Investigation On Saint-Venant End Effects Of Piezoelectric-Piezomagnetic Sandwich Structures

Composites consisting of piezoelectric (PE) and piezomagnetic (PM) media are a class of new functional materials. PE-PM composites have the potential for novel device applications such as magnetic field sensors, resonators, electric field tunable filters, phase shifters and delay lines. As is well-known, Saint-Venant principle can be used to provide the fields of end effect and decay characteristics. And these decay characteristics may be helpful for the test and design of structures and parts in theory and engineering. Thus, several basic problems for Saint-Venant end effects of PE-PM sandwich structures are investigated in this dissertation. The effects of PE material properties^electromagnetic boundary conditionsN weak interfaces and volume fractions on decay rates are revealed. The main contents are as follows.(1) The decay of Saint-Venant end effects for anti-plane deformation of PE-PM sandwich structures is studied theoretically. The end of the sandwich structure is subjected to a set of self-equilibrated magneto-electro-elastic loads. The upper and lowers surfaces of the sandwich structure are assumed to be traction-free and subjected to four kinds of electromagnetic boundary conditions. These electromagnetic boundary conditions are electrically short-magnetically short (SS), electrically short-magnetically open (SO), electrically open-magnetically open (OO) as well as electrically open-magnetically short (OS). Based on the fully coupled controlling differential equations for magneto-electro-elastic fields, the exact closed-form solutions of magneto-electro-elastic fields and characteristic equation for decay rates are derived. By using the obtained characteristic equation, the decay rates are calculated for PE-PM-PE and PM-PE-PM sandwich structures. The results show that material properties of PE layeres have significant influence on the decay rates for PE-PM-PE structures under SS case for PM-PE-PM structures under OO case. For orther electromagnetic boundary conditions, the effect of the material properties of PE layers on decay rates is small.(2) The decay of Saint-Venant end effect for the anti-plane deformation of PE-elastic sandwich structures with weak interfaces is studied theoretically. The end of the sandwich structures is subjected to a set of self-equilibrated electro-elastic loads. The upper and lower surfaces of the sandwich structure are assumed to be traction-free and subjected to two kinds of electric boundary conditions. These electric boundary conditions are electrically short and electrically open. Based on the constitutive equations of PE materials, the characteristic equation for decay rates are derived and the closed-form solutions are obtained. The numerical results indicate that the weak interfaces reduce the values of decay rates. When the interface parameters are greater than zero and less than one, decay rates approach to zero with the increase of the imperfect bonding.(3) The decay of Saint-Venant end effects for plane deformations of PE-PM sandwich structures is studied. The end of the sandwich structure is subjected to a set of self-equilibrated magneto-electro-elastic loads. The upper and lower surfaces of the sandwich structure are mechanically free, electrically open or short as well as magnetically open or short. By using the simplified state space approach and the transfer matrix method, the characteristic equations for decay rates are derived. Based on the obtained characteristic equations, the decay rates of the sandwich structures are calculated. The results show that the influences of material properties of PE layeres, electromagnetic boundary conditions and volume fractions on decay rates are similar to the PE-PM sandwich structures under anti-plane deformation.(4) The decay of Saint-Venant end effects for PE-PM sandwich axisymmetric cylinder is considered. A PM layer is located between two PE layers with same material properties or reversely. The end of the sandwich cylinder is subjected to a set of self-equilibrated magneto-electro-elastic loads. The inner and outer surfaces of the sandwich cylinder are mechanically free, electrically open or short as well as magnetically open or short. Firstly the constitutive equations of PE materials and PM materials under cylindrical coordinate system are given and normalized. Secondly, the simplified state space approach is employed to arrange the constitutive equations into the differential equations of matrix form. Finally, by using transfer matrix method, the characteristic equation for eigenvalues or decay rates are derived. Based on the obtained characteristic equation, the decay rates for the PE-PM-PE and PM-PE-PM sandwich cylinder are calculated. The results show that the change of magnetic conditon has significant effect on the decay rates for PE-PM-PE sandwich structures when the boundary condition is electrically short. For the PM-PE-PM sandwich structures, the influence of the magnetic boundary conditions is obvious for the electrically open case.