Acoustics: Sound Fields, Transducers and Vibration, 2nd Edition

14.9. Green's function for a circular membrane

Let us now write an inhomogeneous membrane equation by adding a driving pressure distribution p ˜ 0 ( w , ϕ ) to the homogeneous one of Eq. (14.26)

( ∇ 2 + k D 2 ) η ˜ ( w , ϕ ) = − p ˜ 0 ( w , ϕ ) T ,

(14.33)

where

η ˜ ( w , ϕ ) = ∑ m = 0 ∞ ∑ n = 1 ∞ A ˜ m n cos ( m ϕ ) J m ( α m n w / a ) .

(14.34)

Using the recursion formulas of Eqs. (A2.83) and (A2.84) from Appendix II it ...