Let us now write an inhomogeneous membrane equation by adding a driving pressure distribution
${\tilde{p}}_{0}(w,\varphi )$
to the homogeneous one of Eq. (14.26)

$\left({\nabla}^{2}+{k}_{D}^{2}\right)\tilde{\eta}\left(w,\varphi \right)=-\frac{{\tilde{p}}_{0}\left(w,\varphi \right)}{T}\text{,}$

(14.33)

where

$\tilde{\eta}\left(w,\varphi \right)=\sum _{m=0}^{\infty}\sum _{n=1}^{\infty}{\tilde{A}}_{mn}\mathrm{cos}\left(m\varphi \right){J}_{m}\left({\alpha}_{mn}w/a\right)\text{.}$

(14.34)

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

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