Structural Acoustics

256 Structural Acoustics: Deterministic and Random Phenomena

© 2011 by Taylor and Francis Group, LLC

With integration, we have

G r r g

e

T i j nm

n

M

m

M

i r r

C

jn im

( , , ) ( )

[ (

 

ω ω

ω

=

==

−

∑∑

11

))]

r r

jn im

(13.54)

and the autospectrum at the point j will be

G r r g

e

r

T j j nm

n

M

i r r

jn

C

jn jm

( , , ) ( )

[ ( )]

 

ω ω

ω

=

=

−

∑

1

rr

jm

m

M

=

∑

1

(13.55)

where

g

T

F F

nm

T

nT mT

( ) lim ( ) ( )

*

ω ω ω=

→∞

1

2

(13.56)

The g

mn

(ω) are the cross spectra among the sources. If we have M

2

mea-

surements of G(r

j

, r

j

, ω), then Equation 13.55 contains a series of M

2

complex

algebraic equations for the unknown cross spectra g

mn

(ω). Once these source

cross spectra, g

mn

(ω), are obtained, then ...