宁波大学毕业设计(论文)

2006 届宁波大学毕业设计（论文）题目功能梯度板中的表面波姓名周乐辉学 号 024090534指导教师王骥专业工程力学宁波大学工学院摘要传统上认为成层结构沿板厚度方向功能梯度材料属性是呈线性变化，但是在实际情况下，因为材料的正常老化和衰变，放射物、激光设备、晶体以及其他一些杂质都是呈指数规律变化的，所以以指数形式的变化规律来定义功能梯度材料对材料的实际运用是十分重要的。

定义沿板厚度方向功能梯度材料的属性呈指数规律变化，我们来研究这种材料对声表面波传播的影响。

在研究中发现直接修改相关方程的材料属性就可以影响声表面波的衰减系数、相位速度以及位移传播方式。

当指数函数的变量很小时，就能够得到忽略非线性参数条件下的解析解。

利用这些解，比较各向同性材料以及半无限大功能梯度板中的结果，就能够检验表面波的波速和位移在功能梯度板中的变化。

这些结构将有利于评测声表面波器件谐振器，滤波器，压电材料的年限，内部杂质、放射性物质以及其他方面的影响。

另外，功能梯度材料的研究为表面波压电材料的研究有着直接关系，通过这项研究不仅能够提供理论结果也能提供确切的数值方法，这些在工程实际运用中有着重要作用。

关键词：功能梯度材料压电材料石英谐振器声表面波ABSTRACTThe layered structures assumed as the linear varying along the thickness direction on traditionally,but in the true-life materials, because the natural modification or degradation of material properties due to radiation, laser treatment, quartz,contamination, among others, is always exponential,so the properties with the exponential in FGM is very important in practical applications.By allowing material properties of a plate varying in an exponential manner along the thickness direction, we studied its effect on surface acoustic waves (Rayleigh waves). It is found that the known equations of decaying parameters and phase velocity of surface acoustic waves, as well as wave modes, are directly affected by the material property varying parameter through modifying related equations.For a small variation parameter of the exponential function, analytical solutions can be obtained by neglecting the nonlinear terms of the parameter.With these solutions, effects of material gradient are examined for the velocity and mode shapes in comparison with known results for homogeneous solids.These results can be used in the evaluation of the aging, contamination, radiation, and other natural effects on surface acoustic wave devices such as resonators. As a result, a study of the effect of such phenomena on structures and devices can be simplified with exponential models of material property variation. In addition, such an investigation can always provide theoretical results for the validation of numerical methods, which are important in practical engineering applications.Keywords: FGM Piezoelectric Materials Quartz Responser SAW目 录第一章绪论....................................................................................................................................５1. 1 毕业论文的背景、意义........................................................................................................５1.2 毕业论文所作的工作以及创新点.........................................................................................５第二章功能梯度板中表面波..............................................................................................................６2.1 固体中的弹性波方程建立.......................................................................................................６2.2表面波相关公式推导................................................................................................................７2.2.1基本公式.................................................................................................................................７2.2.2变量α足够小的情形.............................................................................................................８2.2.3没有作近似的解答.................................................................................................................９2.3本章小结....................................................................................................................................９第三章数值计算和讨论..................................................................................................................１０3.1 速率的计算...........................................................................................................................１０3.2位移的计算.......................................................................................................................................１７3.3本章小结................................................................................................................................２７第四章结论和展望......................................................................................................................２８参考文献..............................................................................................................................................２９致谢..............................................................................................................................................３０附录1：毕业设计电子刻录光盘..........................................................................................................３１附录2：功能梯度板中声表面波传播*综述........................................................................................３１附录3：G. W. Farnell. Properties of elastic surfaces waves. Physical Acoustics (W. P. Mason and R.N. Thurston, editors), New York: Academic Press, vol. 6.Chapter 2...............................................３１附录4：G. W. Farnell. Properties of elastic surfaces waves. Physical Acoustics (W. P. Mason and R.N. Thurston, editors), New York: Academic Press, vol. 6.Chapter 2...............................................３１第一章 绪 论1. 1 毕业论文的背景、意义目前的材料处理技术工艺允许通过改变材料的弹性常数和热膨胀系数来改进材料的某些功能，如改变热阻、局部强度来适应不断变化的需要。