Thick Disc Axisymmetric Bending Vibration,

The flexural vibration of circular plate with large surface area has used in producing ultrasound of high directivity in air. Under the high-frequency, high power sound radiation conditions, the mechanical strength of thin disk get insufficient. Then the thick disk is a good choice because it possesses advantages of small transverse dimension and high frequency. The flexural vibration characteristics and sound field of circular plate have been studied, mostly based on "thin plate theory", that is the "hypothesis of Kirchhoff'. This assumption ignores the transverse shearing deformation and increases the stiffness of the plate, so the frequencies of it are always higher than the actual frequencies. When the ratio of thickness to diameter of plate gradually increases (greater than 1/5), the limitations of the classical thin plate theory will visibly displayed. So we have to re-explore and research the basic assumption of classical thin plate theory, and establish new theory that is to say thick plate theory, including the effects of rotatory inertia and shear. In applied acoustics field, we concern about the structural vibration properties of thick disk, as well as hope to obtain the resonance frequency equation and displacement analytic solution under some boundary conditions. It is beneficial to design and calculate sound field.In most of previous research, from the engineering mechanics pinot of view, the flexural vibrations of thick disk were studied. In this article, staring from the acoustics research point, it is systematically introduced the Kirchhoff's thin plate theory and thick plate theory. Further the different hypotheses of the two theories are analyzed then the difference of the two theories is found out. This paper studied the flexural vibration characteristics of thick disk based on Mindlin's theory. Which mainly includes radial displacement,transverse displacement and resonance frequency equation of the flexural vibration thick disk.The research method is general and universal.In this paper a general solution of radial displacement and transverse displacement for flexural vibration thick disk under the Mindlin theory are derived. The resonance frequency equation is derived when the boundary conditions are free, simply supported and clamped, and the resonant frequency compared with ANSYS calculation verification and experiential verification. The numerical examples show that, with the increasing of thickness of disk, the frequency became relatively inaccurate owing to the influence of the "hypothesis of Kirchhoff". In the same geometry, the resonant frequencies by thin plate theory calculated are always higher than the Mindlin theory calculations. Especially calculating high order-frequency, the error of thin plate theory calculations show greater, but the thick disk theory calculations are satisfactory.These results can be referred for the design of the flexural vibration thick disk radiator. And these provide a good foundation for the studying radiation impedance and directivity of flexural vibration thick disk.