The Method Of Wavenumber Space Analysis For Acoustic Natures Of Periodically Stiffened Plate

Plate and the sophisticated structures consisted of it have wide application in the area of mechanics, ship, airlines etc, such as manufacturing hull, fuselage and many kinds of mechanical components. With the development of science and technology, people's requirement for the all-side performance of plate becomes higher and higher. It has become a concerning focus in this field recently that how to effectively control or reduce the vibration and sound radiation of plate caused by outside excitement. And research on the vibration and acoustic radiation of periodically stiffened plate has become one of the spotlights in recent decades.Through periodically stiffening on plate, coupling effect is generated between stiffeners and plate. The stiffening can improve plate's vibrating natures and forcing stability, meanwhile increase plate's radiating impedance under certain conditions, effectively decrease plate's sound radiation, thus improve plate's comprehensive performance, which is proved by examples in this paper. This paper mainly researches the vibration and radiation natures of periodically stiffened plate excited by outside fluid and the analysis on the changing law of plate's vibration response and acoustic radiation by some main physical factors, such as outside force's frequency, the incidence, periodical interval and so on. And it's proved by corresponding value examples. At present, there are two main methods in this area: one uses the idea of FEM and BEM, dispersing the stiffened plate into many elements, combining the periodicity of plate's elements, applying Ansys software to analyze and process. The other uses analyzing method to do theoretical analysis and solve problems. But it's difficult to use pure analyzing method to solve the complicated structure problems, the numerical calculation is always needed in the process of solving. In this way. the half-analyzing method is generated. .This method is used in this paper, through Fourier transforms and inverse transforms, combining some basic mathematical principles and many kinds of mathematical methods to derivale theoretically, applying Matlab software to program and calculate.Through Fourier transforms, the expressions in physical space are transformed into wavenumber space, which facilitates the application of many mathematical natures and principles. At last, the needed results are got by approximate formula or inverse Fourier transforms from frequency domain into time domain. Apply Matlab software to program and calculate examples, get the figures of plate's vibration and acoustic pressure of radiation. Three mathematical methods are used in this paper, method of constructing function, method of periodic function and Green function, respectively for three different models of stiffened plate, one-dimensional periodically stiffened plate, one-dimensional periodically stiffened plate with consideration of torque, two-dimensional periodically stiffened plate. Corresponding examples are calculated by programming, and the model's main parameters' effect to the vibration and acoustic radiation is analyzed.