A Theoretical and Experimental Investigation of a Dynamically Loaded Ring with Radial Elastic Support

摘要

Equations are developed for the frequencies of flexural vibration, and infinite series solutions are obtained for displacements and bending moments with an impulsive load analytically defined as a half-sine wave. Harmonically varying and static loads are also treated. In the development of the theory, the vibrations are assumed to be inextensional, and effects of damping, rotary inertia, and shear are neglected. The theory was investigated experimentally by tests of a 24-in. diameter ring radially supported by a large number of coil springs. Impulses of half-sine characteristic were delivered by means of a pendulum during which time the force of impact was accurately measured with a dynamometer especially developed for this study. The parameters of elastic support and the duration and intensity of load were varied during the test, and recordings were made of strains and radial displacements as well as external load. The observed frequencies of vibration were found to agree with those computed by the theory within a few percent up to the seventh mode of flexural motion. Also the observed strains and displacements were found to correlate for the time interval during the pulse and for subsequent free vibrations. It is concluded that the theory is valid within the bounds of the assumptions provided that the depth of cross section of the ring is small compared with the diameter. (Author)