【作者】 郭琳；

【导师】 王建国；

【作者基本信息】 合肥工业大学 ， 工程力学， 2003， 硕士

【摘要】 本文探讨了利用状态变量法求解简支压电压磁、压电、压电复合材料层合板的静力学问题和动力学问题，着重研究了电、磁、力互相耦合的效应，并阐述了Mathematica在本课题中的应用。 对于简支压电压磁弹性层合板问题，从它的基本方程出发，建立了压电压磁弹性层合板的状态变量方程。对状态变量方程进行Fourier变换，得到了状态变量表示的单层压电压磁弹性层合板在Fourier变换空间中的解，导出了多层压电压磁弹性层合板的表达式。根据边界条件，求解静力问题和动力问题。并用Mathematica编制了相应的计算程序，给出算例，绘出板内状态变量分布图，给出自由振动频率。在体现状态变量法有效性和正确性的同时，也显示了Mathematica编程的优势。 对于简支压电弹性层合板问题，根据简支压电压磁弹性层合板问题的理论推导，不考虑其磁耦合效应，令相关系数为零，即可得到多层压电弹性层合板状态变量的表达式。同样根据其边界条件，解静力问题和动力问题。给出算例。 对于简支压电复合材料层合板问题，首先由简支压电压磁弹性层合板问题的理论推导，不考虑其磁、电耦合效应，可以得到一般层合板的状态变量表达式。再由层间连续条件，计算由压电层到一般层的传递矩阵。用Mathematica编制相应的计算程序，给出算例，计算不同压电复合材料的振动频率，在实际应用中具有一定的价值。 此外，还介绍了Mathematica在辅助设计和编制程序两方面的经验，为相关领域的理论推导及其程序化，提供了一种可借鉴的模式。更多还原

【Abstract】 Applications of the state vector method into the analysis of lamina and the current research state of piezoelectric materials are briefly reviewed based upon literature search. Solutions for simply supported and multilayered magneto-electro-elastic plates via the state vector method is investigated. We also present the application of Mathematica in the study.Simply supported and multilayered magneto-electro-elastic plates: The state vector equation of transversely isotropic magneto-electro-elastic solid is established from its governing equations in a Cartesian coordinate system. Using the Fourier transform due to boundary conditions of simply support, solutions of a single magneto-electro-elastic layer in the form of initial state vector and transfer matrix are obtained in Fourier transform space from the state vector equations. Using the perfectly bonded contact conditions between the layers, the general solution formulation of multilayered magneto-electro -elastic plates is given. We can also solve out the frequencies of the multilayered magneto-electro -elastic plates according to the free vibration conditions.As a numerical i llustration, four-layered p lates w ith t wo s tacking sequences under a mechanical load or charge and their frequencies are analyzed.Simply supported and multilayered electro-elastic plates: Using the theories of simply supported and multilayered magneto-electro-elastic plates, without considering the magneto effect, we can easily get the general solution formulation of simply supported and multilayered electro-elastic plates. Four-layered electro-elastic plates with two stacking sequences under a mechanical load or charge are analyzed. And free vibration frequencies of simple layer a electro-elastic plates re given.Electro-elastic plates accompanied with normal material plates: Firstly Using the theories of simply supported and multilayered magneto-electro-elastic plates, without considering the magneto and electric effect, the general solution formulation of simply supported and multilayered plates are given. Secondly, using the perfectly bonded contact conditionsbetween the layers, the delivery matrix between the electro-elastic layer and normal layer is worked out. Mathematica is used to design the programs so as to solve the free vibration frequencies. Three examples of different layer numbers and different putting methods of electro-elastic layers are given. The calculation of the frequencies of the electro-elastic and normal material plates is of some practical value.In addition, experiences in Mathematica used in both aided design and programming are introduced, in order to offer a reference mode for theoretical deduction and its programming in related fields.更多还原