Bending Vibration Of Rectangular Plates With Acoustic Characteristics

Rectangle radiators with flexural vibration are widely used in the air and water.flexural vibration type flat panel speaker has many advantages compared to traditional speaker,such as broad bandwidth, good sound quality, cheap price and do not box.Therefore, rectangle radiators with flexural vibration have a good application in the field of speaker and develop rapidly. In the field of underwater sound. There are a lot of research on the acoustic characteristics of the acoustic emission transducer and its array for the emission energy is concentrated in some specific direction. As far as boundary conditions are concerned, Rectangle radiators with flexural vibration include rectangle radiators under free boundary conditions, under simply supported boundary conditions and under fixed boundary conditions.Many literatures have studied the rectangle radiator under simply supported boundary conditions previously. The acoustic characteristics of the flexural vibration radiators under free boundary conditions and under fixed boundary conditions are very little in the Present literature,because of their vibration equations have no analytical solution.In order to solve these problems, taking rectangular thin plate with flexural vibration under free boundary conditions and fixed boundary conditions for example, its numerical expression of the the acoustic characteristics 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 acoustic characteristics.In order to verify the correctness of this method, the directivity pattern of acoustic field radiated by sound source is computed numerically, the results are compared to the analytic ones in order to confirm the validity of this procedure.The detailed work is as fellow:1.Numerical expression of rectangular 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.2.From radiated power, numerical expression of rectangular plate resistance is derived.Substitution from discrete array values of the finite element into numerical expressions, the numerical solution of radiation resistance is calculated by computer program..3.Take the same size rectangular plate for example, the acoustic characteristics of the flexural vibration radiators under free boundary conditions and under fixed boundary conditions are computed.three-dimensional directivity pattern is obtained, in order to more directly study the sound field of rectangular plate in flexural vibration, two-dimensional directivity pattern is obtained. Then map of radiation impedance-frequency relationship is computed.