The Wave Propagation Analysis Of Magneto-electro-elastic Nanostructures

With the development of material preparation technology and miniaturization of smart devices,magneto-electro-elastic(MEE)nanomaterials and their nanostructures have attracted wide attention by researchers.Compared with macroscale MEE materials,MEE nanomaterials not only have the mechanical-electro-magnetic coupling performance,but also show excellent performance in mechanics,electricity,magnetism and optics.The size effect of mechanical properties(such as wave,vibration,buckling,etc.)is one of the most important problems in the application of MEE nanostructures.In order to describe the size dependence of mechanical properties of MEE nanostructures,this thesis will first study the wave propagation characteristics of MEE nanobeams using the nonlocal theory.Then,the nonlocal strain gradient theory is applied to study the wave propagation characteristics of MEE nanoplates,nanoshells and functionally graded porous piezoelectric(FGPP)nanobeams.The effects of nonlocal parameter,size parameter,and magneto-electric-thermal-mechanical loads on wave propagation characteristics are analyzed.The discussion in this thesis is divided into the following sections:(1)This thesis first discusses the wave propagation characteristics of MEE nanobeams.The nonlocal MEE Euler nanobeam model and Timoshenko nanobeam model are established with the aid of the nonlocal theory.Using the Hamiltonian principle,we derive the equations of motion for wave propagation,from which the dispersion relation of the MEE nanobeams is obtained.The effect of the nonlocal parameter and thermo-mechanical-magnetic-electrical loads on the dispersion relation is discussed.It is found that the nonlocal effects reduce the stiffness of the nanobeam,and positive potential,negative magnetic potential and temperature rise can cause the cutoff wavenumber in the dispersion curve of the first mode.(2)Based on the nonlocal strain gradient theory,the wave propagation characteristics of MEE nanoplates are studied.Two MEE nanoplate models,namely Kirchhoff plate model and Mindlin plate model are established with the consideration of both nonlocal effect and strain gradient effect.The effects of nonlocal parameter,size parameter and thermo-mechanical-magnetic-electrical loads on the dispersion relation of MEE nanoplates are analyzed.It is found that the nonlocal effect causes the stiffness-softening effect of MEE nanoplates,while the strain gradient effect causes the stiffness-hardening effect of MEE nanoplates.It is found that positive electric potential,negative magnetic potential and pressure can cause the critical wavenumber and the cutoff wavenumber in the dispersion relation curve of the first-order mode.(3)Based on the nonlocal strain gradient theory,the Kirchhoff-Love nanoshell and the first order shear deformation nanoshell model were established.The wave propagation characteristics of MEE nanoshells are studied.The effects of nonlocal parameters,size parameters and thermo-mechanical-magnetic-electrical loads on the dispersion relation of MEE nanoshells are analyzed.(4)Based on the nonlocal strain gradient theory,the wave propagation of FGPP nanobeams is further studied.The FGPP nanobeam model is established by considering three kinds of the porosity distribution:symmetric distribution,asymmetric distribution and uniform distribution.The results discuss the effects of the porosity distribution,porosity,nonlocal parameter,size parameter and electro-thermal-mechanical loads on the dispersion relation.