Theoretical Considerations for Supporting Composite Beams and Circular Plates Undergoing Flexural Vibrations

摘要

Flexural vibrators, in the form of beams or circular plates, have been proposed as a means of achieving relatively small, low-frequency sonar transducer elements. The original designs were based on symmetric bilaminar elements composed of polarized ferroelectric ceramic material. Later designs used a symmetric trilaminar configuration with active ceramic bounding a center lamination of inactive material. More recently, however, several designers have advocated the use of bilaminar (ceramic-metal) configurations in order to increase the depth capability of flexural vibrators without using internal pressure compensation for the hydrostatic loading. This report investigates and explains some of the implications involved in physically supporting these designs from a viewpoint of defining a neutral surface (plane) in any particular structure. The results indicate that some configurations have true planes at which supports may be attached, whereas the neutral plane for other configurations is not explicitly defined but may be approximated. The dynamic equations of equilibrium are derived for some of the cases that are considered, and similar equations for the other cases can be inferred from the derived equations when certain conditions are satisfied. (Author)