Vibration Characteristics Of Piezoelectric-piezomagnetic Bilayer Nanostructures

The magnetoelectric laminated structures formed by alternate deposition of piezoelectric materials and piezoelectric materials have the advantages of simple preparation process and easy realization of magnetoelectric conversion.It can meet the engineering requirements for the miniaturization of magnetoelectric devices,and present broad application prospects in information storage,microwave modulation,and magnetic field detection.The magnetoelectric conversion capability and many application forms of the magnetoelectric laminated nanostructures are closely related to its own vibration characteristics.For this reason,this thesis researched the free vibration characteristics of piezoelectric-piezomagnetic bilayer nanobeams and nanoplates by using the nonlocal theory to characterize the scale effect of nanostructures.Firstly,ignoring the magnetic field in the piezoelectric layer and the electric field in the piezomagnetic layer,the expressions of displacement,electric potential in the piezoelectric layer and magnetic potential in the piezomagnetic layer are assumed respectively based on the zigzag structure theory.The number of independent variables is reduced by satisfying the conditions of surface free and interlayer continuity.Secondly,the differential form of the nonlocal piezoelectric-piezomagnetic constitutive equations is applied to provide the strain energy of the structure,and the external power and kinetic energy are introduced to obtain the total energy of the system.Finally,the governing equations and boundary conditions of the one-dimensional nanobeam model and two-dimensional nanoplate model are established by the Hamilton principle.For the beam structure,the differential quadrature(DQ)method is used to solve the frequency and mode of free vibration under three types of boundary conditions: simply supported at both ends(SS),one end fixed and one end simply supported(CS),and fixed at both ends(CC).The results for SS condition are compared with Navier's solution to verify the reliability of the DQ method.For the plate structure,Navier's solution is used to obtain the natural frequency of free vibration for the simply supported boundary condition.According to the numerical results,the influences of nonlocal parameters,structure size,external load and boundary conditions on the vibration frequency and modal characteristics of the above two types of nanostructures are analyzed.The conclusion is expected to provide theoretical reference for the optimization design and engineering application of magnetoelectric laminated nanostructures.