In Thick Plate Bending Vibration Characteristics And Directivity

In high-power ultrasonic field, flexural vibration of circular radiators with large surface area is widely used. Under the high-frequency and high power sound radiation conditions, the mechanical strength of moderately thick plate gets sufficient and the transverse dimension is small, it is a good choice. At present the flexural vibration characteristics and sound field directivity of circular plate have been calculated and studied through "thin plate theory". This theory ignores the influence of the transverse shearing deformation. Because the stiffness of the plate increasing, the flexural vibration frequencies are always higher than the actual frequencies. This theory applies to thin plate (the ratio of thickness to diameter less than 1/5). With the thickness increasing, the thin plate theory is no longer applicable, so we have to establish the moderately thick plate theory. The moderately thick plate theory mainly considers the effects of rotatory inertia and shear. We hope to get the vibrational characteristics of moderately thick plate and obtain the directivity pattern of the sound field at high-power ultrasonic field.Directivity pattern is one of the key indicators describing on the radiated acoustic field of sound source. In order to get effective sound intensity in some certain directions, and decrease interference of other directions, sound radiated bodies are widely used in actual life. In underwater acoustic applications, emitting energy should be concentrated on certain direction in order to launch little power to detect more distant direction. So the underwater acoustic transducers and their base array were studied. In electro-acoustic aspect, the panel speakers of flexural vibration compared with traditional speakers are so bandwidth, timbre and cheaper that obtained a rapid development. It has important theoretical and practical significance to research the directivity pattern of the panel speaker. At present, the flexural vibration characteristics and sound field of circular plate have been studied, mostly based on "thin plate theory". The flexural vibration characteristics and directivity pattern of moderately thick plate hasn't obtained analytical solutions. It is very little studied. The detailed work is as fellow.The flexural vibration characteristics of plate are calculated from thin to thick by numerical method using finite element method. The variations of the fundamental frequency and nodal circular with the thickness of the plate are derived. So the limitation of the classical thin plate theory is visibly displayed. The experimental results are basically consistent with the results of theoretical analysis. Numerical expression of moderately thick plate directivity pattern is derived through discrete Rayleigh's integral formula, and its surface vibration displacement of the source is obtained by the finite element method, on these bases, a method is proposed for calculating its directivity pattern. These results can be referred for the design of the flexural vibration moderately thick plate radiator.