Research On The Vibro-acoustic Properties Of Two-dimensionally Periodically Stiffened Plate Of Infinite Extent

The study of the vibration and acoustic properties of periodically stiffened plates is practically important due to their widely applications in mechanical engineering, aerospace, submarine and automotive engineering fields, etc. To better analyze the vibro-acoustic properties of the periodically stiffened plates, their vibration response, acoustic radiation, reflection and transmission characteristics are systematically studied here. Furthermore, the acoustic absorption performance of the micro-perforated and periodically stiffened plates is also investigated. The doctoral dissertation mainly consists of five sections, which includes:(1) The vibration response and acoustic radiation of two kinds of periodically rib-stiffened plates under fluid loading are analyzed by employing the space harmonic method, Green function, Possion’s summation formulas and Fourier transforms, comprehensively. The two kinds of stiffened plates include infinite plates periodically stiffened by two orthogonal sets of ribs and stiffened by two different sets of ribs along one direction respectively, both of which are exerted by a harmonic plane pressure. For the orthogonally rib-stiffened plate, the vibration displacement and acoustic radiation are expressed as sums of a series of harmonic amplitudes by using the space harmonic method. For the one-directionally rib-stiffened plate, the infinite amplitude summation formula and the periodic property of stiffened plates are utilized for obtaining its vibration response and acoustic radiation expressions. The vertical forces and torsional moment applied on the plate by the ribs are considered together. Through numerical analysis, it is found that the ribs can help degrading the acoustic radiation pressure of the plate in the middle and low frequency ranges.(2) The vibration response and acoustic radiation of an infinite fluid-loaded plate, which is two-dimensionally periodically stiffened by various kinds of structures and excited by a harmonic plane pressure, are investigated deeply. The periodic structures can be given as any geometrical shapes including the ribs. And a semi-analytical approach based on the finite element method (FEM) and the space harmonic method is also proposed for analyzing periodically stiffened plates. To obtain the reaction forces of the periodic structures exerted on the plate, each structure is discretized into a sufficient number of finite elements and nodal points with the FEM, and then the reaction forces are approximated by the equivalent nodal forces. Finally, the vibration displacement and acoustic radiation pressure of the periodically stiffened plate are expressed as functions in terms of discrete point displacements of the studied plate. With employing the periodic property of the stiffened plate, only one periodic structure need be actually discritized, which greatly reduces the task of computational work.(3) The acoustic reflection and transmission pressures of a double-plate structure periodically linked by rib-like structures are studied respectively through the smeared model and periodic model. And another kind of two-layered rib-stiffened plate structure periodically linked by rods is also investigated by using the periodic model based on the single rib-stiffened plate. It is found that for the first kind of structures, the periodic rib-like structures lead to higher averaged acoustic reflection pressure and lower acoustic transmission pressure in the studied frequency range. For the second kind, the influences of the rods on the stiffened plates are mainly in the low and middle frequency ranges of several thousand hertzs.(4) The transmission coefficients of single layered and multilayered periodically stiffened plates are investigated by respectively using the coupled method and cascade connection method. The coupled method is to simultaneously analyze the multilayered plate structures and all the unknown vibro-acoustic parameters will be solved in one matrix equation. The cascade connection method is to firstly analyze the vibro-acoustic equations of one single layered plate, and then the acoustic propagation property and the cascade connection of acoustic pressure coefficient matrix of each plate will be applied to obtain the whole acoustic reflection and transmission coefficient matrices. Numerical result shows that the flexural vibration of the stiffened plate is significant and the periodic structures can decrease the plate’s transmission coefficient in the water.(5) Based on the fundamental acoustic formulas of micro-perforated plates, the acoustic absorption performance of two-dimensionally periodically stiffened and micro-perforated plates is investigated. Meanwhile, the cascade connection method is employed to study the multilayered micro-perforated and periodically stiffened plate with using the reflection and transmission matrices of the single layered perforated plate. Furthermore, the absorption coefficients of one single layered and multilayered such plates are also compared. Numerical results indicate that the stiffened micro-perforated plate has better sound absorption property than the unstiffened perforated plate in the water. Also, multilayered plates have larger absorption coefficient than single layered ones, which increases with layer numbers. Consequently, attaching periodic structures to the plate and perforating it with micro-holes can effectively improve the sound absorption property of plates in the water, which is promising for the future research and practical design of acoustic absorption structures.