Some Experiments on the Vibration of a Hemispherical Shell

Abstract

The paper describes the experiments on the vibration of a thin hemispherical shell having a free edge and constant thickness. The test data are compared with the analytical data obtained through various methods originated by Rayleigh, Love-Federhofer-Naghdi, and Mushtari-Vlasov. For the axisymmetrical case, the test results compare favorably with the numerical data based on the method of Love-Naghdi. For the asymmetrical cases, it is found that the latter method fails to predict the most significant modes in the low-frequency region, while Rayleigh’s inextensional theory yields favorable frequency data. The reason for the failure of the more sophisticated method to predict the shell vibration is explored. The failure may be due to a characteristic inherent in the linear shell theory, or may be due to difficulties in numerical computation which are explained in the paper. Also noted is a typical modal shape where the deformation pattern is concentrated in the free-edge region. The phenomenon, which justifies the use of the dynamic edge effect solutions, is explained analytically.