Green's Functions
Green's Functions
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DOI：
10.1007/978-0-387-89498-0_2
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发表时间：
2009
期刊：
影响因子：
--
通讯作者：
E. Pan
中科院分区：
文献类型：
--
作者：
E. Pan
机械场和电场之间的耦合激发了与微机电系统相关的有趣研究[1，2]。其主要应用是在传感器和致动器设备中，通过这些设备，电压可以引起弹性变形，反之亦然。由于许多新材料，如氮化物半导体，是压电的，量子纳米结构的研究是目前的前沿课题，其中应变能带工程是中心[3，4]。新型层压复合材料（具有自适应和智能组件）不断吸引机械，航空航天和土木工程分支的极大关注[5]。在材料性能研究中，以Eshelby为基础的细观力学理论一直非常流行[6]。在大多数这些令人兴奋的研究课题，基本解决方案的一个给定的系统下的一个单位集中力/电荷或简单的绿色的功能解决方案是必需的。这是本章写作的动机。然而，在本章中，只考虑一般各向异性压电的静态情况，即使对振动和/或动力学（时谐）波传播的几个密切相关的参考文献进行了简要回顾。此外，虽然重点是广义点和线力，绿色的功能，相应的点和线位错，以及点和线的本征应变的Betti的互易定理的基础上进行了讨论或介绍。
Coupling between mechanical and electric fields has stimulated interesting research related to the microelectromechanical system [1, 2]. The major applications are in sensor and actuator devices by which an electric voltage can induce an elastic deformation and vice versa. Because many novel materials, such as the nitride group semiconductors, are piezoelectric, study on quantum nanostructures is currently a cutting-edge topic with the strain energy band engineering in the center [3, 4]. Novel laminated composites (with adaptive and smart components) are continuously attracting great attention from mechanical, aerospace, and civil engineering branches [5]. In materials property study, the Eshelby-based micromechanics theory has been very popular [6]. In most of these exciting research topics, the fundamental solution of a given system under a unit concentrated force/charge or simply the Green’s function solution is required. This motivates the writing of this chapter. In this chapter, however, only the static case with general anisotropic piezoelectricity is considered, even though a couple of closely related references on vibration and/or dynamics (time-harmonic) wave propagation are briefly reviewed. Furthermore, although emphasis is given to the generalized point and line forces, the Green’s functions to the corresponding point and line dislocations, as well as point and line eigenstrain are also discussed or presented based on Betti’s reciprocal theorem.