Buckling and vibration of a thin tensioned sheet with an elliptical hole

The out-of-plane deflection which can be developed in a thin tensioned sheet containing a central opening is discussed. It is noted that this behavior is of practical importance because it can alter the stress concentration and fatigue properties. The results of an experimental and analytical study of the buckling and vibration behavior of tensioned sheets with an elliptical opening are presented. Data from buckling and vibration experiments for several opening shapes ranging between a crack and a circle are presented. A generalized Galerkin method for solving the governing differential equations is used and the results obtained are presented in terms of buckling loads and natural frequencies. The experimental-buckling-stress estimates are correlated with the analytical results. The data from the vibration experiments indicate that the load-frequency behavior is dependent on the size of the test specimen and the opening shape. The analytical results display a load-frequency behavior which is experimentally observed for a narrow elliptical hole; i.e., for a small value of the ratio of minor axis to major axis. Some features of the analytical and experimental vibration results differ substantially, however. The analysis indicates that the frequency decreases to zero as the applied load approaches the buckling load. The experimental results do not exhibit this behavior. The sources of this difference in behavior are discussed.