Analytical and experimental investigation on transverse vibrations of solid, circular and annular plates carrying a concentrated mass at an arbitrary position with marine applications

Abstract

This investigation arose from the practical necessity of placing a centrifugal pump rigidly attached to a thin, circular cover plate of a water tank in a medium size ocean vessel. Due to lack of space, it was necessary to locate the system off—center of the circular configuration. It was considered necessary to calculate the fundamental frequency of the coupled system. The first part of the present study is concerned with the determination of the fundamental frequency of vibration of a circular plate carrying a concentrated mass at an arbitrary position, using a variational approach. Numerical results are obtained for the stated problem for several combinations of the intervening geometric and mechanical parameters. An experimental investigation is also performed in the case of clamped plates. Based on the results for solid circular plates, the fundamental frequency of annular plates with a free inner edge and a concentrated mass is also obtained. Circular plates are fundamental structural elements in ocean engineering applications: from off-shore platforms to underwater acoustic transducers. In a great variety of circumstances, they must carry operational systems in an eccentric fashion. Since the dynamic performance is always of interest, one must know at least some of the basic dynamic parameters.