Stability of Inviscid Shear Flow over Flexible Membranes

Abstract

A minimum of four terms in the solution form was necessary to predict accurately the divergence velocities as a function of the length-to-radius ratio ?/a. Divergence velocities varied widely before approaching a limit as the number of terms in the assumed solution was increased. This was particularly true for ?/a> 10 and for higher-order modes (/?>3). A study of the effect of the thickness-to-radius ratio on critical divergence velocities showed that higher-order circumferential modes are associated with shorter and/or thinner shells. The lowest critical divergence velocity, for long shells (£/tf>40), is associated with the beam-type mode (n=\). Critical divergence velocity as a function of lamina orientation, for a given circumferential mode, is shown in Fig. 3 for £/#=10 and hi a = 0.01. The present analysis was repeated for the isotropic case and compared with the results given in Ref. 7. Good agreement was noted. Conclusions Natural frequencies of fiber-reinfor ced shells decrease with increasing fluid velocity, as do isotropic shells, until static divergence occurs. Natural frequency is a function of the length-to-radius ratio, the radius-to-thickness ratio, the circumferential mode number, and the orientation of the lamina. Beam-type theory was found to be suitable for long shells, but in any other case shell theory must be used. Qualitatively, the behavior of anisotropic shells appears to be much the same as that of isotropic shells. However, it is reasonable to expect that certain lamina stacking sequences will result in considerably different numerical values of divergence velocity as a function of lamina orientation.