【作者】 徐步青；

【导师】 杨绍普；

【作者基本信息】 北京交通大学 ， 车辆工程， 2010， 博士

【摘要】 功能梯度材料(Functionally Graded Material,简写FGM)是一种特殊的非均匀材料。自从1984年日本科学家首次提出其设计概念以来,FGM在制造、设计和应用方面引起了广大学者的极大关注。虽然提出FGM的最初设想是作为热隔栅应用于航空航天领域,但目前发现它在电子、化学、核能、光学、声学、生物医学、土木工程和机械工程(例如汽车的发动机、高速机车的刹车盘和车轮)等诸多领域,都有十分广阔的应用前景。对FGM结构声学问题的研究,既有声学理论的需要,也有实际工程应用的需要。本文首先建立了镶嵌在无限障板中功能梯度材料矩形板和无限长板条声辐射模型。根据功能梯度复合材料矩形板的基本动力方程,利用模态叠加法求出不同激励载荷作用下功能梯度材料矩形板和无限长板条横向振动位移,然后对振动位移进行傅立叶变换,根据Rayleigh积分公式求解,最终得到功能梯度材料矩形板和无限长板条远场辐射声压近似解析解。由于功能梯度材料矩形板近场辐射声压无法利用积分得到解析解,只能利用数值积分进行研究,因此本文利用数值积分方法分析了功能梯度材料矩形板近场辐射声压频率特性。其次,本文建立了敷设阻尼层功能梯度材料圆柱壳在径向点激励载荷作用下的声辐射模型,研究了在阻尼层和圆柱壳不同参数下的振动和声辐射特性。研究时通过功能梯度材料圆柱壳的动力方程、流场Helmholtz方程、壳体表面边界条件和对有限长圆柱壳声压的傅氏积分变换来求解耦合声场中声压的表达式,其中阻尼层的运动采用Navier方程来描述。最后通过阻尼层与壳体的边界条件求解流固耦合振动方程,进而解得功能梯度材料圆柱壳在外流场的辐射声场表达式,并计算了表征壳体振动与声辐射的两个物理量:辐射声功率级和振动均方速度级。再次,本文建立了旋转载荷作用下功能梯度材料圆柱壳的声辐射模型,研究了不同旋转速度下功能梯度材料圆柱壳在空气和水两种流场中的振动和声辐射特性。旋转载荷采用频率域表示,这种基于频率域的方法便于解释振动及声辐射响应与功能梯度材料圆柱壳模态之间的关系。最后,本文还研究了功能梯度材料圆柱壳的声散射特性。首先将材料参数沿厚度方向连续变化的功能梯度材料圆柱壳,简化成多层横观各向同性柱状复合结构。然后利用传递矩阵法研究功能梯度材料圆柱壳声散射特性。研究发现,通过改变板和壳的几何参数、材料参数和梯度指数等,可以改变FGM板壳结构的动力响应和声学特性。本文的研究对FGM板壳结构的声学设计具有重要的指导意义。更多还原

【Abstract】 Functionally graded material (FGM) is special nonhomogeneous material. And it was first introduced by Japanese scientists in 1984. Since then, FGM has received more and more attention. Nowadays, FGM has extended their first applications in aerospace to electronics, chemistry, optics, biomedicine, acoustics, nuclear engineering, civil engineering, mechanical engineering (auto-engine, brake and wheel of bullet train) and the like. Research on the behavior of FGM structures acoustic problen not only benefits the needs of acoustic theory, but also satisfies the needs of practice.First, the models of radiated sound of baffled functionally graded material rectangular plate and infinite length plate strip are set up and investigated theoretically in this dissertation. By basic dynamic equation of FGM rectangular plate, the flexural displacement is obtained by modal analysis method that they are excited by various excitation forces. And using Fourier transform and Rayleigh’s formula, a far-field approximation solution of the radiated sound field is derived in a closed form. And the near acoustic field is investigated by a numerical integral method.Second, the sound radiation model of a finite FGM cylindrical shell driven by a harmonious point force with the outer shell coated with compliant layer is set up, and the vibroacoustic characteristics of different FGM shell’s and damping layer’s parameters are systematically studied. The acoustic pressure expression is attained by the FGM shell’s dynamic equation, the Helmholtz equation, the boundary conditions of the FGM shell surface and the Fourier integral transform of finite shell, where the layer motion is described by means of the three-dimensional Navier equations. Lastly, through the boundary conditions of the damping layer combined with the shell the coupled oscillation equation was solve, and radiation sound field expression was shown using the shell displacements. In the end, the parameters of the acoustic radiated power level and the radial quadratic velocity level are calculated. And these two parameters indicate the general characteristics of the FGM shell vibration and sound radiation.Third, a theoretical model is developed to evaluate the vibration and sound radiation of a FGM cylindrical shell excited by a constant point load continuously traveling along the circumferential direction at a rotational speedΩ, and the FGM shell is immersed in two different fluids of air and water. The present approach is based rather on a frequency-domain solution of the vibratory and acoustic responses of the FGM shell, and such a frequency-domain solution is convenient to interpret the vibratory and acoustic responses in terms of shell modes.Finally, the sound scattering by functionally graded material cylindrical shell is investigated in this dissertation. The original inhomogeneous shell with the material parameters’s change along the thickness is approximated by a laminate modal. So the FGM shell is turned into a cylindrical layered structure with transversely isotropic symmetry. The transfer matrix solution is expected to gradually involves a system global transfer matrix formed as the product of the individual transfer matrices by applying continuity of the displacement and stress components at the interfaces of neighbouring layers, is employed to solve for the scattering coefficients.We find that geometric parameters, material paratemers and power law index of the plate and shell affect the responses of FGM structures’s vibroacoustic behaviour. This dissertation hopes to bring some insights on the acoustic designing of the FGM structures.更多还原