Investigation On Thermal-Mechanical Coupling Behavior Of Micro/Nano Structures Considering Size-Dependent And Thermal Lagging Effects

With the rise of micro/nano manufacturing technology and the rapid development of miniaturization and integration of devices,micro/nano-structure is the basic component of micro/nano electromechanical system,and its mechanical performance analysis plays an important role in the safe operation of the system.The mechanical properties will be changed when the characteristic geometric size of structure falls within the scope of miro/nano scale,and the mechanical response of the elastic body at miro/nano scale shows a strong size-dependent effect.The theory of classical continuum mechanics cannot explain the size-dependent phenomenon of the structure at miro/nano scale,so scholars proposed some theories of size-dependent effect to establish the space miro/nano-scale model,such as the nonlocal elasticity theory,the modified couple stress theory and the surface elasticity theory.Additionally,the micro/nano electromechanical system generates heat during operation,resulting in uneven temperature distribution in the system,so the thermal stress and deformation cannot be ignored in the mechanical analysis of micro/nano-structure.In order to describe the heat transfer of micro/nano-structure at time microscale,scholars developed the generalized thermoelastic theory considering the influence of heat flow phase-lag to establish the time microscale model.In recent years,the micro/nano-structures made of polymer materials,functionally graded composite materials,graphene reinforced composite materials,and other advanced materials have been researched and applied in micro/nano electromechanical system due to the excellent thermodynamic properties.Therefore,it is of great significance for the safe and functional design of the micro/nano device and system to accurately analyze and predict the thermoelastic static and dynamic responses of micro/nano-structures made of advanced materials.Based on the size-dependent effect theory and the generalized thermoelastic theory,the generalized thermoelastic coupling theories with size-dependent effect and thermal lagging effect are established in the thesis.The thermoelastic dynamic responses,the thermoelastic damping analyses,the thermoelastic bending wave propagation characteristics and the thermoelastic vibration characteristics of micro/nano-beam/plate structures made of polymer materials and composite materials are investigated.The variations of the physical quantities such as temperature,displacement,stress,inverse quality factor,phase velocity and natural frequency of micro/nano-beam/plate structures are quantitatively obtained.The investigation and analysis of the physical quantities is used for revealing the thermolastic coupling mechanism of micro/nano-structures and providing a theoretical basis for the thermoelastic static and dynamic response analyses of micro/nano-structures.The main research contents of this thesis include:(1)The thermoelastic dynamic responses of micro-beam/plate structures are investigated.Firstly,three different types of the fractional-order generalized thermoelastic theory considering nonlocal effect are established on the basis of the thermodynamic laws,and the thermoelastic dynamic response of a functionally graded microbeam heated by a ramp-type thermal shock is studied by the Laplace transform method.The influences of ramp-heating time parameter,fractional-order parameter,elastic nonlocal parameter and functionally graded parameter on the distributions of the dimensionless temperature,the dimensionless stress,the dimensionless deflection and the dimensionless displacement are discussed.Secondly,based on the generalized thermoviscoelastic theory with the model of fractional-order heat conduction and fractional-order strain considering the nonlocal effect,the thermoviscoelastic dynamic response of a polymer microplate subjected to a moving heat source is studied by the Laplace transform method.The distributions of the dimensionless temperature,the dimensionless stress,the dimensionless strain and the dimensionless displacement with the influences of fractional-order parameter,fractional-order strain parameter and elastic nonlocal parameter are discussed.(2)The thermoelastic dampings of micro-beam/plate structures are investigated.Firstly,according to the Moore-Gibson-Thompson generalized thermoelastic theory,the thermoelastic damping of a functionally graded graphene reinforced composite sandwich microbeam with surface effect is studied by the complex frequency method.The influences of thermal relaxation time,surface effect and total weight fraction of graphene nanoplatelets on the distribution of the normalization inverse quality factor are discussed.Secondly,based on the modified couple stress theory and the three-phase-lag generalized thermoelastic theory,the thermoelastic damping of a functionally graded graphene laminated composite microplate is studied by the complex frequency method in Hamilton system.The distributions of the normalization inverse quality factor with the influences of four graphene nanoplatelets distribution forms,thermal relaxation time,material length-scale parameter and total weight fraction of graphene nanoplatelets are discussed.(3)The thermoelastic bending wave propagation characteristics of micro/nano-beam/plate structures are investigated.Firstly,by introducing the fractional-order parameter into the nonlocal elasticity theory and combining the Lord-Shulman generalized thermoelastic theory,the thermoelastic bending wave propagation characteristic in a bi-anisotropic functionally graded microbeam with surface effect is studied by solving the analytical solution of the dispersion relation.The variations of the dimensionless frequency and the dimensionless phase velocity of the thermoelastic bending wave with the influences of thermal relaxation time,surface effect,elastic nonlocal parameter,fractional-order parameter and functionally graded parameter are discussed.Secondly,based on the modified couple stress theory and the nonlocal dual-phase-lag generalized thermoelastic theory,the thermoelastic bending wave propagation characteristic in a functionally graded graphene reinforced polymer composite nanoplate is studied by calculating the analytical solution of the dispersion relation in Hamilton system.The influences of four graphene nanoplatelets distribution forms,material length-scale parameter,thermal nonlocal parameter and total weight fraction of graphene nanoplatelets on the dimensionless frequency and the dimensionless phase velocity are discussed.(4)The thermoelastic vibration characteristics of micro/nano-beam/plate structures are investigated.Firstly,based on the modified couple stress theory and the dual-phase-lag generalized thermoelastic theory,the thermoelastic vibration characteristic of a bi-anisotropic functionally graded porous microbeam with surface effect is studied by the Navier method.The influences of four porous distribution forms,material length-scale parameter,surface effect,porous volume fraction and functionally graded parameter on the dimensionless natural frequency are discussed.Secondly,on the basis of the fractional-order nonlocal elasticity theory and the nonlocal dual-phase-lag generalized thermoelastic theory,the thermoelastic vibration characteristic of a functionally graded graphene reinforced polymer composite nanoplate is studied by the Navier method.The variations of the dimensionless natural frequency with the influences of four graphene nanoplatelets distribution forms,elastic nonlocal parameter,fractional-order parameter,thermal nonlocal parameter and total weight fraction of graphene nanoplatelets are discussed.