Magneto-electro-elastic Coupling Effect Research Of Laminated Plates

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.