Page 18 - Spring 2007

cle—non-resonant sound radiation can be higher than resonant sound radiation. The sound radiated by the (2,2) mode at its res- onance frequency just below 100 Hz is a good example—it is lower than the non-resonant sound radiated by the (1,1) mode!
When we coupled the radiation resistance of a baffled piston to a simple harmonic oscillator (where the piston head was the mass), we added it to the resistance of the oscillator. For finite structures, most analysts use mechanical loss fac- tors to model structural damping. We can compute a radia- tion loss factor which can be used in a structural analysis to represent the radiation damping of an acoustic fluid. A use- ful equation for the radiation loss factor of a uniform thick- ness, homogenous plate or shell structure (flat or curved) is
.
(15a)
The equation shows that the radiation loss damping is directly proportional to fluid density, meaning that the heavier the fluid, the more sound power is radiated, and the more heavily damped the structure. An example would be a vibrat- ing bell dunked in water. While in the air, the bell’s vibrations would ‘ring’ for a long time. When immersed in water, the vibrations decay quickly. An extension of the above equation, well known in the Statistical Energy Analysis (SEA) commu- nity, relates the radiation loss factor to the radiation resistance:
, (15b)
where M is the mass of the plate or shell.
Table 1 provides a useful list of the various sound radia-
tion quantities and how they inter-relate.
The complementary problem—Structural vibrations induced by acoustic pressure waves
Whereas the sound radiated by vibrating objects is often just an annoyance, the vibrations induced in structures by impinging acoustic waves can be so high that the structures crack and fail. This is clearly a more serious problem, and has
Table 1. List of sound power radiation quantities and their interrelationships.
Fig. 9. Mobility magnitude (top), radiation efficiency (middle), and radiated sound power transfer function (bottom) of a simply supported 1m square 5 mm thick flat steel plate in water driven at its quarter point (x=0.25 m, y=0.25 m).
16 Acoustics Today, April 2007