Decay rate of saint-venant end effects for plane deformations of piezoelectric-piezomagnetic sandwich structures

This paper is concerned with the decay of Saint-Venant end effects for plane deformations of piezoelectric (PE)-piezomagnetic (PM) sandwich structures, where a PM layer is located between two PE layers with the same material properties or reversely. 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 shorted as well as magnetically open or shorted. Firstly the constitutive equations of PE materials and PM materials for plane strain are given and normalized. Secondly, the simplified state space approach is employed to arrange the constitutive equations into differential equations in a matrix form. Finally, by using the transfer matrix method, the characteristic equations for eigenvalues or decay rates are derived. Based on the obtained characteristic equations, the decay rates for the PE-PM-PE and PM-PE-PM sandwich structures are calculated. The influences of the electromagnetic boundary conditions, material properties of PE layers and volume fraction on the decay rates are discussed in detail.