节点文献
层合压电结构的瞬态响应和波动特性分析
Transient Responses and Characteristic Waves of Layered Piezoelectric Structures
【作者】 龚双；
【导师】 韩旭；
【作者基本信息】 湖南大学 ， 机械设计及理论， 2014， 博士
【摘要】 层合压电结构具有较高的比强度和比模量,良好的接收性能和更宽的工作频率等诸多优势,广泛地应用于航空航天、动力测量、无损检测、生物医学等众多工程和技术领域。研究电弹性波在层合压电结构中的传播特性对于压电智能结构的设计制造及其工程中的应用有着重要理论意义和实际应用价值。由于压电材料和基体材料的各向异性,材料层的交错铺设,以及压电介质中机电耦合特性,使得层合压电结构是一个具有不连续分布、不连续材料属性以及机电耦合性质的复杂系统,目前对层合压电结构的动力响应分析在数值模型的建立、求解精度和效率等方面存在着一系列的技术难点尚待完善和解决。为此,针对层合压电板壳结构在机电耦合载荷作用下的瞬态响应问题,本文力求建立一套能够兼顾求解效率和精度,同时准确描述层合压电结构动力响应的分析体系。本文的主要工作如下：(1)提出了适用于层合压电结构瞬态响应分析的压电层单元模型。针对层合压电结构中电弹性耦合波主要以面波形式传播的特性,将压电层单元中的位移场和电势场两个基本量离散为相应的节点面向量,利用层单元三个节点面内的位移和电势的二维分布函数来拟合层合压电结构中位移场和电势场的实际状态。基于压电层单元建立了层合压电板和层合压电圆柱壳的半解析数值模型,相比较有限元分析模型大幅减少了瞬态问题分析中所需单元数量和密度,只需较少的单元划分即可满足数值模拟的精度。(2)提出了力、电载荷激励下的层合压电结构的瞬态位移响应和电势响应的高效求解算法。将层合压电结构半解析数值模型应用于层合压电板和层合压电圆柱壳的瞬态响应求解,基于Hamilton变分原理推导了结构在时空域内的运动控制偏微分方程。利用傅里叶变换的性质,将关于位移和电势完全耦合的运动控制偏微分方程,变换为波数域内的位移控制常微分方程,以及位移和电势之间的线性耦合方程,从而避免了数值计算中耗时低效的偏微分方程组直接求解。在波数域控制方程中,引入等效力载荷和等效耦合刚度矩阵的概念,降低了控制方程的阶次,减少了在线计算的存储空间。利用压电铺层材料参数矩阵的对称性,对复数域内的波数域运动控制方程和相应的特征值问题进行了实数化处理,进一步提高了算法的求解效率(3)提出了层合压电圆柱壳中电弹性波传播的波动特性分析方法。基于层合压电圆柱壳半解析数值模型,建立了结构的自由振动控制方程。基于模态分析方法,推导了层合压电圆柱壳中电弹性波传播的相速度面、相慢度面、相波面、群速度面、群慢度面和群波面六个波动特征面的具体形式,可以直观的描述材料的各向异性和压电效应对结构波动特性的影响,观察不同波动传播方向上波动特性评价指标的变化。(4)提出了层合压电板电势和位移瞬态响应对载荷参数和材料本构参数的敏感性分析方法。基于所提出的层合压电板瞬态响应求解算法,采用直接求导的方式在波数域内建立了瞬态响应的敏感性方程,并给出了两类设计参数下敏感性方程中虚载荷的计算方法。所推导的敏感性方程与瞬态响应求解中的运动控制方程对应着相同的广义特征值问题,因此本方法尤其适用于较多设计参数情况下的瞬态响应敏感性分析,并可在结构瞬态分析的基础上,增加很小的计算成本即实现瞬态响应和响应敏感性的同时输出。结合区间结构分析理论,用于计算层合压电板在不确定材料参数和载荷参数条件下的位移和电势瞬态响应边界。
【Abstract】 Piezoelectric materials, as ideal materials of sensors and actuators in intelligent structure systems, have the characteristics of piezoelectric and inverse piezoelectric effects, which can perceive and respond to environment. These materials, forming the laminated piezoelectric smart structure with the function of self-test, self-adaption and quick response, are always pasted on the surface or embedded in the internal part of base layer material in the form of clad layer and chip. With so many advantages, such as better receptivity and wider working frequency, piezoelectric laminated structure has higher specific strength and specific modulus applied into the aerospace, dynamometry, nondestructive testing and biomedicine. There is a significantly important point doing research on the application of electric elastic wave to design and manufacture of laminated piezoelectric smart structure.Because of the anisotropy matrices of composite material and piezoelectric materials, the interactive laying of materials and the coupling in piezoelectric media, laminated piezoelectric smart structure is dynamic system with discontinuous distribution, discontinuous material properties and electromechanical coupling. At present, a series of technical difficulties on numerical model of laminated piezoelectric structure’s dynamic response analysis and the balance between accuracy and efficiency. Therefore, based on the transient response of electromechanical coupling from the structure of piezoelectric laminated plate and shell, this paper tries to build an analysis system which can both consider the balance between accuracy and efficiency and describes precisely dynamic response of laminated piezoelectric smart structure. The corresponding work is as follow:(1) Based on the propagation characteristic of electric-elastic wave and three dimensional electric-elastic theory, a numerical model of laminated piezoelectric plate has been built based on piezoelectric layer element, which can deduce the deformation, transient distribution and response time of potential under the common action among force load, potential incentive and electromechanical coupling load. This method can solve structure transient response efficiently by associating several numerical methods such as Finite element method and overcome several difficulties in traditional method.(2) The transient problem of electric elastic wave has been for piezoelectric laminated cylindrical shell has been analyzed. On the radial direction of cylindrical shell, displacement field and electric potential field will be dispersed in the form of three nodes isoparametric element. The coupling physical field of piezoelectric laminated cylindrical shell can be fitted by the vector function of cylindrical element’s surface distribution and the scale and precision of calculation can be controlled by changing the density of cylindrical shell element. Based on Hamilton theory, the whole motion control equation of structure will be built after twice independent variational methods for node displacement and electric potential. In addition,, semi-analytical solutions of the wave number domain displacement and transient distribution of electric potential under several kinds of force-electric load are deduced. Bringing in equivalent load of the wave number domain and equivalent coupling stiffness matrix makes solving process more unified and it is convenient to analyze directly the influence of electrical coupling effect on laminated piezoelectric structure dynamic response. At the same time, this measurement will decrease the degree of freedom of control equation and workload of calculation. When the material properties of the piezoelectric layer and substrate layer meet certain conditions, motion control equation of the wave number domain and corresponding eigenvalue problem will be a real treatment increasing the calculation efficiency further.(3) Based on the modal analysis theory, researches about problems of the propagation and scattering characteristics have been done. Free vibration control equation has been built according to piezoelectric laminated structure mechanics model of single layer cell. Moreover, six concepts of characteristic face are used for expressing the influence of material anisotropy and piezoelectric effect on structure fluctuation characteristics.(4) Based on semi-analytical calculation model for laminated panels pressure dynamic response analysis, both transient responses of electric potential and displacement for loading parameters and the first-order sensitivity of the material constitutive parameters are deduced. Using properties of space domain-wave number domain transform, the first-order sensitivity of wave number domain response has been deduced from the control equation of wave number domain. The comparison between this method and finite difference method verifies advantages of efficiency and accuracy in this proposed method. Combing with interval structure analysis theory, a new method has been proposed for obtaining transient response border of displacement and electric potential quickly on the premise that there are many uncertain parameters and constraints.