2 - 1 + i8]-\ (28) 



M c being the mass of the cylinder. The sound pressure amplitude p is then given by 



Eq. (25), with U and F replaced by 2-n-if^ and 2 7 r// 1 (F° + M a U°), respectively, 

 and p s (t) by p . 



At resonance, f 1 — /,.; the sound pressure amplitude is then given by 



fiF° 



Po = 



2rc 



i + 



M a 



.7 



8(M a + M c ) 

 211 



