The paper considers the steady-state harmonic response of an elastic fluid-loaded membrane supported by irregularly spaced ribs. Under the assumption of subsonic wave coupling, the solution is given exactly for any configuration as a product of 2 $\times $ 2 transfer matrices. It is well known that the response of a periodically ribbed membrane exhibits a pass/stop band structure. Although this structure is destroyed in the irregular case, we find that two distinct regimes remain: smooth and fluctuating exponential decay. The transfer matrix solution is used to explain these regions. The average transfer matrix is obtained exactly; where the decay is smooth its eigenvalues approximately determine the localization length.