无穷大二维周期加强板的声振特性研究
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摘要
周期加强板结构广泛应用于机械工程、航空航天、船舶潜艇和车辆工程等领域,因而与其相关的振动及声学特性的研究具有十分重要的工程价值。为了深入分析周期加强板的声振特性,本文对其振动响应、声辐射、反射和透射等性质进行了系统研究,并对周期加强的微穿孔板的吸声性能进行了分析。其中主要研究内容包括：
(1)综合运用空间波数法、格林函数、泊松迭加公式和傅里叶变换等数学方法分析了流体负载下的,异向正交周期加筋和同向双周期加筋两种不同类型加筋薄板结构在谐振面力作用下的振动响应和声辐射。对于异向正交周期加筋薄板,采用空间波数法将其振动位移及辐射声压表达为一系列谐波分量的迭加。对于同向双周期加筋薄板,利用分量迭加公式及结构周期性质,求解得到其振动位移及辐射声压方程。同时分析了加强筋对薄板的法向力作用及扭矩作用。计算结果表明周期加强筋在中低频域区间起到了降低薄板辐射声压的作用。
(2)研究了流体负载下的不同类型双周期加强薄板,在谐振面力激励下的振动响应和声辐射,并提出了一种基于有限元和空间波数法的半解析半数值方法；附加的周期结构可以是包含筋在内的任意不同形状的结构。为了得到不同类型周期结构与薄板间的作用力,基于有限元的思想对周期结构进行单元离散,将薄板与周期结构的面力等效为离散节点力的作用,并最终将周期加强板的振动位移和辐射声压方程表达为薄板离散点位移的函数。运用加强板结构周期性质及空间波数理论,在实际分析时只需要计算一个周期单元的离散点位移,有效地降低了计算工作量。
(3)分别通过均匀等效模型和周期模型两种建模方法研究了双周期肋骨连接的双层板结构的反射和透射声压；并在单层周期加筋板的基础上,对另外一种类型的拉杆连接的双层周期加筋板结构采用周期模型方法进行了研究。双层薄板结构附加周期连接肋后增加了结构的平均反射声压而降低了其透射声压。拉杆对双层加筋板结构反射和透射声压的影响主要是在几千赫兹内的中低频域区间。
(4)采用耦合法和级联法两种方法研究了单层及多层双周期加强板的透声系数。耦合法是同时对整体多层加强板结构进行分析,并将所有声振未知量在统一的矩阵方程中计算求解得到。级联法是首先分析单层板结构的振动及声压方程,并在此基础上通过声波的空间传播性质以及各层板声压矩阵的级联得到整体多层结构的反射及透射声压系数矩阵。在水中环境下加强板结构的弯曲振动作用显著,且周期结构起到了降低结构透声系数的作用。
(5)基于微穿孔板相关声学理论的基本公式,研究了周期加强微穿孔板的吸声性质,并在单层板结构反射与透射系数矩阵的基础上,通过级联的方法进一步分析了多层周期加强微穿孔板的吸声特性,并与单层结构进行了比较。分析结果表明,水中周期加强的微穿孔板的吸声性能远高于未加强的微穿孔板的吸声性能,多层板结构具有比单层结构更优良的吸声性能,且吸声系数随穿孔板层数的增加而增大。通过对薄板加工微孔和附加适当周期结构的方法可以有效地提高水下薄板的吸声性能,对吸声结构的设计和研究具有重要价值。
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.
(1)综合运用空间波数法、格林函数、泊松迭加公式和傅里叶变换等数学方法分析了流体负载下的,异向正交周期加筋和同向双周期加筋两种不同类型加筋薄板结构在谐振面力作用下的振动响应和声辐射。对于异向正交周期加筋薄板,采用空间波数法将其振动位移及辐射声压表达为一系列谐波分量的迭加。对于同向双周期加筋薄板,利用分量迭加公式及结构周期性质,求解得到其振动位移及辐射声压方程。同时分析了加强筋对薄板的法向力作用及扭矩作用。计算结果表明周期加强筋在中低频域区间起到了降低薄板辐射声压的作用。
(2)研究了流体负载下的不同类型双周期加强薄板,在谐振面力激励下的振动响应和声辐射,并提出了一种基于有限元和空间波数法的半解析半数值方法；附加的周期结构可以是包含筋在内的任意不同形状的结构。为了得到不同类型周期结构与薄板间的作用力,基于有限元的思想对周期结构进行单元离散,将薄板与周期结构的面力等效为离散节点力的作用,并最终将周期加强板的振动位移和辐射声压方程表达为薄板离散点位移的函数。运用加强板结构周期性质及空间波数理论,在实际分析时只需要计算一个周期单元的离散点位移,有效地降低了计算工作量。
(3)分别通过均匀等效模型和周期模型两种建模方法研究了双周期肋骨连接的双层板结构的反射和透射声压；并在单层周期加筋板的基础上,对另外一种类型的拉杆连接的双层周期加筋板结构采用周期模型方法进行了研究。双层薄板结构附加周期连接肋后增加了结构的平均反射声压而降低了其透射声压。拉杆对双层加筋板结构反射和透射声压的影响主要是在几千赫兹内的中低频域区间。
(4)采用耦合法和级联法两种方法研究了单层及多层双周期加强板的透声系数。耦合法是同时对整体多层加强板结构进行分析,并将所有声振未知量在统一的矩阵方程中计算求解得到。级联法是首先分析单层板结构的振动及声压方程,并在此基础上通过声波的空间传播性质以及各层板声压矩阵的级联得到整体多层结构的反射及透射声压系数矩阵。在水中环境下加强板结构的弯曲振动作用显著,且周期结构起到了降低结构透声系数的作用。
(5)基于微穿孔板相关声学理论的基本公式,研究了周期加强微穿孔板的吸声性质,并在单层板结构反射与透射系数矩阵的基础上,通过级联的方法进一步分析了多层周期加强微穿孔板的吸声特性,并与单层结构进行了比较。分析结果表明,水中周期加强的微穿孔板的吸声性能远高于未加强的微穿孔板的吸声性能,多层板结构具有比单层结构更优良的吸声性能,且吸声系数随穿孔板层数的增加而增大。通过对薄板加工微孔和附加适当周期结构的方法可以有效地提高水下薄板的吸声性能,对吸声结构的设计和研究具有重要价值。
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.
引文
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