| Piezoelectric,piezomagnetic materials which are used as sensor and actuator integrating with structure form a intelligent material system, which can also be called piezoelectric,piezomagnetic composite materials.。The primary work for the research in this kind of intelligent structure is to establish analytical model which can accurately indicate the interaction between piezoelectric,piezomagnetic sensor and actuator and body structure. This model is not only able to exhibit the internal relation of mechanics-electricity coupling interaction in piezoelectric intelligent structure from the global aspect, but also easy to analyze and calculate with necessary mathematical tools. According to the study domains which are appropriate to the models, the analytical models of piezoelectric,piezomagnetic intelligent structure can be divided into static and dynamic models; On the basis of the different assumptions of the elastic,electric and magnetic fields in the models, they can be divided into precise theory analytical model and simplified model or low- order analytical model i.e. elastic,electric and magnetic fields are simplified as one-order linear distribution and high-order analytical model. When analyzing and comparing the existing analytical models of piezoelectric,piezomagnetic material and intelligent structure, the correlations of piezoelectric,piezomagnetic apparatus and structure can be divided into embedding and surface pasting. However, these simplified models usually adopt linear or high-order distribution assumptions of displacement and electricity potential and neglect or partly neglect the nonuniformity of local deformation, thus can not demonstrate the local stress and electric field of the joint part of piezoelectric,piezomagnetic apparatus and the structure. In order to correctly describe the characteristics of different forces,electricity and magnetism demonstrated by three-dimensional theory, a high-order theory model is developed in this paper, which gives up several excessively simplified assumptions applied in all existing analytical models, that is to say, which neglects the linear distribution of transverse positive strain and electric potential along transverse direction. Based on three-dimensional linear elastic theory, adopting state space method,Laplace transform,Hankel transform and series expansion methods, etc. the static and dynamic characteristics of piezoelectric,piezomagnetic composite structure are systematically analyzed in this paper.This paper breaks through the local knowledge in micro and macro physical properties of magnetism,electricity and mechanism involving intelligent material, integrating piezoelectric and piezomagnetic material, and further studies the mechanics analytical model and theory frame. 1) By means of drawing the potential function the general solution for three- dimensional transversely isotropic magneto-electro-elastic is derived.2) By means of using Almansi's theorem the general solution for two- dimensional transversely isotropic magneto-electro-elastic is derived. Then is used to simplify the general solution and all physicals quantity are expressed by fou"r harmnic function". This general solution is easy and convenient for application.3)The methodology is based on a state space formulation . The state vector equation of transversely isotropic space for thick laminated circular plate is established. By the use of the Hankel integral transform and the Caylay-Hamilton theorem, the solutions of state vector equation for thick laminated circular plate are obtained which are the product of initial state variables and transfer matrix. 4) By the use of the Hankel integral transform to study vibration of the piezoelectric,piezomagnetic materials in spherical symmetry and free vibration of piezoelectric,piezomagnetic and elastic circular plate of single layer and multilayered , in order to provid theoretical basis for dynamic control of piezo-electric-magnetic material in space spherical symmetry.The investigation in this paper aims to explore the basic law of mechanics-electricity-magnet- ism coupling action in piezoelectric,pizomagnetic composite structure and systematically proposes general mechanics model and calculating method of analyzing piezoelectric,piezomagnetic composite materials structure with considering a variety of boundary conditions, thus relatively accurately estimates the mechanics behaviors of structure made up of this composite materials influenced by all kinds of elements, accordingly provides elementary theory basis and analytical method for the following research and application research in intelligent structure composed of piezoelectric,piezomagnetic composite materials. It can be found from the study result that the behavior characteristics of mechanics,electricity,magnetism in laminar structure involving piezoelectric,piezomagnetic composite materials are quite complex, even for the thin piezoelectric,piezomagnetic structure, the electric potential,magnetic potential are not necessarily linear distributions along the thickness direction.In a word, the physical nature of mechanics-electricity-magnetism coupling action in piezoelectric,piezomagnetic composite materials is closely grasped, and mathematical physical model which is appropriate to piezoelectric,piezomagnetic structure is explored in this paper. Several fundamental problems, including static and dynamic characteristics of piezoelectric,piezomagnetic composite materials structure, the distributions of stress,electric and magnetic fields occurred in piezoelectric,piezomagnetic composite materials structure , the interaction of piezoelectric,piezomagnetic structure and viscosity elastic medium and the Green function of piezoelectric,piezomagnetic structure containing fixed electrode, etc. are researched deeply and in detail here. These researches show important theoretical significance and practical application value not only for the basic theory study but also for the design and industrial application in the future about piezoelectric,piezomagnetic materials and intelligent structure. |
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