Deformation and stability of short cylindrical membranes

Analysis of the deformation of cylindrical membranes is important for understanding various mechanical systems, including biological structures such as the incudostapedial joint in the middle ear. Although the deformations of long cylindrical membranes have been extensively investigated, studies of short cylindrical membranes have not been published. Here we present an analytical solution for the deformation of moderate-length and short cylindrical membranes using the Mooney-Rivlin form for the strain-energy function. The membrane profiles and the internal pressures fit well with a finite-element model. We show that both moderate-length and short membranes become unstable when passing a certain limit pressure, and this instability persists even for very short membranes. Furthermore, we show that increasing the initial length, the pre-stretch and the stiffness all tend to stabilize a short membrane. The results may furnish insight into the mechanical behaviour of the incudostapedial joint.