Static And Dynamic Mechanical Behaviors Of Magneto-electro-elastic Nanobeams And Nanoplates

Magneto-electro-elastic nanomaterials have piezoelectric,piezomagnetic and magnetoelectric coupling effects,which can achieve the conversion of mechanical energy,electrical energy and magnetic energy.They have shown broad application prospects in sensing,information storage,microwave modulation,and energy collection.In recent years,with the rapid development of miniaturized magnetoelectric devices,micro/nano magneto-electro-elastic materials have been made to meet current demands.The magnetoelectric conversion ability and many application forms of micro and nano magneto-electro-elastic structures are closely related to their own mechanical properties.Therefore,it is of great engineering and scientific significance to extend the theory and method of solid mechanics to study the vibration and buckling characteristics of micro/nano magneto-electro-elastic beams and plates under force,electricity and magnetic coupling loads.The surface effects caused by high surface area is one of the most important structural characteristics of nanomaterials,which plays a decisive role in the overall properties of the material.Taking into account the effects of surface elasticity,surface piezoelectricity,and surface piezomagnetism,this thesis systematically studies the vibration and buckling characteristics of magneto-electroelastic nanobeams and nanoplate.The main contents include:(1)Based on the theories of Euler beam and Timoshenko beam,two typical models of magneto-electro-elastic nanobeams are established.The governing equations and boundary conditions corresponding to the two types of beam models are derived using the Hamilton’s principle.The analytical expressions for bending deflection,natural frequency,and critical buckling electric/magnetic load at three typical boundary conditions are obtained.The effects of surface material parameters,surface residual stress,and applied electric/magnetic loads on the static and dynamic mechanical behaviors of magneto-electro-elastic nanobeams were discussed in detail.(2)Two types of magneto-electro-elastic nanoplates models with the consideration of surface effects were established,and their corresponding governing equations and boundary conditions were obtained based on the Hamilton principle.For the Kirchhoff plate model,the Ritz method is used to obtain the natural frequencies and critical buckling loads under three typical boundary conditions The results for simple supported condition are compared with the Navier’s solution to verify the reliability of the Ritz method.For the Mindlin plate model,the Navier’s solution is used to obtain analytical expressions of the natural frequency and critical buckling load in the case of all edges simply supported.The influence mechanisms of surface related parameters,applied electric and magnetic potentials,boundary conditions,and geometric dimensions on the free vibration and buckling behavior are analyzed numerically.